9.5.0: Exercises
- Page ID
- 171749
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, determine the most reasonable value for each temperature.
Human body:
- 37 °C or
- 37 °F
An ice cube:
- 32 °C or
- 0 °C
Boiling water:
- 212 °C
- or 212 °F
Summer day:
- 8 °C,
- 23 °C, or
- 75 °C
Winter day:
- 33 °C,
- 30 °C, or
- 3 °C
Lava:
- 700 °C,
- 70 °C, or
- 7 °C
For the following exercises, use mental math to approximate the temperature.
500 °F = __________ °C
25 °C = __________ °F
350 °F = __________ °C
150 °C = __________ °F
–4 °F = __________ °C
73 °C = __________ °F
72 °F = __________ °C
10 °C = __________ °F
1,020 °F = __________ °C
For the following exercises, convert the temperatures to the nearest degree.
450 °F = __________ °C
35 °C = __________ °F
525 °F = __________ °C
140 °C = __________ °F
–40 °F = __________ °C
67 °C = __________ °F
85 °F = __________ °C
15 °C = __________ °F
1,200 °F = __________ °C
112 °F = __________ °C
105 °C = __________ °F
125 °F = __________ °C
A cup of tea is 30 °C. After adding ice, the temperature of the tea decreased 3 °C. What is the temperature of the tea now?
A liquid with a temperature of 15 °C is placed on a stovetop. The liquid is heated at the rate of 1.5 °C per minute. What is the temperature of the liquid after 10 minutes?
The temperature inside a store is 22 °C. Outside the temperature is 37 °C. How much cooler is it in the store than outside?
A boiling pan of water is 212 °F. As the water cools the temperature drops 6 °C every 2 minutes. How many minutes until the temperature of the water reaches 40 °C?
On May 1 the temperature was 79 °F. On June 1 the temperature was 25 °C. Which day was warmer?
For each log placed on a fire, the temperature increases 45 °C. How many logs are needed for the campfire to increase 315 °C?
The temperature of a Bunsen burner flame increases 572 °F each minute. About how many minutes does it take for the flame to increase 1,200 °C?
The instructions to cook a pizza say to set the oven at 425 °F. To the nearest degree, what is the temperature in degrees Celsius?
In the evening the temperature was 3 °C. By morning, the temperature had fallen 4 °C. What is the temperature now?
An 8,000 BTU air conditioner can cool a room 1 °C every 5 minutes. If the temperature in the room is 24 °C, how long will it take the air conditioner to cool the room to 20 °C?
What is 95 °F in degrees Celsius?
What is 50 °C in degrees Fahrenheit?
Which is a reasonable value for the temperature of a room:
- 60 °C,
- 40 °C, or
- 20 °C?