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Expert: - 7/27/2011


Question
QUESTION 1: A can (right circular cylinder) is to be made to hold 1,000 cm^3 of oil. Find the dimensions that will minimize the cost of the metal to make the can.
QUESTION 2: An architect wants to design a window in the shape of a rectangle capped by a semicircle. If the perimeter of the window is constrained to be 24 feet, what dimensions should the architect choose for the window in order to admit the greatest amount of light?
QUESTION 3: An isosceles triangle has a base of 6 units and a height of 12 units. Find the maximum possible area of a rectangle that can be placed inside the triangle with one side on the base of the triangle.

Answer
1) The volume of a cylinder is equation [1], V = pi*r^2*h where r is the radius and h is the height.  The surface area is given by equation [2] A = pi(2*r^2 + r*h).  Set the volume V to 1000, solve equation [1] for h in terms of r, and put that in the equation [2].  Once this has been done, find the derivative of this equation with respect to r, and set equal to 0 to solve for r. Once r is know, use equation [1] to find h, since [1] is 1000.

2) The semicircle has radius r, so the window has with 2r.  The height of the rectangle is h.
The area is given by equation [1], A = 2rh + pi*r^2/2 and the perimter is the bottom plus the sides plus the semicircle at top, or, [2] P = 2r + 2h + pi*r.  Equation [2] is 24, so use that to  solve for h in terms of r.  Once this has been found, put that h(r) in equation [1].  Take the derivative with respect to r, set it equal to 0, solve for r, and put that back into equatioin [2] to find h.

3) Put the triangle on a graph with the center of the bottom on the origin.
Mark a point at (x,0).  This is one end of the base, and the other is at (-x,0).
The top point is at (0,12) and the two base points are at (-3,0) and (3,0).
This makes the equation of the right side into y = 12 - 4x.

Now, since the base was chosen to be x units out, the width of the base is 2x and
the height is 12 - 4x.  The area is then base*height = 2x(12-4x) = 24x-8x^2.
The derivative of this area is 24 - 16x.  Setting to 0 gives x = 3/2.
This makes y = 6, so the area is 2xy = 2(3/2)6 = 18.  

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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