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Two Calculus word problems...
I am in dread help of need with these word problems. If you could show your work, that would be so helpful. Thank you!
Question 1: A seven foot ladder, leaning against a wall, touche the wall x feet above the ground. Write and expression(in terms of x) for the distance from the foot of the ladder to the base of the wall.
Question 2: A piece of wire 5 inches long is to be cut into two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x.
Thank you so much!
Calculus, schmalculus. This is just algebra.
1. Let d be the distance from the foot of the ladder to the base of the wall. By the Pythagorean Theorem,
d^2 = 7^2 - x^2
i.e.,
d = √(49-x^2)
2. The piece to be bent into a square is x in. long, so the square will be x/4 in. on a side. The area of the square is consequently (x^2)/16 sq.in.
The piece to be bent into a circle is 5-x in. long, so the circle has a circumference of 5-x in.: from this we find it has a radius of (5-x)/2π in., and consequently an area of
π[(5-x)/2π]^2 = (5-x)^2/4π sq. in.
The total area is thus
(x^2)/16 + [(5-x)^2]/(4π) sq. in.