Respuesta :
Answer:
The area of the given rectangle increasing when l=20cm and w=25 cm by fast is [tex]300cm^2 per s[/tex]
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.
To find the how fast is the area of the rectangle increasing when the length is 20 cm and the width is 25 cm:
Let l be the Length of Rectangle (cm)
Let w be the Width of Rectangle (cm)
Let A be the Area of Rectangle ([tex]cm^2[/tex])
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
[tex]\frac{dA}{dt}=(l)(\frac{dw}{dt})+(\frac{dl}{dt})(w)[/tex] ( by using the product rule formula [tex]\frac{d(uv)}{dx}=u(\frac{dv}{dx})+\frac{du}{dx}(v)[/tex])
[tex]=l(5)+8(w)[/tex]
when l=20 and w=25
[tex]=(20)(5)+8(25)[/tex]
[tex]=100+200[/tex]
[tex]=300[/tex]
∴ [tex]\frac{dA}{dx}=300 cm^2 per s[/tex]
