Calculus Vacation HomeworkName:

Calculus Vacation HomeworkName:Directions: Complete these three related rate problems.

Happy Holidays!

1. On Halloween UMass Amherst had classes

cancelled due the 8” of snow that fell the night

before. Xuyen Mai, former RHS student and

current UMASS frosh decided to make a snow

jack-o-lantern with a radius of 18”. When the sun

came out sphere-shaped snow pumpkin began

melting at a rate of 5 cubic inches per hour.

After one hour, how fast was the circumference

of the jack-o-lantern changing.

2. Today, promptly at 11:01 am I plan to be sipping candy cane

martini (non alcoholic of course) through a straw from a conical

cup, 15 cm deep and 8 cm in diameter at the top. When the

non alcoholic liquid is 10 cm deep, I will be drinking at the rate

of 20 cm^3/s. How fast is the level of the non alcoholic liquid

dropping at that time?"

3. Because of the threat of biological warfare, Santa has decided to make a new circular pen with a hemispherical roof to allow his reindeer to practice flying

indoors away from any threat of anthrax or smallpox. He has decided that to be comfortable there should be 10 cubic meters of per reindeer (9 including Rudolph)

A. Write an equation for the volume of the pen and another equation for the surface area of the pen

The material Santa has decided to used for the walls will cost $15 per square meter and the material for the ceiling will cost $25 per square meter.

B. Adapt the surface area equation to represent the cost of materials

C. Graph and sketch your cost equation

D. What dimensions should the building have to minimize the cost?

4. Herbie the Elf is still making toys while he is working toward a degree in dentistry. Before he can apply to dental school he must complete the prerequsite courses in Biology, Organic Chemistry, Physics and of course Calculus. While working at Santa’s workshop this year he realized that he could apply some of what he has learned in calculus to the following problem. When designing and building a bicycle the frame’s front fork, which holds the front wheel, should curve forward at the bottom where the wheel is bolted on. The fork is bent in the shape of a a cubic of the form y = ax3 + bx. What should the constants a and b be so that the curve joins smoothly to the straight part of the fork at (10 cm, 20 cm) with a slope equal to 5?

(0,0)

(10,20) .

From the textbook please do pp.291-294 #43, 47, 49, 61, 63, 64, 73, 93, 94 & Section Project