# College Math 117 Week 6 Answer Guide- Algebra 1B -

### Week Six Algebra 1B study guide and Soultions

1. Many people know that the weight of an object varies on different planets, but did youknow that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation *w *= *Cr *-2 , where *C *is aconstant, and *r *is the distance that the object is from the center of the Earth.

a. Solve the equation *w *= *Cr *-2 for *r*.

The answer is **r = sqroot[C/w]**

b. Suppose that an object is 100 pounds when it is at sea level. Find the value of *C *that makes the equation true (Sea level is 3,963 miles from the center of the Earth).

**C = 100*3963^2 = 1570536900**

c. Use the value of *C *you found in the previous question to determine how much the object would weigh in

i. Death Valley (282 feet below Sea level).

First, calculate *r*:

Convert 282 feet to miles: 282/5280 = 0.0534

3963- 0.0534 = 3962.946

100.003 pounds

1570536900(3962.946)-2

ii. the top of Mount McKinley (20,320 feet above Sea level).

First, calculate *r*:

Convert 20,320 to miles: 20320/5280 = 3.848 miles

3963 + 3.848 = 3966.848

99.806 pounds

1570536900(3966.848)-2

2. The equation *D *= 1.2 *h *gives the distance, *D*, in miles that a person can see to the horizon from a height, *h*, in feet.

a. Solve this equation for *h*.

b. Long’s Peak in Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see

Cheyenne, Wyoming (about 89 miles away)?

143.27 miles

1.2(119.394)

1.2 14255

1.2

You can see 143.27 miles. Since Cheyenne is only 89 miles away, you can easily see Cheyenne.

a. Solve the equation *w *= *Cr *-2 for *r*.

b. Suppose that an object is 100 pounds when it is at sea level. Find the value of *C *that makes the equation true (Sea level is 3,963 miles from the center of the Earth).

c. Use the value of *C *you found in the previous question to determine how much the object would weigh in

i. Death Valley (282 feet below Sea level).

ii. the top of Mount McKinley (20,320 feet above Sea level).

2. The equation *D *= 1.2 *h *gives the distance, *D*, in miles that a person can see to the horizon from a height, *h*, in feet.

a. Solve this equation for *h*.

b. Long’s Peak in Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)?

You can see 143.27 miles. Since Cheyenne is only 89 miles away, you can easily see Cheyenne.