Homework Help

# How fast is the area of the rectangle changing if one side is 10 cm long and it is...

Student

eNoter

• Up
• 0
• Down

How fast is the area of the rectangle changing if one side is 10 cm long and it is increasing at a rate of 2cm/s and the other side is of 8cm long..

..and it is decreasing at a rate of 3cm/s?

Posted by idaberg on May 21, 2011 at 3:48 PM via web and tagged with area of the rectangle, calculus, math

College Teacher

Valedictorian

• Up
• 1
• Down

The dimensions of the rectangle, at the time t, are x and y cm.

We'll compute the area of the rectangle, at the time t:

A = x*y cm^2 (1)

We'll have to determine dA/dt if we want to know how fast the area of the rectangle is changing.

We'll differentiate (1) with respect to t:

dA/dt = [(dx/dt)*y + (dy/dt)*x] (2)

We know, from enunciation, that dx/dt = 2 and dy/dt = -3.

We'll replace the values into (2):

dA/dt = 2*8 + (-3)*10

dA/dt = 16 - 30

dA/dt = -14 cm^2/s

Since the value obtained for dA/dt is negative, it means that the area of the rectangle is decreasing at the rate of 14 cm^2/s.

Posted by giorgiana1976 on May 21, 2011 at 3:57 PM (Answer #1)

See all »