rates of change

I’m trying to learn for my Mathematics class and I’m stuck. Can you help?

1- Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm2?
cm2/s .
2_ This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 14 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

Using A = lw, we have


A cylindrical tank with radius 7 m is being filled with water at a rate of 3 m3/min. How fast is the height of the water increasing?

in m/min ??



y =

2x + 1

, where x and y are functions of t.

(a) If dx/dt = 3,




x = 4.



(b) If

dy/dt = 2,




x = 12.



5-Two sides of a triangle have lengths 13 m and 16 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)

rates of change

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