Respuesta :
Answer:
The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm
Step-by-step explanation:
The area of the rectange is given by the following formula:
[tex]A = l*w[/tex]
In which A is the area, measured in cm², l is the lenght and w is the width, both measured in cm.
The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s.
This means that [tex]\frac{dl}{dt} = 3, \frac{dw}{dt} = 9[/tex]
When the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
We have to find [tex]\frac{dA}{dt}[/tex] when [tex]l = 13, w = 5[/tex]
Applying implicit differentitiation:
We have three variables(A, l, w). So
[tex]A = l*w[/tex]
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + \frac{dl}{dt}w[/tex]
[tex]\frac{dA}{dt} = 13*9 + 3*5[/tex]
[tex]\frac{dA}{dt} = 132[/tex]
The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm
