# geometry

posted by .

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 wire as a function of the length x of the side of the square.

b)What is the domain of A?

c) Graph A=A(x). For what value of x is A smallest?

• geometry -

area square = x^2
diameter circle = d = (10-4x)/pi
so area circle = pi d^2/4
= (1/4pi)(10-4x)^2

A = x^2 +(1/4pi)(100 -80x +16 x^2)
= (1/pi)pi x^2 + (1/pi) (25-20x+4x^2)
= (1/pi)( (pi+4)x^2 -20 x + 25)
that is a parabola, look for zeros and vertex
note that negative A is meaningless as is negative x.
negative 10-4x is also meaningless so right off the bat you know x>10/4 is outside the domain
so x can only be between 0 and 10/4

## Similar Questions

1. ### 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 possible?
2. ### Calculus

a piece of wire 12 ft. long is cut into two pieces. one piece is made into a circle and the other piece is made into a square. Let the piece of length x be formed into a circle. allow x to equal 0 or 12, so all the wire is used for …
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. ### pre calculus

A wire 10m long is cut into 2 pieces. one piece will be cut into a square the other piece will be shaped into a circle. Graph A= A(x) for what value of x is A smallest?
5. ### math

a piece of wire 24 ft. long is cut into two pieces. one piece is made into a circle and the other piece is made into a square. Let the piece of length x be formed into a circle. allow x to equal 0 or 24, so all the wire is used for …
6. ### Pre algebra

25ft piece wire cut into 2 pieces one piece is 19ft shorter than the other piece how long was each piece
7. ### math

a piece of wire 12 meters long is cut into two pieces.one piece is bent into the shape of an equilateral triangle and the other into the shape of a circle.how should the wire be cut so that the combined area of the two figures is as …
8. ### math

An electrician cuts a 12-ft piece of wire into two pieces one piece is 8 feet shorter than the other piece how long was each piece
9. ### 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 …
10. ### Calculus

A 100 inch piece of wire is cut into two pieces. Each piece of wire is used to make a square wire frame. Let x be the length of one piece of the wire. Determine an algebraic representation A(x) for the total area of the two squares.

More Similar Questions