# rates-of-change

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 cm^{2}?

cm^{2}/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

3-

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

in m/min ??

4-

Suppose

* y* =

2x + 1 |

, where *x* and *y* are functions of *t*.

(a) If * dx*/

*= 3,*

*dt*find

* dy*/

*dt*when

* x* = 4.

dy |

dt |

=

(b) If

* dy*/

*= 2,*

*dt*find

* dx*/

*dt*when

* x* = 12.

dx |

dt |

=

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.)

m/min