Calculus

A piece of wire 7 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
A. How much wire should be used for the square in order to maximize the total area?
B. How much wire should be used for the square in order to minimize the total area?

1. 0
2. 0
3. 2
1. let x = side of triangle
let s = side of square
then
7 = 3 x + 4 s so s = (1/4)[7-3x]
A = (1/4)x^2sqrt 3 + s^2
A = (1/4)x^2 sqrt 3 +(1/16)[49-42x+9x^2]
dA/dx= (x/2)sqrt 3 +(1/16)[18x-42]
set to zero for max and min value of x
for which is max
d^2A/dx^2 = (1/2)sqrt3 + (9/8)x
if positive, min
if negative, max

Remember x is the triangle side, s = (1/4)(7-3x)

1. 0
2. 0
posted by Damon

Similar Questions

1. Calculus

A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a maximum= minimum= Find the
2. Calculus

A wire 7 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be
3. Calculus

A wire 4 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be
4. Calculus

A piece of wire 12 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. How should the wire be cut so that the total area enclosed is: a) a maximum?
5. math problem

A piece of wire 24 cm long is cut into two pieces and each piece is bent to form a square . Find the lenght of each piece of wire in order to maximize the sum of the area of the two squares?
6. Calc Optimization

A piece of wire 9 m long is cut into two pieces. one piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. how should the wire be cut so that the total area enclosed is: I have found
7. Calculus

A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
8. calculus

A five feet piece of wire is cut into two pieces. One Piece is bent into a square and the other is bent into an equilateral triangle. Where should the wire be cut so that the total area enclosed by both is minimum.
9. Calculus

A piece of wire 40 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much of the wire should go to the square to minimize the total area enclosed by both
10. Math

A piece of wire 9 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. How should the wire be cut so that the total area enclosed is: I need help
11. calculus

A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area?

More Similar Questions