Homework Answers

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

Sand is being dropped at a rate of 10 cubic feet per minute onto a conical pile. If

the height of the pile is always twice the base radius, at what rate is the height

increasing when the pile is 8 feet high?

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DEADLINE : 05/03/2022 11 : 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A spherical balloon is being inflated so that its volume is increasing at rate of 5

cubic feet per minute. At what rate is the diameter increasing when the diameter

is 12 feet?

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DEADLINE : 05/03/2022 11 : 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A boy is flying a kite, which is at a height of 40 feet. The kite is moving horizontally

at a rate of 3 feet per second. If the string is taut, at what rate is the string being

paid out when the length of the string released is 50 feet?

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DEADLINE : 05/03/2022 11 : 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

An automatic travelling at a rate of 30 feet rate second is approaching an

intersection. When the automobile is 120 feet from the intersection, a truck

traveling at a rate of 40 feet per second crosses the intersection. The automobile

and the truck going, separating 2 seconds after the truck leaves the intersection?

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DEADLINE : 05/03/2022 11 : 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

Out of frustration, Arceli throws a stone into a river. This caused ripples in the form

of concentric circles. The radius of the outer ripple increases constantly at 1.5 feet

per second. At what rate is the total area of the disturbed water changing when the

radius is 5 feet?

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DEADLINE : 05/03/2022 11 : 00 PM

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A water tank in the form of an inverted cone is being emptied at the rate of 6 cubic

feet per minute. The altitude of the cone is 24 feet and the base radius is 12 feet.

Find how fast the water level is lowering when the water is 10 feet deep.

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DEADLINE : 05/03/2022 11: 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the

horizontal. If the bottom of the ladder is being moved horizontally toward the

embankment at 1 foot per second, how fast is the top of the ladder moving when

the bottom is 4 feet from the embankment?

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DEADLINE : 05/03/2022 11: 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A man on a dock is pulling in a boat at a rate of 50 feet per minute by means of a

rope attached to the boat at water level. If the man’s hands are 16 feet above the

water level, how fast is the boat approaching the dock when the amount of rope

released is 20 feet?

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DEADLINE : 05/03/2022 11 : 00 PM

Related Rates: Problem Solving

Direction: Solve each word problem involving a related rates. Make a sketch of your work

if necessary, and then apply differentiation.

A light is hung 15 feet above a straight horizontal path. If a man 6 feet tall walking

away from the light at a rate of 5 feet per second, how fats is the man’s shadow

lengthening when the man is 8 feet from the base of the light source?

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DEADLINE : 05/03/2022 11 : 00 PM

1. A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 6 science courses, any of 4 humanities, and any of 4 mathematics courses, how many ways can she arrange her program?

2. The store at your school wants to stock sweatshirts that come in four sizes (small, medium, large, extra-large) and in two colors (red and white). How many different types of sweatshirts will the store have to stock?

3. Rysel received a new wardrobe consisting of 6 shirts, 4 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?