The length of a rectangle is increasing at a rate of 8cm/s8cm/s and its width is increasing at a rate of 5cm/s5cm/s. When the length is 20cm20cm and the width is 25cm,25cm, how fast is the area of the rectangle increasing

Step-by-step explanation:

Given that the length of a rectangle is increasing at a rate of 8cm per s and its width is increasing at a rate of 5cm per s.

Let l be the Length of Rectangle (cm)

Let w  be the Width of Rectangle (cm)

Let A  be the Area of Rectangle ()

Let t  be the Time (s)

From the given we can write

cm per s and  

cm per s

The formula for Area of the rectangle is:

A=lw  square units

Differentiating with respect to t

 ( by using the product rule formula )

when l=20 and w=25

∴  

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)