| Subject | Date Asked |
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| related rates ladder | 11/17/2009 |
Q: i am trying to understand this problem: 1- A ladder 25 feet long is leaning against the wall of aa ...
A: In the first part, there were no xy terms and it was straightforward to differentiate. We ...
|
| Trig | 11/16/2009 |
Q: Suppose that cos θ = 3/5 and that θ is a Quadrant IV angle. Find the exact value of sin ...
A: cos²θ + sin²θ = 1 sin²θ = 1 - cos²θ sinθ = √(1 - cos²θ) But, ...
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| Logarithmic Functions | 11/13/2009 |
Q: Use Logarithmic differentiation to find the derivative of the function. y= (rad ...
A: y = √x . e^x² . (x² + 2)^10 Taking logarithms, ln y = ln[√x . e^x² . (x² + 2)^10] ln y = ...
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| Related Rates. | 11/12/2009 |
Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of ...
A: The formula for the area A of a rectangle with length l and width w is A = lw differentiating with ...
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| Differentiating Volume of a Sphere | 11/11/2009 |
Q: Ahmed V=4/3.pi.r3 dV/dr=4.pi.r2 (total surface area) d2V/dr2=8.pi.r=4.pi.d (what would this ...
A: Well, i'm afraid that in this case both d²V/dr² and d³V/dr³ dont actually represent any physical ...
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| Optimization Problem | 11/9/2009 |
Q: Can you see if you can help me with the following problem? Thank you. 7. (1 pt) The manager of a ...
A: Revenue is found by multiplying number of units N by the rent of each unit r. R = N.r If there are n ...
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| Pre-Calculus | 11/7/2009 |
Q: I need help with this problem, please: Suppose points A, B, and C have coordinates A (0, 0), B (1, ...
A: Vector AB, u = (1-0)i + (-2-0)j = i - 2j where i and j are the unit vectors in the ...
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| Related Rates ladder | 11/4/2009 |
Q: A 20 foot ladder leans against a building. The top of the ladder starts sliding down the side at .5 ...
A: Let the height of the ladder on the wall at any time be y, and the distance to the foot of the ...
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| Calculus | 10/31/2009 |
Q: Find the equation to the line tangent to the curve y = 3arccos(x/2) at the point (1, pi).
A: y = 3arccos(x/2) dy/dx = 3.(1/2).-1/√[1 - (x/2)²] = -3 / 2√(1 - x²/4) at x = 1 ...
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| calculas | 10/31/2009 |
Q: f(x)= a-x/(a+x) where a is some real number that we can choose. for what value of a is f(x) its own ...
A: f(x) = a-x/a+x Let f(x) be y and its inverse z y = a-x/a+x y(a+x) = a-x ay + xy = a - x xy + x = a - ...
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| Calculus homework help | 10/29/2009 |
Q: The function f(x)=ax^3 + 3x^2 + bx has a local minimum at x=3 and a point of inflection at x=1 . ...
A: f(x) = ax³ + 3x² + bx f'(x) = 3ax² + 6x + b f''(x) = 6ax + 6 If x = 1 is a point of inflection, then ...
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| Help | 10/29/2009 |
Q: A carpenter has been asked to build an open box with a square base. The sides of the box will cost ...
A: let the square base have sides with length x and the height be h. The base area = x² The box has ...
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| calculus | 10/28/2009 |
Q: what happens if you try to use l'hopital's rule to evaluate limit as x goes to infinity of x ...
A: L'Hopital's rule is used to evaluate a limit when direct substitution results in the indeterminate ...
|
| Sinusoidal Functions | 10/27/2009 |
Q: I hope you can help cause I've been banging my head on this one... Ok, I have a problem where we ...
A: The delay is terribly regretted. The general equation of simple harmonic motion is written x = ...
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| Calculus | 10/25/2009 |
Q: How many lines which are tangent to the curve y= x/x+1 pass through the point (1,3)? where do they ...
A: A line tangent to the curve y has a slope equal to dy/dx at (x,y) where it touches the curve. If ...
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| Integral | 10/23/2009 |
Q: Why the average value of the square of the sine function taken over one period is <[sin(wt)]^2>= ...
A: The average value of a function f(x) is the definite integral of the function within the interval ...
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| Implicit Function | 10/21/2009 |
Q: Kindly assist with the below: a) A curve follows the implicit function x^3+3x^3y^2-2y^4 = 2x+3y ...
A: We differentiate every term accordingly but always remembering to add dy/dx whenever we ...
|
| Implicit differentiation | 10/20/2009 |
Q: Using implicit differentiation, find dy/dx if tanxy=x I don't know how to even start. Thank you in ...
A: Lets start by letting v = xy dv/dx = x(1.dy/dx) + 1.y = x(dy/dx) + y Note that when we ...
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| Related Rates | 10/16/2009 |
Q: Hey Ahmed, im dealing with a related rates problem and the question is, "The formula for the volume ...
A: If h = 3r dh/dt = 3.dr/dt And so, yes, if dr/dt = 2in/min and h = 3r, then dh/dt = 6in/min But i'm ...
|
| the equation of the tangentline through the given point | 10/13/2009 |
Q: f(x)=x^2-3x+4, at P(2,2)
A: The tangent line through any point on f(x) has the same slope as that of f(x) at the point. f(x) = ...
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| Calculus | 10/12/2009 |
Q: A truck uses (4x -240)²/250 gallons per hour when traveling on a highway. The driver gets paid ...
A: I was unsure about what you meant since you didnt state what x represented. So, lets do this again ...
|
| calculus/ trig | 10/11/2009 |
Q: find the limit as theta goes to zero of the function cos theta minus 1 divided by sin theta.
A: (cosθ - 1)/sinθ = (cosθ - 1)(cosθ + 1)/sinθ.(cosθ + 1) Note that we ...
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| Calculus | 10/10/2009 |
Q: A truck uses (4x -240)²/250 gallons per hour when traveling on a highway. The driver gets paid ...
A: I take it that you meant (4v - 240)²/250 i.e v and not x!!! In one hour, (4v - 240)²/250 gallons of ...
|
| Continuity | 10/6/2009 |
Q: I've been viewing some of the answers to problems that you've been receiving, and thanks to you, I ...
A: In part (a), f is not continuous for all x because at x = 1 the limit does not equal to the y-value ...
|
| Functions | 9/30/2009 |
Q: p(1+5x) = 6/(2-3x). What is p(x)?
A: Let y = 1+5x x = (y-1)/5 p(y) = p(1+5x) = 6/(2-3x) = 6/[2 - 3(y-1)/5] = 6/[2 - ...
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| Calculus 2 Integrate through long division | 9/26/2009 |
Q: I'm in calculus 2 and I am having a little trouble with this problem. It must be evaluated through ...
A: To divide x²+2 by x+3, a. Divide x² by x to get a quotient of x b. Use the quotient x to multiply ...
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| Calculus | 9/25/2009 |
Q: I have just began derivatives and differential notation. I don't know how to solve the following ...
A: Are you trying to find [f(x+h) - f(x)]/h ? If so, [f(x+h) - f(x)]/ h = (5xh - 1h + 4h^2)/h ...
|
| Intergration | 9/18/2009 |
Q: intergrate, using the suggested substitution. x over square root (x-3) and x=3+u^2
A: Using the substitution x = 3+u² ∫[x/√(x-3)]dx becomes ∫[(3+u²)/√(3+u²-3)]dx ...
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| Implicit differentiation | 9/15/2009 |
Q: Can you check the error in this problem I tried to solve it but it turned out different than the the ...
A: Just go through my solution. x^2 + y^2 - 2xy = x + y - 1 2x + 2y(y') - 2(xy' + y) = 1 + y' 2x + ...
|
| Calculus | 9/1/2009 |
Q: How do i take the derivative of a function with respect to y. Ex. d/dy( 2(x^2)y+(y^3)x)
A: If you're finding the derivative of a multivariable function such as this one with respect to y, the ...
|
| Instantaneous Velocity | 8/29/2009 |
Q: I have a question saying a car is at position x= the square root of(7t+2). I need to find the ...
A: The position of the car x at any time t is represented by the relation x = √(7t+2) Lets say we ...
|
| Calculus Problem | 8/27/2009 |
Q: Please help me find the limit of this problem: (2-x)/(x^2-4), with the limit x->2. Thank you so ...
A: Inserting the limit directly creates a problem because we get an indeterminate form of 0/0 so what ...
|
| tangent lines | 8/25/2009 |
Q: can you find the slope of the tangent line on the curve at a given point. y=3x^2-4 : (-1,-1) ...
A: The slope function of a curve is the derivative of the curve function. The tangent line at any given ...
|
| calculus maxima/minima | 8/6/2009 |
Q: Find the area of the largest rectangle that can be inscribed in a right triangle with legs of ...
A: It makes it easier if we use a coordinate system involving the x and y axes for this problem. ...
|
| calculus with applications | 8/5/2009 |
Q: a rectangular plot of farmland will be bounded on one side by a river and on the other three sides ...
A: Let y be the length of the fence opposite the river and the other two sides each having length x. ...
|
| taking a derivative of an equation w/ 2 variables | 8/1/2009 |
Q: I know how to take a derivative of a straightforward function with only one variable, but can you ...
A: The key to finding the derivative of a function involving variables x and y with respect to x is to ...
|
| integration | 7/30/2009 |
Q: Can you tell me, can i use integration by part or u sub for 2secX/2+tanX, or both, i cant find secx ...
A: This is where you got it all mixed up; 2secx/2+tanx is not (1/cosx)/(sinx/cosx) because it is not ...
|
| functions and lines | 7/29/2009 |
Q: In the equation y=mx+c.Finding the gradient and the intercept on the y-axis.why is 2x-3y=18 arranged ...
A: The general equation of a straight line is y = mx + c where m is the gradient and c is the intercept ...
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| integration | 7/27/2009 |
Q: Can you tell me, can i use integration by part or u sub for 2secX/2+tanX, or both, i cant find secx ...
A: First, secx = 1/cosx 2secx / (2 + tanx) = (2/cosx) / (2 + tanx) = 2/(2 + ...
|
| Rate Problem | 7/26/2009 |
Q: Two straight roads intersect at right angles. At 10 am a car passes through the intersection headed ...
A: Lets start at 11am, the car is then 30 miles east of the intersection. At any time t(hours) after ...
|
| integration by parts | 7/25/2009 |
Q: can you help me integrate (arctan x)/1+x^2? I would be most pleased,
A: To solve ∫(arctan x)/1+x² dx, you dont even need to integrate by parts. Just a change of ...
|
| Multi-Variable Epsilon-Delta | 7/1/2009 |
Q: For some reason or another I can't seem to get the idea of epsilon-delta definitions of limits into ...
A: Remember that lim (A/B) = lim A/lim B where lim B is not equal to zero. lim(x,y)->(0,0) [y/(x^2 + ...
|
| Taking a derivative of a function in two variables | 6/27/2009 |
Q: How do you take the derivative of a function in two variables? For example how would I take the ...
A: By the method of partial derivatives, dy/dx = -(&z/dx)/(&z/dy) where & represents the partial ...
|
| Taking a derivative of a function in two variables | 6/27/2009 |
Q: How do you take the derivative of a function in two variables? For example how would I take the ...
A: The trick is to always add a dy/dx whenever u differentiate a function in y. I hope you know the ...
|
| Calculus involving sin and cos | 6/6/2009 |
Q: If f(x) = sinx+cosx, find the value of n such that f^n(x) = f(x). I'm not sure really what its ...
A: What the question is asking is how many times would you differentiate f(x) to arrive at a function ...
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| calclus | 6/5/2009 |
Q: what is the diffrentiation of f(x)log5^(lnx)+log2^(lnx+2)
A: f(x) = log5^(lnx) + log2^(lnx+2) = (lnx)(log5) + (lnx+2)(log2) = (lnx)(log5) + (lnx)(log2) ...
|
| Calculus probem | 5/30/2009 |
Q: A 5,000 m² rectangular area of a field is to be enclosed by a fence, with a moveable inner fence ...
A: Let the fence have dimensions of length l and width w, then the length of the movable inner fence is ...
|
| trig. funtion proof. | 5/20/2009 |
Q: prove this trig. funtion. (Tanx + sinx)/2tanx= cos^2(x/2)
A: By the double angle formula, cos 2A = 2cos^2 A - 1 i.e cos^2 A = (cos 2A + 1)/2 = (1/2)cos ...
|
| The volume of a function rotated about an axis | 5/19/2009 |
Q: Find the volume of the function formed by revolving the function x=-(y- 2)^2+1 around the x-axis. I ...
A: The volume of the solid formed when y = f(x) is rotated around the x axis is V = ∫#y^2 dx |a ...
|
| Algebra | 5/18/2009 |
Q: I have a cylinder wet well with the volume of 188 cubic feet. What is the height and diameter of the ...
A: What exactly do you mean? A cylinder with a specific volume can have an infinite combinations of the ...
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| Calculus (Differentiation) | 5/16/2009 |
Q: There is an exercise in my mathematics book that asks me to find dV/dp of this formula: ...
A: The expressions dont seem clear enough but i'm guessing you're wondering how d/dV[nRT/(V-nb)] = ...
|
| calculus question | 5/12/2009 |
Q: Suppose the height of the tide is given by the equation h(t) = 4 sin {2Pi(t+8)/P} T is measured in ...
A: h(t) = 4sin {2Pi(t+8)/P} P = 24 hrs a)Starting from midnight 29 december 2008, there are exactly 2 ...
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| trapezoidal rule | 5/10/2009 |
Q: need to evaluate the integral using T-Rule e ^ x^2 .dx with lower limit 1 and upper limit 2 and ...
A: To find the definite integral (Area) of a function between the limits a and b using the trapezoidal ...
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| precalculus/trigonometrey | 5/8/2009 |
Q: Can you show me how to solve these? A) tan^-1 square root 3 B) sin^-1( -square root 3/2) C) ...
A: a)tan pi/3 = sqrt3 and so tan^-1 sqrt3 = pi/3 but tan is also positive in the third quadrant and so ...
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| calc w/ trig | 5/6/2009 |
Q: given y=sinx(1-cosx) show dy/dx=(1+2cosx)(1-cosx)
A: y = sinx(1-cosx) Using the product rule dy/dx = sinx d/dx(1-cosx) + (1-cosx)d/dx(sinx) = ...
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| calculus | 5/6/2009 |
Q: solve for the derivative of x^x^2
A: Let y = x^(x^2) Finding the natural log (ln) of both sides, ln y = ln [x^(x^2)] ln y = (x^2).lnx ...
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| calculas | 5/2/2009 |
Q: what is mean by picewise continuos?
A: A function or curve is piecewise continuous if it is continuous on all but a finite number of points ...
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| math | 4/30/2009 |
Q: So I have a worksheet that is just to help us get started before we start our next lesson and I was ...
A: I'll be representing theta by # and writing the limit as theta approaches zero as just 'lim'. ...
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| calculus | 4/27/2009 |
Q: how to I get the maximun profit of -.01x^3+.3x^2+15x-100
A: The maximum value of -0.01x^3 + 0.3x^2 + 15x - 100 occurs when its first derivative equals zero and ...
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| Measurements | 4/26/2009 |
Q: How do I measure properly with a ruler. Please explain measurements. Thanks
A: Well, it depends on what kind of ruler you're measuring with. Anyway, the most important thing is to ...
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| calculus | 4/25/2009 |
Q: I have a relative growth function 1/P∙dP/dt= b + aP where a = -.00009175 and b = .02866 and P ...
A: This is exactly what we have done. By partial fractions, 1/P(b + aP) = 1/bP - a/b(b + aP) and we ...
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| Calculus - finding an automobile's velocity | 4/23/2009 |
Q: The driver of an automobile applies the brakes at time t=0 and comes to a halt after traveling ...
A: For constant acceleration (or deceleration) v^2 = u^2 + 2as where v is the final velocity u is the ...
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| help please | 4/22/2009 |
Q: let r be the monthly rent per unit in an apartment building with 100 units. A survey reveals that ...
A: a)Suppose that there are n rented apartments, then there are 100 - n vacant ones. Each vacant ...
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| Squeeze theorem | 4/20/2009 |
Q: What is the purpose of squeeze theorem and its application in the real world?
A: The Squeeze Theorem is a theorem regarding the limit of a function. It is used in an effort to ...
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| vertical asymptote | 4/20/2009 |
Q: what does it mean when they say that a functions graph approaches infinity as it gets closer to a ...
A: The line x = k is a vertical asymptote of a curve y = f(x) if the limit of f(x) as x approaches k is ...
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| Calculus | 4/19/2009 |
Q: A wire of length 12in. can be bent into a circle, bent into a square, or cut into two pieces to make ...
A: Let's say that the wire has been cut into two with x being the length to make a circle and y the ...
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| Calculus | 4/18/2009 |
Q: cot squared 0- c0s squared 0= cot squared 0 x cos squared 0
A: What exactly am i supposed to do for you here? You have not exactly specified but i take it that you ...
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| calculus | 4/17/2009 |
Q: I have a relative growth function 1/P∙dP/dt= b + aP where a = -.00009175 and b = .02866 and P ...
A: We have to solve the differential equation. 1/P∙dP/dt= b + aP separating variables, dP[1/P(b + ...
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| calculus | 4/15/2009 |
Q: I am in calculus class and i need help in this Homework question, so i would apreciate if you could ...
A: The surface area of a sphere with radius r, S(r) = 4#r^2 where # represents pi The surface ...
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| Trigonometric Differenciation | 4/9/2009 |
Q: I was just wondering if you could help me with differentiating a few of these problems. I tried to ...
A: 1)h = cos2x/sin2x Using the quotient rule for h = u/v h' = (vu' - uv')/v^2 (i hope you ...
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| calculus finding dimension of a dorm | 4/7/2009 |
Q: A university has decided to build a new, creative dorm! After a contest to determine the shape, it ...
A: Part 1 This is what i understand (correct me if i'm wrong). The volume of the building should be ...
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| Calculus Finding Position Function | 4/1/2009 |
Q: A particle moves on the x-axis so that at any time t its velocity v(t) = sin 2t subject to the ...
A: v(t) = sin 2t To get x(t) from this, we integrate. We do this because v = dx/dt dx = vdt x = {vdt ...
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| Pre calc proofs | 4/1/2009 |
Q: I am trying to verify the following identity but don't know where to get started...... The question ...
A: I think you meant to prove that [(1-sin t)/cos t]^2 = 1-sin t / 1+sin t Consider the left hand ...
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| Algebraic Functions in Quantitative analysis | 3/30/2009 |
Q: Am attending my MBA-HR examinations in May 2009 where in the paper Quantitative Analysis for ...
A: a)y = 3x - 5 at x = 0, y = -5 at y = 0, x = 5/3 This graph is a straigth line (its of the form y = ...
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| math | 3/29/2009 |
Q: draw a circle with center point o and an angle of 40 degrees and a raduis of 20 cm. the question is ...
A: If the person is moving at the same speed on the circle then the time spent is proportional to the ...
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| the minimal distance | 3/27/2009 |
Q: Determine the minimal distance from point (-3,3) to the curve given by y=(x-3)^2 I've been trying ...
A: The general point on the curve is (x,y) or simply (x,(x-3)^2) If D is the distance from any point on ...
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| calc | 3/23/2009 |
Q: determine the dimensions of a rectangular solid(w/a square base) w/maximum volume if its surface ...
A: Let the length of the square base be x and the height be y. The volume of the solid is V = (x^2)y ...
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| derivative of e^(1/2*x) | 3/22/2009 |
Q: Why is the derivative of e^((1/2)x) 1/2e^((1/2)x)? I thought the rule was f'(e^kx)=(e^kx)/k. ...
A: f'(e^kx) = k(e^kx) Lets rewrite in a simpler form and consider it as a composite function. y = e^kx ...
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| factorsssss | 3/19/2009 |
Q: How do I factor : x^3 + 3x^2 + 1 (I set y as zero because i need to find the x intercept to graph ...
A: If all you need do is graph the expression, then you can go on without the x intercepts i.e the ...
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| Problem | 3/16/2009 |
Q: I have a problem that says : express sin11pi/12+sin5pi/12 as a product and find the exact value of ...
A: First, you need to remember the double angles identity; sin(A+B) = sinA.cosB + sinB.cosA sin(A-B) = ...
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| Related Rates | 3/12/2009 |
Q: The altitude of a triangle is increasing at a rate of 1500 centimeters/minute while the area of the ...
A: The relationship between the area A, altitude h and base b of a triangle is; A = (1/2)bh Finding the ...
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| Integration | 3/6/2009 |
Q: I don't understand why, when you take the definite integral of the function (1000-10x^2) on the ...
A: The integral of (1000 - 10x^2)dx is 1000x - 10x^3/3 + c where c is an arbitrary constant Finding the ...
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| algebra | 3/5/2009 |
Q: what is the result if you divide -12x^8y^8 by 3x^4y^2= I'd really appreciate it if you could answer ...
A: x^n = x.x.x.x....... (n times) x^m = x.x.x.x....... (m times) So, (x^n)/(x^m) = x^(n-m) This is ...
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| calculus | 2/19/2009 |
Q: I just got stuck while solving a problem and don't know the answer to this... How do you solve ...
A: You can let (75-y)^2 = x The equation then becomes 25/9x = 2500 + x multiplying through by 9x, 25 = ...
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| Particle Motion | 2/13/2009 |
Q: A particle moves along the X-axis so that at time t its position is given by x(t)=sin(pi*t^2) for -1 ...
A: Yes, its a friendly site but some people decide to give you unfriendly ratings because of a mix up ...
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| proving an identity | 2/9/2009 |
Q: So I'm having trouble solving this problem. 1. Prove the Identity Sin2x= 1/(tanx+cot2x) ...
A: Remember the double-angle identities sin2x = 2sinx.cosx cos2x = cos²x - sin²x and sin²x + cos²x = 1 ...
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| Particle Motion | 2/8/2009 |
Q: A particle moves along the X-axis so that at time t its position is given by x(t)=sin(pi*t^2) for -1 ...
A: a)x = sin(#t^2) v = dx/dt = 2#t.cos(#t^2) b)a = dv/dt = [2#t.2#t.-sin(#t^2) + ...
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| Mechanics Calculus | 2/7/2009 |
Q: A particle with acceleration=2t-3 passes a point O with velocity=2m/s , t=0 . find time t & ...
A: If acceleration, a = 2t - 3, the velocity function would be the integral of that function while the ...
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| math help | 1/27/2009 |
Q: If you could help me get started and run me through the steps of how to solve these it would be ...
A: cos(A + B) = cosA.cosB - sinA.sinB cos(A - B) = cosA.cosB + sinA.sinB (cosx)^2 + (sinx)^2 = 1 cosx = ...
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| Calculus integration by parts | 1/27/2009 |
Q: the problem is= p^5ln(p)dp u = Ln p dv= p^5 dp du= (1/p)dp v= (1/6)p^6 i'm stock on the second ...
A: You've really done well. The last part is to integrate v.du i.e &(1/6)p^6.(1/p)dp where & ...
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| Calculus | 1/22/2009 |
Q: You are living in a time before Newton and Leibniz. One night as you sleep, you have a dream ...
A: a)(x^2/27^2) + y^2 = 1 when x = 27cosθ [(27cosθ)^2/27^2] + y^2 = 1 (cosθ)^2 + y^2 = 1 ...
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| Calculus | 1/22/2009 |
Q: You are the marketing vice president of the bamboo pen tablets company, and you forecast that the ...
A: a)q = -0.5p + 140 Revenue, R = pq R = p(-0.5p + 140) R = -0.5p^2 + 140p b)Well, i cant sketch, can ...
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| Seperation of Variables | 1/20/2009 |
Q: y'=9xy y=-2 and x=0
A: Differential equations, right? y' = 9xy dy/dx = 9xy separating variables, dy/y = 9x dx integrating ...
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| Calculus A, HTL | 1/19/2009 |
Q: I'm having a problem finding the horizontal tangent line of this eqt. f(x)= x^5/3-5x^2/3+1 i kno ...
A: Well, the horizontal tangent line occurs when the derivative is zero. f(x) = x^5/3 - 5x^2/3 + 1 ...
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| very confused can you help? | 1/18/2009 |
Q: I need to know what is the relationship between the mass and volume of water
A: The mass is a measure of the matter making it up while the volume is simply a measure of how much ...
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| math | 1/13/2009 |
Q: Determine the positive radian measure of the angle that the second hand of a clock traces out in the ...
A: A)60 seconds represent a radian measure of 2#. 55 seconds, therefore, represents 55/60 x 2# = 11/12 ...
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| math | 1/13/2009 |
Q: need by today please! Find the radian measure of the angle in standard position formed by rotating ...
A: Let's take it this way. The radian measure when we rotate a full circle is 2# radians where # ...
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| Pre calculus | 1/11/2009 |
Q: How do I solve 2 cot^2 2X = 3 csc 2X if 0 </= X < 360 degrees? Thanks so much for your help!
A: Right, i'll show you. Remember, csc^2 y = 1 + cot^2 y Therefore, csc^2(2x) = 1 + cot^2(2x) and ...
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| Probabilities | 1/10/2009 |
Q: I have been a member on a dating website since 10/29/2008. I've noticed every week or so since ...
A: Ok Mark, This makes your question less confusing. In your '6 day period' paragraphs, i'm sure you ...
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| Precalculus Polynomial functions | 1/8/2009 |
Q: what are the roots of x^3-4x^2+x-6 I've tried 1,-1,2,-2,and other number I've used are too large so ...
A: I figure you've been trying to take advantage of the remainder theorem. Well, this equation happens ...
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| related rates- Thanks for your help!! | 1/2/2009 |
Q: Let V be the volume of a circular cylinder having a height h and a radius r, and assume h and r vary ...
A: V = #r^2.h where # represents pi The total differential with respect to time; dV/dt = (&V/&h)(dh/dt) ...
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| minimizing surface area | 12/18/2008 |
Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total ...
A: The volume of the solid is that of a sphere plus a cylinder. If the length of the cylinder is h, the ...
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| Vector Proof | 12/17/2008 |
Q: Give a vector proof that the midpoints of the sides of a square are the vertices of a square. If ...
A: I hope you're familiar with position vectors. Let the square have a length k and two of its sides ...
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| Maximizing box size | 12/12/2008 |
Q: A private shipping company will accept a box for domestic shipment if the sum of its length and ...
A: For the described box, V = h.h.w = wh^2 but, 2h + 2w = 90 h + w = 45 w = 45 - h So, V = (45-h)h^2 ...
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| implicit differentation | 12/11/2008 |
Q: I need help implicitly differentiating cos(x+y) + sin (x-y) = 0 @ y' = (pi/4, -pi/4). There is ...
A: You've obviously been mixing things up. First you send me a different question from the one on that ...
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| implicit differentation | 12/10/2008 |
Q: I need help implicitly differentiating cos(x+y) + sin (x-y) = 0 @ y' = (pi/4, -pi/4). There is ...
A: I think you mean y' at (#/4, -#/4) where # represents pi What you need to do is first determine the ...
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| derivatives | 12/10/2008 |
Q: if a and b are the lengths of two sides of a triangle, and x the measure of the included angle, the ...
A: When A = (1/2)absinx, it is clear that A is dependent on the three values of a, b and x. If these ...
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| Calculus | 12/8/2008 |
Q: I have a test in two days and i know that something similar to this will be on it. The radius r of ...
A: Let # represent pi The volume of a sphere V = (4/3)#r^3 We're interested in rates with respect to a ...
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| Calculus 1 | 12/8/2008 |
Q: This comes from a sample final for my final on Monday, Dec. 8. Thanks. A rectangular box with ...
A: I regret the error. Yes, the cost of the bottom panel is 2b^2 which means a revise to the solution. ...
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| Calculus 1 | 12/6/2008 |
Q: This comes from a sample final for my final on Monday, Dec. 8. Thanks. A rectangular box with ...
A: Let the box have a base length of b and a height h, the volume V is therefore V = b^2.h = 18 The ...
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| volume | 12/2/2008 |
Q: I recently purchased an expensive freezer unit for my business (Physicians vaccines)the vendor tells ...
A: 1 inch = 0.0254m The volume of the freezer is 15x15x11 cubic inches = 15(0.0254) x 15(0.0254) x ...
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| calculus | 11/30/2008 |
Q: A point moves along the curve y=x^2 + 1 in such a way that when x=4, the x coordinate is increasing ...
A: Note that in this question we are differentiating with respect to a third variable, time t. We have ...
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| Calculus question | 11/29/2008 |
Q: Given the function f(x)=e^-x^2 (a). Find the derivative of f (b). Find the critical values (c). ...
A: Sorry it took some time. a)Yes, you're correct with the derivative. The derivative f'(x) = ...
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| dimensions for the building that minimize the total cost | 11/25/2008 |
Q: the volume of the dorm must be exactly 225,000 cubic feet, which is one cubic foot for each sprout ...
A: This is what i understand (correct me if i'm wrong). The volume of the building should be exactly ...
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| Calculus | 11/25/2008 |
Q: which factors has to be considered in determining the continuity and differentiability of a function
A: A function f(x) is continuous at a point x = c if lim f(x) as x approaches c = f(c) The function is ...
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| calculus help please! | 11/24/2008 |
Q: A particle moves in the plane along a curve C with representation. r(t)=tcos(t)i+tsin(t)j for ...
A: Very good work. Lets consider the dot product of two vectors A and B. A.B = |A||B|cos# where |A| and ...
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| this ones really hard.... | 11/17/2008 |
Q: y- (((e^sinx)(tan^3)x)/(3x^2-1)^8) a) use logarithmic differentiation to find y' b) use quotient ...
A: This is a bit long to work through and so because of time i would just let you know how to go about ...
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| So confused | 11/17/2008 |
Q: f(x)= ln(sin^-1(2x)) a) find domain of f b) find f'(x)
A: f(x) = ln [sin^-1 (2x)] a) For the domain of f(x), sin^-1 (2x) needs to be positive because of the ...
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| AP Calculus BC | 11/16/2008 |
Q: The sum of the first and twice the second is 100 and the product is a maximum.
A: The first and second terms of an AP are a and a+d where d is the common difference. If the sum of ...
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| drawing and plotting graph | 11/15/2008 |
Q: Sir I am very confused that how to shade graph of inequalities?In my book the shaded part is a ...
A: A straight line divides the coordinate system into two regions, one of them satisfying a particular ...
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| pre-calculus | 11/14/2008 |
Q: How do I simplify: 7log base7^4 - ^2log base7^2 + 3log base3^5 + log base3^2 - 2 ln e^3? I believe ...
A: You're right about the second part being 10 because log(3) 5 + log(3) 2 = log(3) 5x2 ...
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| a calculas question! | 11/13/2008 |
Q: let f(x)=(1-x),g(x)=x/(x²-1) find fog and domin (f),domain (g) and domain (fog)
A: f(x)= 1 - x , g(x) = x/(x²-1) fog = f[g(x)] = 1 - g(x) = 1 - [x/(x²-1)] The domain of f is ...
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| Finding Parameter Values | 11/12/2008 |
Q: What values of a and b make f(x) = x^3 + ax^2 + bx have a)a local maximum at x = -1 and a local ...
A: The cubic function f(x) = x^3 + ax^2 + bx has stationary points when f'(x) = 0 f'(x) = 3x^2 + 2ax + ...
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| Pre-calculus | 11/10/2008 |
Q: How do I convert 9 cis 300 degrees to rectangular coordinates? I need to find an exact answer. ...
A: The polar coordinates r and θ can be converted to cartesian coordinates x and y by using the ...
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| Epsilon-delta method for a limit | 11/10/2008 |
Q: I was asked to find a delta such that: abs( 1/(x-1) -1 ) < .01 when 0<abs(x - 2) ...
A: |1/(x-1) - 1| = |(2-x)/(x-1)| = |(x-2)/(1-x)| = |(x-2)/(x-1)| since |A| = |-A| = |x-2|/|x-1| So ...
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| Calculus. | 11/9/2008 |
Q: I need an explanation for the following math. f(x)= 4Xpower3-9Xpower2+6X-1. Since the sum of the ...
A: f(x) = 4x^3 - 9x^2 + 6x - 1 f(1) = 4(1^3) - 9(1^2) + 6(1) - 1 = 4 - 9 + 6 - 1 = 0 x = 1 is a ...
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| Word Problems | 11/7/2008 |
Q: I'm having trouble with word problems in my calculus class, hope you can help me understand better. ...
A: V(t) = 10[1 - (t/100)]^2 The rate of change of volume at any time t is, dV/dt = 10.2[1 - ...
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| Optimization | 11/7/2008 |
Q: You run a small furniture business. You sign a deal with a customer to deliver up to 400 chairs, ...
A: I dont think the question is complete for optimization. But anyway, quite straightforward, the ...
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| Maximizing Area | 11/4/2008 |
Q: What is the largest possible area for a right triangle whose hypotenuse is 5 cm long, and what are ...
A: Let the right angle have sides x and y. Its area A = (1/2)xy but by the pythagoras theorem, x^2 + ...
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| pre-calculus | 11/4/2008 |
Q: How do I evaluate: sin (Arctan 2/5)? I don't understand how to do this. Is the answer ...
A: Let sin(arctan 2/5) = sin x x = arctan 2/5 tan x = 2/5 Consider x to be one angle of a right-angle ...
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| Differentiaion help! | 11/1/2008 |
Q: The manager of a supermarket usually adds a mark-up 20% to the wholesale prices of all the goods he ...
A: The manager has a loyal core of F customers i.e those who'll always buy, whatever the price. By ...
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| student in the college of eng | 10/31/2008 |
Q: I WANT YOU PLEASE TO PROVE THAT COSHAX+SINHAX=e^AX AND COSHAX-SINHAX=e^AX
A: By definition, sinh ax = (e^ax - e^-ax)/2 and cosh ax = (e^ax + e^-ax)/2 So, cosh ax + sinh ax = ...
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| Trig Identities | 10/29/2008 |
Q: 1/tan squared x- 1/cot squared x=csc squared x - sex squared x
A: Lets start with the identity cos^2(x) + sin^2(x) = 1 dividing through by cos^2(x), we have ...
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| caculus- reduction formula ( need this question asap plz, like in the next hour or 2) | 10/24/2008 |
Q: cos(x) e^x dx need this question asap plz...
A: What part of it was hard for you to clearly understand? Or what part showed any sign of a lack of ...
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| Max/min | 10/22/2008 |
Q: need some help minimizing this equation... (58+Rpi)(500000/pi)(r^-1)+19*pi*r^2 where R is a ...
A: Its really good that you've made some effort and so i'll just be guiding you to the right path from ...
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| derivatives | 10/21/2008 |
Q: Can you show me how to find the derivative of yx^1/2 - xy^1/2 = 16 implicitly?
A: The trick to implicit differentiation is to always add dy/dx after differentiating any expression in ...
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| find dy/dx using implicit differentation | 10/21/2008 |
Q: I need to find dy/dx if xey + 1 = xy using implicit differentiation. Can you please help me?
A: I'm taking it you meant to write xe^y + 1 = xy The trick to implicit differentiation is to always ...
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| derivatives | 10/19/2008 |
Q: 1.) 3x^2-x/(x-1)^3 2.) 5(x+3)^2(2x-1)^5
A: For y = (3x^2 - x) / (x-1)^3 Using the quotient rule, dy/dx = [(x-1)^3][(6x-1)] - [(3x^2 - ...
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| Optimization | 10/10/2008 |
Q: An open box is to be made from a twelve-inch by twelve-inch square piece of material by cutting ...
A: I cant see the diagram but i picture the situation. You end up with a box with a height x and a ...
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| Slope of a Tangent | 3/8/2006 |
Q: Find the points on the graph of y = (x^3)/3 - 5x - 4/x at which the slope of the tangent is ...
A: Sorry for the time it took. The tangent of a curve at any point is horizontal when dy/dx = 0 (i.e ...
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| Calc 2 | 3/3/2006 |
Q: how do you integrate cos^(-1)x dx
A: Sorry for the time it took. Did you mean the integral of arccos x? Arccos x is the inverse cosine of ...
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| prove that (z=a+bi,absolute... | 3/2/2006 |
Q: prove that (z=a+bi,absolute value z-zconjugate)=2b
A: If z = a + bi The conjugate of z is defined as z' = a - bi And so z - z' = (a + bi) - (a - bi) ...
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| logarithmic differentiation | 2/27/2006 |
Q: use logarithmic differentiation to find the derivative of: y=((x^2+1)/(x^2 -1) )^(1/4)
A: Sorry for the time it took. For y = [(x^2 + 1)/(x^2 - 1)]^(1/4) we raise both sides to the power of ...
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| Calculus | 2/26/2006 |
Q: Why does the definite integral of tan(x)dx evaluated from zero to pi diverge instead of evaluating ...
A: Sorry for the time it took. The integral tanx dx evaluated from zero to #(pi) = log(sec #) = log(-1) ...
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| Functions | 2/25/2006 |
Q: I am having a hard time creating functions for data since functions have always been a weak aspect ...
A: Sorry for the time it took. What you require here is knowledge on the topic of 'curve fitting. ...
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| Calculus | 2/24/2006 |
Q: Compute the Derivative f(x)=4x2-3x+5
A: Sorry for the time it took. The formula for finding the derivative of y = ax^n is dy/dx = nax^(n-1) ...
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| Calculus Questions | 2/16/2006 |
Q: 1) Find the equation of the tangent line to the graph: y^2 + ln(xy) = 2 at the point (e, 1) 2) ...
A: Sorry for the time it took. The slope of the tangent line at any point is the value of dy/dx at that ...
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| Calculus AB | 2/13/2006 |
Q: 1. State the domain: g(x)= 2 + ln x 2. Write the expression as a log of a single quantity: 3 ln x ...
A: Sorry for the time it took. For f(y) = lny The domain is y > 0, because the logarithm of a negative ...
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| limits | 2/10/2006 |
Q: Evaluate the following limit: limit as x approaches negative 2 from the right of: (the absolute ...
A: The modulus of y, |y| = y for y > 0 |y| = -y for y < 0 And so, |x+2| = x+2 for x+2 > 0 i.e x > -2 ...
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| calculus related rates | 2/9/2006 |
Q: An aircraft climbing at a constant angle of 30o above the horizontal passes directly over a ground ...
A: Sorry for the time it took. I'm sorry i'm unable to give a sketch of the situation here, try doing ...
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| Integrate ((t-1)^1/2)/(t-2)... | 2/8/2006 |
Q: Integrate ((t-1)^1/2)/(t-2) by substituting u = (t-1)^1/2
A: Sorry for the time it took. To find the integral of [sqrt(t-1)]/t-2 by the substitution u = ...
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| calc. | 2/7/2006 |
Q: integrate 1/xrootx dx from 0 to 3
A: Sorry for the time it took. We start by simplifying 1/x(sqrtx) using the laws of indices. sqrtx = ...
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| calculus | 2/6/2006 |
Q: How do I find the slope of this problem? (x,3x) and (x + h, 3(x + h))
A: Sorry for the time it took. The slope of the line joining the points (x1,y1) and (x2,y2) is (y2 - ...
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| Simple Integration | 2/5/2006 |
Q: What is the integral of: e^ ((x^2)/2)
A: Sorry for the time it took. Simple integration? I'm not sure i'll call it that. There are some ...
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| Integration | 1/29/2006 |
Q: Integrate by part with respect to x: (x^5)*(e)^(x^3). Please list the exponent integration used in ...
A: Sorry for the time it took. Technical problem with the site. To find the integral of x^5 . e^(x^3) ...
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| Pre-Calculus Question | 1/28/2006 |
Q: Instructions from textbook: Advanced Mathematical Concepts, Pre-calculus with Applications, by ...
A: Sorry for the time it took. Technical problem with the site. If 2x^2 + 4xy + 2y^2 + 2(sqrt2)x - ...
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| epsilon delta proof of limit | 1/25/2006 |
Q: lim as x approaches 3 of the square root of (x cubed - 2)=5; PROVE USING EPSILON DELTA METHOD. I ...
A: Sorry for the time it took. To prove that the limit of a function f(x) is equal to L as x approaches ...
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| I have a graph with the y... | 1/24/2006 |
Q: I have a graph with the y axis as Cost of Goods Sold and the x axis is Price. The plotted points ...
A: I'm only askng you to do this in order to save time. Do all the points fall on a single line? If ...
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| limits and continuity | 1/18/2006 |
Q: I need help in the general areas of limits and continuity (i.e. calculating limits, defining limits, ...
A: Sorry for the time it has taken. I really can't help you with these at the moment. But you can, ...
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| Related rates | 1/16/2006 |
Q: The length of a rectangle is changing at a rate of 2 cm/s, while the width is changing is such a way ...
A: Take the width and length of the rectangle to be x and y respectively and the formula for the area ...
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| Calculus | 1/15/2006 |
Q: I am taking this course for University prep. Q: Let f(x) = x^2 + 2 and g(x) = (square root of) 1 - ...
A: a) For f(x) = x^2 + 2 x can take all real values while f(x) >= 2 For g(x) = sqrt(1 - x^2) 1 - x^2 >= ...
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| Calculus | 1/13/2006 |
Q: I'm a retired (66) photographer who has had a life-long interest in mathematics. However, my brain ...
A: Let's make use of the equation of motion involving velocity and distance v^2 = u^2 + 2as where u,v,s ...
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| e | 1/12/2006 |
Q: how do you multiply e^.18 to e^.18 and also how would you divide it?
A: I don't quite get your question, you seem to have written the same expression twice. Dividing them ...
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| distance and velocity and acceleration | 1/9/2006 |
Q: A particle starts at time t=0 and moves along the x-axis so that its position at any time t>=0 is ...
A: Please forgive the delay. First you simplify [(t-1)^3](2t-3) to get x(t) = (t^3 - 3t^2 + 3t -1)(2t - ...
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| reduction formula for tan^n(y) | 1/6/2006 |
Q: salam alikom i need the detailed solution for tan^n(y) integral best regards
A: Sorry for the time taken. To find the reduction formula for tan^n(x) we know that tan^2(x) = ...
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| Calculus | 1/5/2006 |
Q: find the function f that has the derivative f prime of x = 4x-1 and whose graph passes through the ...
A: Sorry for the time taken. For f'(x) = 4x - 1 we have to integrate to get f(x) f(x) = $(4x - 1)dx ...
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| a calculuc hater | 1/4/2006 |
Q: can u please send information or notes that fully explains and teaches calculus for trigonometry. or ...
A: Sorry for the time taken. I actually don't have any links to give to you but i could still give you ...
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| what is 0/0? | 12/17/2005 |
Q: What is zero over zero? Please give me a proof of the answer?
A: Sorry for the time taken. The expression 0/0 in mathematics is referred to as the indeterminate ...
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| Calculus | 12/12/2005 |
Q: Find Center and Radius for x^2-6x+y^2+2y-15=0
A: For a circle with centre (h,k) and radius r, its equation is (x-h)^2 + (y-k)^2 = r^2 So for the ...
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| Volume of a Solid | 12/12/2005 |
Q: I need to find the volume of the resulting solid: Region bounded by y=sin(x), x=pi/6, x=pi/3, and ...
A: Sorry for the time taken. The integral is of course $pi.(sinx)^2 dx To solve this, we make use of ...
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| limited | 12/11/2005 |
Q: can you find anther simple way to analyis lim (1-cosx)/x^2 x_ 0 ...
A: Inserting the limit directly results in the indeterminate form 0/0 We therefore insert the limit ...
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| intergration | 12/7/2005 |
Q: intergrate 1/3+4coshx
A: Forgive the time taken. For our purpose, $ represents the integral sign. By definition, cosh x = ...
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| Calculua | 12/6/2005 |
Q: The motorcycles memorabilia Company wishes to design an open top box with a square base whose volume ...
A: Forgive the time taken. The volume of the tank V = lx^2 where l is the height of the tank and x is ...
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| calculus | 12/5/2005 |
Q: f(x)= 4x^3+ ax^2+ bx + k a,b,k are constants. f(x) has a local minimum at x=-1 and the graph has a ...
A: A local maximum or minimum occurs when dy/dx = 0 Typically, points of inflexion occurs when ...
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| integration by parts. | 12/5/2005 |
Q: do you know how to integrate sin(ln(x))dx between the limits 1 and e using integration by parts? ...
A: I hope you're already familiar with the topic because my explanation would require that. Integrate ...
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| Calculus-Power series | 12/2/2005 |
Q: How would you write a power series for a double alternating sign without spliting the series up? ...
A: I'm sorry for the time taken, i was away for the weekend. Well, it looks like you could put it as ...
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| Trig/Calc | 12/1/2005 |
Q: How do you simplify the trig function sin(theta + pi)/ cos(theta - pi)
A: I'm sorry it took some time. Well, as it happens on the sin and cos graphs, any movement of pi units ...
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| integration | 2/11/2005 |
Q: my girlfriend is having major trouble integrating (x^5)/((x^4)-16)dx. She has broken the problem up ...
A: Please forgive the delay. I've been on vacation and i still am. I'm just taking time out to do this. ...
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| hard polynomials | 2/8/2005 |
Q: (x^3-1)/(x-1) I know the answer is x^2 +x +1,however I don't understand how to get that. One reason ...
A: Please forgive the delay.I'm on vacation. I'll just take it from where you stopped. After getting ...
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| Calc. 2 | 2/2/2005 |
Q: This is my second week of Calc two and we are learning how to do integration of inverse trig. ...
A: Please forgive the delay. I'm sorry i can't help with these at the moment. I'm on vacation,forgive ...
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| Calculus--critical points | 2/2/2005 |
Q: Ok... I have a problem, and don't understand how to solve it...start to finish.. The book asks for ...
A: Please forgive the delay. I'm sorry i can't help with these at the moment. I'm on vacation,forgive ...
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| tangent lines | 1/31/2005 |
Q: I am stuck on a problem. Find the equation of the tangent line to the graph of y=x to the third at ...
A: For y = x^3 The equation of the tangent at any point is dy/dx = 3x^2 At the point (1,1) i.e x = 1 ...
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| Integration by parts | 1/30/2005 |
Q: The question is first make a substitution and then use integration by parts to evaluate the ...
A: Sorry for the delay. I'll have to say you've done really well and got the right result. But it would ...
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| Calculus | 1/13/2005 |
Q: Find the area bounded by the curves y=x^2 and x=y^2
A: Please forgive the delay. I've been on vacation, but didn't notify the allexperts board. The two ...
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| trigonometry | 1/8/2005 |
Q: cos^4A- sin^4= cos2A prove this with steps
A: Please forgive the delay. I was on vacation. Firstly, we know that cos(A+B) = cosAcosB - sinAsinB ...
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| AP Calculus. | 1/1/2005 |
Q: Consider the curve defined by the equation y+cosy=x+1 for 0 i less then or equal to y which is less ...
A: Please forgive the delay. For y + cos y = x + 1 differentiating with respect to x (1 - sin y)dy/dx = ...
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| helppppppppppppp | 12/25/2004 |
Q: i need help cause i havent pay any attention t my math class and now i want to learn and the thing ...
A: I think i really need you to be specific about your requirements. For this example, the actual ...
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