# Calculus

A wire 60 cm long is to be cut into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of an equilateral triangle, as shown in the diagram below:

a diagram showing a 60 cm wire cut into two pieces of length x and 60 minus x respectively. The wire of length x is bent into a square with side length x over 4 cm. The wire of length 60 minus x is bent into an equilateral triangle with sides of length 60 minus x over 3 cm

The wire is to be cut in order that the sum of the areas of the square and the triangle is to be a maximum. An equation that can be used to model the sum of the areas is A at x equals the sum of x squared over 16 and root 3 times quantity 60 minus x squared, over 18. Determine the boundaries and the corresponding areas. You need not solve further.

4. A cylindrical tank is to have a capacity of 1000 m³. It is to fit into a foundry that is 12 m wide with a height of 11 m.

1. 👍
2. 👎
3. 👁
1. f(x) = x^2 /16 + 3^.5 (60-x)^2 / 18
min or max when derivative = 0
f'(x) = 0 = (1/8) x + sqrt 3 * (60-x) (-1) /18
0 = x/8 - sqrt 3 (60/18) + sqrt 3 ( /18) x

x(sqrt 3 / 18 + 1/8) = (30/9) (sqrt 3)

1. 👍
2. 👎
👤
Damon
2. 1000 = h * pi D^2/4

1. 👍
2. 👎
👤
Damon
3. could you explain the first problem in a different way

1. 👍
2. 👎
4. recall that the area of an equilateral triangle of side s is √3/4 s^2. So, s = (60-x)/3
the side of a square of perimeter x is x/4, so the area is x^2/16

1. 👍
2. 👎
👤
oobleck
5. A wire 60cm long is to be cut into two pieces, one of which is to be bent into the shape of a square and the other of which is to be bent into an equilateral triangle. Find how the wire should be cut so that the combined area of the square and equilateral triangle is minimum.

1. 👍
2. 👎
6. A wire 60cm long is to be cut into two pieces, one of which is to be bent into the shape of a circle and the other of which is to be bent into an equilateral triangle. Find how the wire should be cut so that the combined area of the circle and equilateral triangle is minimum.

1. 👍
2. 👎
7. HAHAHAHAHA glglgl

1. 👍
2. 👎

## Similar Questions

1. ### maths

a 10m piece of wire is cut into two pieces one piece is 2m longer than the other. how long are the pieces?

2. ### math

Edith wants to cut pieces of ribbon 1/3 meter long from a piece of 5/6 meter.how many pieces can be cut?

3. ### Related rates

A piece of wire 10 feet long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of the square. How should the wire be cut so that the combined area of the two figures is as small as

4. ### math

jill has 8 yards of cloth. she wants to cut it into pieces that are 1/4 yard long. How many pieces can she cut from the length of cloth

1. ### geometry

A wire 10 meters ong is to be cut into two pieces. One piece wil be shaped as a square, and the other piece will be shaped as a circle. (piece one is 4x, piece two is 10-4x) a)Express the total area A enclosed by the pieces of

2. ### math

Mother cut a cake in 20 pieces.l ate 3/5 of the pieces. How many pieces did l eat?

3. ### math

A length of string that is 22 feet long is being cut into pieces that are 1/3 foot long. How many pieces will there be? 22x3=66 pieces

4. ### Math

William cut a 90-inch wire into 3 pieces. The longest piece was three times as long as each of the other 2 pieces, which were the same length. What was the length of the longest piece of wire? THANK YOU!

1. ### algebra

a 28 ft rope is cut into 2 pieces. one is 3 feet longer than the other. how long are the pieces?

2. ### math

Yoshi has a rope 30 feet long. He must cut it into pieces that are 1/4 long. Will he get more or fewer than 30 pieces? I think more because he will divide it. So I think he will get 120 pieces. Is this correct?

3. ### 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?

4. ### Maths

A metere long strip is cut into 12 equal pieces. What is the length of each pieces