Question

1. Which of the following is not equivalent to the formula for angular velocity, v = wr?

vw = r
v/w = r
v/wr = 1
v/r= w

2. Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?

|c − 450| ≤ 45
|c + 450| ≥ 45
|c − 45| ≤ 450
|c − 45| ≥ 450

Answer 1

1. vw = r
2. |c -450| ≤ 45

Explanation:

1. The first offered choice is equivalent to ...

... v = r/w . . . . . divide both sides by w

which is not the same as v = wr.

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2. The wording "no more than 45" means ≤ 45. There's only one formula with such a relationship—the first one.

Comment on "this scenario"

The problem statement describes several relationships, and never tells us whether Lucy's goal is met. The precise "scenario" that is intended to be modeled is not clear. The first inequality has a solution that is the range of calories Lucy might have burned had she reached her goal.

The other inequalities describe other "scenarios," some of which are harder to describe.

Answer 2

vw = r This is not correct

abs ( c - 450) <= 45

Explanation:

1. v = wr

Divide by w Divide by wr Divide by r

v/w = wr/w =r v/wr = wr/wr =1 v/r = wr/r =w

vw = r This is not correct

v/w = r This one is good

v/wr = 1 This one is good

v/r= w This one is good

2. When working with absolute values, the amount that can vary is on the other side from the absolute value.

abs( value - target) inequality amount that it varies by

the target is 450

no more than is less than or equal to

the amount we can vary by is 45

abs ( c - 450) <= 45