Homework Help: Calculus

Posted by Mishaka on Sunday, January 15, 2012 at 6:02pm.

A piece of elastic is attached to two nails on a flat board, with a button attached to the midpoint of the elastic. The nails are 5 cm apart. You stretch the elastic by pulling the button along the board in a direction that is perpendicular to the line between the nails.
A. Fnd an equation that relates the total length of the elastic x to the distance y that the button has moved.
B. You pull the button at a constant 3 cm/sec. Find the rate at which the length of the elastic is increasing when it is 12 cm long.

Calculus - Steve, Monday, January 16, 2012 at 12:00am
you have two right triangles of height y

2.5^2 + y^2 = (x/2)^2
or
25 + 4y^2 = x^2

8y dy/dt = 2x dx/dt
when x = 12, y = 5.454

8(5.454) = 2(12) dx/dt
dx/dt = 1.818

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