Drill Questions: Chap 3 Rates

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   R-3-11
True     or       False      

A rate is a quantity.

The dimension of a rate is:

R-3-12

The dimension of the numerator (the quantity on top).

The dimension of the denominator (the quantity on the bottom).

The dimension of the numerator divided by the dimension of the denominator.

Rates do not have a dimension.

   d03-3
True     or       False      

A compound rate is a quantity.

What is the conversion factor (“flavor of one”) for converting an angle measured in radians into degrees?

R-3-14

0.01745 radian/degree

57.30 degree/radians

0.01745 degree

57.30 radians

The angle spanning a half circle has 180 degrees or, the same thing, 3.14159 radians. Since the two are the same, dividing one by the other gives a flavor of one. Since we are converting to degrees from radians, degrees need to be be on top and radians on the bottom: \[\frac{180}{3.14159} \ \frac{\text{degree}}{\text{radian}} = 57.30 \frac{\text{degree}}{\text{radian}}\ .\]

..id..

A student wrote, “Multiplying the km value by 0.621371 turns kilometers into miles.” Conversion factors between units with the same dimension always take the form of a flavor of one.

Which of these quantities is a flavor of one?

d03-km-mi
0.621371       0.621371 km per mile       0.621371 mile per km      

If y changes from 0.6 m to 0.4 m while v changes from 5 hour to 7 hour, what is the rate of change of y with respect to v? d03-I
-0.05 hour       -0.2 m       -5 hour       -20 m per hour       -0.1 m per hour      

If x changes from 8 m/s to 9 m/s while z changes from 3 kg to 7 kg, what is the rate of change of x with respect to z? d03-II
0.125 kg       0.25 m/s per kg       2 m/s       8 m/s       4 kg per m/s      

If y changes from 0 pint to 40 pint while v changes from 9 dollar to 3 dollar, what is the rate of change of y with respect to v? d03-III
-6.7 pint per dollar       -13.3 pint       -0.075 dollar per pint       -0.3 dollar-pint       -0.15 pint per dollar      

If u changes from 100 acre-ft to 900 acre-ft while w changes from 600 hour to 0 hour, what is the rate of change of u with respect to w? d03-IV
-0.667 acre-ft per hour       -1.3 acre-ft per hour       -0.375 hour-acre-ft       -1.5 acre-ft       -0.75 hour-acre-ft      

If w changes from 6 cars per capita to 0 cars per capita while y changes from 0.1 million USD to 0.2 million USD, what is the rate of change of w with respect to y? d03-V
-60 cars per capita per million USD       -120 million USD       -0.00833 cars per capita       -0.0333 million USD       -0.0167 million USD per cars per capita      

You’re thinking about going into business hauling packages in your car. Naturally, you want to know if adding cargo weight will cost you extra in gasoline. So you did an experiment.

  1. You measured your van’s fuel economy without cargo: 25 mpg
  2. You added 500 lbs cargo and again measured fuel economy: 23 mpg

Questions:

  1. What is the rate of change of fuel economy with respect to cargo weight?
d03-fuel-a

-0.46 mpg per lb.

-0.004 mpg per lb.

0.004 mpg per lb.

-0.004 lb per mpg

Oops! You charge shipping using a rate of dollars per (pound mile). But you forgot to weight the cargo before heading out. You drive 100 miles and consume 4.8 gallons of fuel. The same trip without cargo would consume 4.1 gallons of fuel. What is the weight of your cargo (in lbs.)? (Hint: You’ll need the rate of change from question (a), or maybe you need its reciprocal.)

  1. What’s your miles per gallon without cargo, according to your measurements? (All the choices below have units of miles per gallon.)
d03-b-VI
0.041       0.48       24.4       28.6       30      

  1. What’s your miles per gallon with cargo, according to your measurement? (All the choices below have units of miles per gallon.)
d03-c-VI
20.8       22.8       23       24.4       27.3      

  1. What’s the change in miles per gallon produced by the cargo weight? (All the choices below have units of miles per gallon.)
d03-d-VI
-3.6       2       3       4       4      

  1. To convert the change in miles per gallon to a cargo weight, will you divide or multiply by the rate of change in part (a)?
d03-e-VI
multiply       divide       neither