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Annette [7]
3 years ago
5

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 le

ngth is 20cm20cm and the width is 25cm,25cm, how fast is the area of the rectangle increasing
Mathematics
1 answer:
Sphinxa [80]3 years ago
6 0

Answer:

<h3>The area of the given rectangle increasing when l=20cm and w=25 cm by fast is 300cm^2 per s</h3>

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.

<h3>To find the  how fast is the area of the rectangle increasing when the length is 20 cm and the width is 25 cm:</h3>

Let l be the Length of Rectangle (cm)

Let w  be the Width of Rectangle (cm)

Let A  be the Area of Rectangle (cm^2)

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

\frac{dA}{dt}=(l)(\frac{dw}{dt})+(\frac{dl}{dt})(w)  ( by using the product rule formula \frac{d(uv)}{dx}=u(\frac{dv}{dx})+\frac{du}{dx}(v))

=l(5)+8(w)

when l=20 and w=25

=(20)(5)+8(25)

=100+200

=300

∴  \frac{dA}{dx}=300 cm^2 per s

<h3>∴ the area of the rectangle increasing by fast is 300cm^2 per s</h3>
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