Advanced Math/algebra

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Expert: - 10/22/2008


Question
I have a few questions.

1. A pasture is twice as long as it is wide. Its area is 115,200 ft squared. How
wide is the pasture

2. What quantity of a 60% acid solution must be mixed with a 30% solution to
produce 300 mL if a 50% solution?

3. A merchant blends tea that sells for $3.00 a pound with tea that sells for
$2.75 a pound to produce 80 lb of a mixture that sells for $2.90 a pound.
How many ponds of each type does the merchant use in the blend?

4. A storage bin for corn consists of a cylindrical section made of wire mesh,
surmounted by a conical tin roof, as shown in the figure. The height of the
roof is one-third the height of the entire structure. IF the total volume of the
structure is 1400 pie ft cubed and its radius is 10 ft, what is the height?

Answer
1. Let w=width, then l=2w.  2*2w=115,200.  Solve from there.

2. 0.6A+0.3(1-A)=.5; solve for A.  It is the percenet of first solution.  1-A is the perecent of second solution.  Multiply these percents by 300.

3. 3A+2.7b(1-A)=2.90; solve for A and multiply the value for A by 80.

4. For a cone, the volume if V1=πr²a/3, where a is the height of the cylinder.  For the cylinder, the volume V2=πr²b, where b is the height of the cone.

Note that b is the same as 1/3 of a+b, so b = (a+b)/3.  From this it can be seen that the varialbe a has to be 2b so that (2b+b)/3=b, so the equation is a=2b.

The total volume V = V1+V2 = 2πr²b/3 + πr²b = πr²b(2/3 + 1) =
πr²b(5/3).  This is equal to 1400 and r is equal to 10.  All you have to do is divide the 1400 by the quatity π*10²*5/3 and you should get the value for b.

Looking back at the way this was formulated, remember that b is the height of only the cone, a=2b is the height of the cylinder, so a+b=3b is the total height.

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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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