Chap 15 Review
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#| show_hints: true 1. Division can accommodate any two quantities, regardless of dimension. [correct] 2.
:::
::: {#exr-dim-02}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$\sqrt{a}$$ Why or why not?<!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. Y ... dimension." id="dim-02-1" w="29" name="dim-02" hint="Yes!" show_hints="TRUE"/>
Invalid. You can't have a non-integer exponent on a dimension.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. It' ... simply 5." id="dim-02-2" w="32" name="dim-02" hint="You forgot about the "feet" unit. That's dimension L and there is no such thing as $L^{1/2}$." show_hints="TRUE"/>
Valid. It's simply 5.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. 2 ... quantity." id="dim-02-3" w="19" name="dim-02" hint="25 feet is a perfectly ordinary quantity. The issue is with the $\sqrt{\ \ \ }$" show_hints="TRUE"/>
Invalid. 25 feet is not a valid quantity.
</p>
<input type="radio" class="devoirs-mcq" name="dim-02" id="dim-02.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-02-hintarea">question id: dim-02</small>
</div>
:::
:::
::: {#exr-dim-03}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$b^c$$ Why or why not?<!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. E ... t allowed." id="dim-03-1" w="32" name="dim-03" hint="Exponention is allowed, so long as the exponent is an integer (or if the operation results in an integer exponent)" show_hints="TRUE"/>
Invalid. Exponentiation of a dimensionful quantity isn't allowed.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. Exp ... s allowed." id="dim-03-2" w="5" name="dim-03" hint="Bullseye!" show_hints="TRUE"/>
Valid. Exponentiation by a dimensionless integer is always allowed.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. I ... dimension." id="dim-03-3" w="32" name="dim-03" hint="Get used to such things. What matters is whether the construction follows the rules. You'll often encounter compound dimensions that seem crazy complicated. For instance, foot-pounds (L$^2$MT$^{-2}$) is a perfectly familiar unit to a mechanic." show_hints="TRUE"/>
Invalid. I can't make any sense out of T$^4$ as a dimension.
</p>
<input type="radio" class="devoirs-mcq" name="dim-03" id="dim-03.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-03-hintarea">question id: dim-03</small>
</div>
:::
:::
::: {#exr-dim-04}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$c^b$$ Why or why not?<!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. E ... t allowed." id="dim-04-1" w="8" name="dim-04" hint="Exponention is allowed, so long as the exponent is an integer (or if the operation results in an integer exponent)" show_hints="TRUE"/>
Invalid. Exponentiation by a dimensionful quantity isn't allowed.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. Exp ... s allowed." id="dim-04-2" w="87" name="dim-04" hint="$b$ isn't a dimensionless integer; it's 3 hours!" show_hints="TRUE"/>
Valid. Exponentiation by a dimensionless integer is always allowed.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. You ... rs like 4." id="dim-04-3" w="32" name="dim-04" hint="Sorry, but you can't add a dimensionless quantity to a dimensionful quantity, no can you raise a dimensionless quantity to a dimensionful power." show_hints="TRUE"/>
Valid. You can do what you want with plain (dimensionless) numbers like 4.
</p>
<input type="radio" class="devoirs-mcq" name="dim-04" id="dim-04.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-04-hintarea">question id: dim-04</small>
</div>
:::
:::
::: {#exr-dim-05}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$\sqrt[3]{a^2 d}$$ Why or why not?<!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. Y ... ger power." id="dim-05-1" w="32" name="dim-05" hint="You can always raise a dimensionful quantity to an integer power. And, if the result of raising to the non-integer power is to produce dimensions that have integer powers, that is valid, too." show_hints="TRUE"/>
Invalid. You can't raise a dimensionful quantity to a non-integer power.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. $a^ ... $^3$ is L." id="dim-05-2" w="8" name="dim-05" hint="Spot on!" show_hints="TRUE"/>
Valid. $a^2 d$ is a volume: L$^3$. The cube root of L$^3$ is L.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. 2 ... by meters." id="dim-05-3" w="7" name="dim-05" hint="Why not? 625 square-feet meters is a volume. It has dimension L$^3$. Admittedly a strange unit, but no stranger than the "acre-foot" used to measure agricultural irrigation." show_hints="TRUE"/>
Invalid. 25 feet squared is 625 square feet. It makes no sense to multiply square feet by meters.
</p>
<input type="radio" class="devoirs-mcq" name="dim-05" id="dim-05.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-05-hintarea">question id: dim-05</small>
</div>
:::
:::
::: {#exr-dim-06}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$\exp(a d)$$ Why or why not? <!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. T ... quantity." id="dim-06-1" w="41" name="dim-06" hint="$a d$ has dimension L$^2$ (with units of feet-meters)." show_hints="TRUE"/>
Invalid. The input to $\exp()$ must be a dimensionless quantity.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. The ... f the $b$." id="dim-06-2" w="7" name="dim-06" hint="No it doesn't. $a d$ has dimension L$^2$." show_hints="TRUE"/>
Valid. The $a$ cancels out the dimension of the $b$.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. 2 ... anything." id="dim-06-3" w="3" name="dim-06" hint="Yes it does. It's the area of a rectangle that is 25 feet long and one meter wide." show_hints="TRUE"/>
Invalid. 25 foot-meters doesn't mean anything.
</p>
<input type="radio" class="devoirs-mcq" name="dim-06" id="dim-06.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-06-hintarea">question id: dim-06</small>
</div>
:::
:::
::: {#exr-dim-07}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$\exp(c d)$$ Why or why not? <!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. T ... quantity." id="dim-07-1" w="14" name="dim-07" hint="$c d$ has dimension L." show_hints="TRUE"/>
Invalid. The input to $\exp()$ must be a dimensionless quantity.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. The ... l be L$^4$" id="dim-07-2" w="3" name="dim-07" hint="This would be right for the combination $d^c$, but $\exp(c d)$ is completely different." show_hints="TRUE"/>
Valid. The dimension will be L$^4$
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. $ ... mension L." id="dim-07-3" w="32" name="dim-07" hint="The dimension of $c d$ is indeed L, but you can't have an argument to $\exp()$ that is dimensionful." show_hints="TRUE"/>
Invalid. $c d$ has dimension L.
</p>
<input type="radio" class="devoirs-mcq" name="dim-07" id="dim-07.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-07-hintarea">question id: dim-07</small>
</div>
:::
:::
::: {#exr-dim-08}
Consider these quantities:<br>$a = 25$ ft <br>$b = 3$ hours<br>$c = 4$<br>$d = 1$ meter<br>$e = 2.718$<br> Is this combination dimensionally valid? $$\exp(c/d)$$ Why or why not? <!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. T ... quantity." id="dim-08-1" w="8" name="dim-08" hint="$c / d$ is not dimensionless." show_hints="TRUE"/>
Invalid. The input to $\exp()$ must be a dimensionless quantity.
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Valid. The ... n of $1/d$" id="dim-08-2" w="7" name="dim-08" hint="This would be right for the combination $d^c$, but $\exp(c d)$ is completely different." show_hints="TRUE"/>
Valid. The L dimension of $c$ is cancelled out by the L$^{-1}$ dimension of $1/d$
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Invalid. $ ... L$^{-1}$." id="dim-08-3" w="19" name="dim-08" hint="Check your arithmetic!" show_hints="TRUE"/>
Invalid. $c / d$ has dimension L$^{-1}$.
</p>
<input type="radio" class="devoirs-mcq" name="dim-08" id="dim-08.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-08-hintarea">question id: dim-08</small>
</div>
:::
:::
::: {#exr-dim-09}
Here are some physical quantities and their dimension:<br>[Force] = MLT$^{-2}$<br>[Distance] = L<br>[Area] = L$^2$<br>[Velocity] = L T$^{-1}$<br>[Acceleration] = L T$^{-2}$<br>[Momentum] = M L T$^{-1}$<br><br> Given that [Force] = [Pressure][Area], what is the dimension of Pressure? <!-- Dimensions -->
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="M L$^{-1}$ T$^{-2}$" id="dim-09-1" w="5" name="dim-09" hint="Right!" show_hints="TRUE"/>
M L$^{-1}$ T$^{-2}$
</p>
<p>
<input type="radio" class="devoirs-mcq" value="M L$^{1}$ T$^{-2}$" id="dim-09-2" w="3" name="dim-09" hint="Not quite right." show_hints="TRUE"/>
M L$^{1}$ T$^{-2}$
</p>
<p>
<input type="radio" class="devoirs-mcq" value="M L$^{-2}$ T$^{-1}$" id="dim-09-3" w="7" name="dim-09" hint="Untrue!" show_hints="TRUE"/>
M L$^{-2}$ T$^{-1}$
</p>
<input type="radio" class="devoirs-mcq" name="dim-09" id="dim-09.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="dim-09-hintarea">question id: dim-09</small>
</div>
:::
:::
::: {#exr-drill-Dimensions-9}
For the following few problems, keep in mind these physical quantities and their dimension:
- [Force] = MLT^-2^
- [Distance] = L
- [Area] = L^2^
- [Velocity] = L T^-1^
- [Acceleration] = L T^-2^<br>
- [Momentum] = M L T^-1^
1. Given that [Force] = [Pressure][Area], what is the dimension of Pressure?
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="M L$^{-1}$ T$^{-2}$" id="drill-Dimensions-9-1" w="8" name="drill-Dimensions-9" hint="Right on the nose!" show_hints="TRUE"/>
M L$^{-1}$ T$^{-2}$
<input type="radio" class="devoirs-mcq" value="M L$^{1}$ T$^{-2}$ " id="drill-Dimensions-9-2" w="23" name="drill-Dimensions-9" hint="Untrue!" show_hints="TRUE"/>
M L$^{1}$ T$^{-2}$
<input type="radio" class="devoirs-mcq" value="M L$^{-2}$ ... T$^{-1}$ " id="drill-Dimensions-9-3" w="19" name="drill-Dimensions-9" hint="Not so!" show_hints="TRUE"/>
M L$^{-2}$ T$^{-1}$
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-9" id="drill-Dimensions-9.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-9-hintarea">question id: drill-Dimensions-9</small>
</div>
:::
2. Which one of the following statements is true?
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Momentum = ... * Velocity" id="drill-Dimensions-10-1" w="18" name="drill-Dimensions-10" hint="Right!" show_hints="TRUE"/>
Momentum = Mass * Velocity
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Velocity = ... Momentum " id="drill-Dimensions-10-2" w="32" name="drill-Dimensions-10" hint="Not so!" show_hints="TRUE"/>
Velocity = Mass / Momentum
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Momentum = ... celeration" id="drill-Dimensions-10-3" w="32" name="drill-Dimensions-10" hint="Mass * Acceleration is Force" show_hints="TRUE"/>
Momentum = Mass * Acceleration
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-10" id="drill-Dimensions-10.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-10-hintarea">question id: drill-Dimensions-10</small>
</div>
:::
3. Which one of the following statements is true?
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Volume = D ... nce * Area" id="drill-Dimensions-11-1" w="41" name="drill-Dimensions-11" hint="Bingo!" show_hints="TRUE"/>
Volume = Distance * Area
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Area = Dis ... / Volume " id="drill-Dimensions-11-2" w="3" name="drill-Dimensions-11" hint="Not so!" show_hints="TRUE"/>
Area = Distance / Volume
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Force = Mo ... eleration " id="drill-Dimensions-11-3" w="32" name="drill-Dimensions-11" hint="Wrong." show_hints="TRUE"/>
Force = Momentum / Acceleration
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-11" id="drill-Dimensions-11.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-11-hintarea">question id: drill-Dimensions-11</small>
</div>
:::
4. Which of the following is true?
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Energy = D ... ce * Force" id="drill-Dimensions-12-1" w="5" name="drill-Dimensions-12" hint="A hit!" show_hints="TRUE"/>
Energy = Distance * Force
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Force = En ... gy / Mass " id="drill-Dimensions-12-2" w="7" name="drill-Dimensions-12" hint="Incorrect choice." show_hints="TRUE"/>
Force = Energy / Mass
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Energy = M ... eleration " id="drill-Dimensions-12-3" w="19" name="drill-Dimensions-12" hint="Not quite right." show_hints="TRUE"/>
Energy = Momentum * Acceleration
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-12" id="drill-Dimensions-12.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-12-hintarea">question id: drill-Dimensions-12</small>
</div>
:::
5. Which of the following is true?
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Length = V ... celeration" id="drill-Dimensions-13-1" w="8" name="drill-Dimensions-13" hint="You've got it!" show_hints="TRUE"/>
Length = Velocity / Acceleration
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Length = F ... Momentum " id="drill-Dimensions-13-2" w="32" name="drill-Dimensions-13" hint="Boo!" show_hints="TRUE"/>
Length = Force / Momentum
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Area = Vel ... eleration " id="drill-Dimensions-13-3" w="32" name="drill-Dimensions-13" hint="Not so!" show_hints="TRUE"/>
Area = Velocity * Acceleration
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-13" id="drill-Dimensions-13.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-13-hintarea">question id: drill-Dimensions-13</small>
</div>
:::
6. Which of the following is true?
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="Time = For ... / Momentum" id="drill-Dimensions-14-1" w="20" name="drill-Dimensions-14" hint="Spot on!" show_hints="TRUE"/>
Time = Force / Momentum
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Length = F ... Momentum " id="drill-Dimensions-14-2" w="23" name="drill-Dimensions-14" hint="You might think so, but ..." show_hints="TRUE"/>
Length = Force / Momentum
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Area = For ... Momentum " id="drill-Dimensions-14-3" w="3" name="drill-Dimensions-14" hint="No." show_hints="TRUE"/>
Area = Force / Momentum
</p>
<p>
<input type="radio" class="devoirs-mcq" value="Mass = For ... Momentum " id="drill-Dimensions-14-4" w="23" name="drill-Dimensions-14" hint="Not quite." show_hints="TRUE"/>
Mass = Force / Momentum
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-14" id="drill-Dimensions-14.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-14-hintarea">question id: drill-Dimensions-14</small>
</div>
:::
7. What kind of thing is $$\sqrt[3]{(\text{4in})(\text{2 ft})(\text{1 mile})}\ ?$$
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="Length" id="drill-Dimensions-15-1" w="5" name="drill-Dimensions-15" hint="Nice." show_hints="TRUE"/>
Length
<input type="radio" class="devoirs-mcq" value="Area " id="drill-Dimensions-15-2" w="87" name="drill-Dimensions-15" hint="Untrue!" show_hints="TRUE"/>
Area
<input type="radio" class="devoirs-mcq" value="Volume " id="drill-Dimensions-15-3" w="87" name="drill-Dimensions-15" hint="You're wrong here." show_hints="TRUE"/>
Volume
<input type="radio" class="devoirs-mcq" value="It is meaningless " id="drill-Dimensions-15-4" w="19" name="drill-Dimensions-15" hint="Nope." show_hints="TRUE"/>
It is meaningless
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-15" id="drill-Dimensions-15.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-15-hintarea">question id: drill-Dimensions-15</small>
</div>
:::
8. What kind of thing is $$\sin(\pi\ \text{seconds})\ ?$$
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="Length " id="drill-Dimensions-16-1" w="32" name="drill-Dimensions-16" hint="Sorry!" show_hints="TRUE"/>
Length
<input type="radio" class="devoirs-mcq" value="1 / Length " id="drill-Dimensions-16-2" w="3" name="drill-Dimensions-16" hint="Sorry!" show_hints="TRUE"/>
1 / Length
<input type="radio" class="devoirs-mcq" value="The number 0 " id="drill-Dimensions-16-3" w="19" name="drill-Dimensions-16" hint="This is wide of the mark." show_hints="TRUE"/>
The number 0
<input type="radio" class="devoirs-mcq" value="It is meaningless" id="drill-Dimensions-16-4" w="14" name="drill-Dimensions-16" hint="right-o The input to the sinusoid (and other trig functions) must be dimensionless" show_hints="TRUE"/>
It is meaningless
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-16" id="drill-Dimensions-16.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-16-hintarea">question id: drill-Dimensions-16</small>
</div>
:::
10. If $t$ is measured in seconds and $A$ is measured in feet, what will be the dimension of $A \sin(2\pi t/P)$ when $P$ is two hours?
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="L" id="drill-Dimensions-17-1" w="16" name="drill-Dimensions-17" hint="Good job!" show_hints="TRUE"/>
L
<input type="radio" class="devoirs-mcq" value="T" id="drill-Dimensions-17-2" w="23" name="drill-Dimensions-17" hint="Remember, the output of $\sin()$ is dimensionless." show_hints="TRUE"/>
T
<input type="radio" class="devoirs-mcq" value="L/T" id="drill-Dimensions-17-3" w="3" name="drill-Dimensions-17" hint="Remember, the output of $\sin()$ is dimensionless." show_hints="TRUE"/>
L/T
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-17" id="drill-Dimensions-17.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-17-hintarea">question id: drill-Dimensions-17</small>
</div>
:::
11. Engineers often prefer to describe sinusoids in terms of their *frequency* $\omega$, writing the function as $\sin(2 \pi \omega t)$, where $t$ is time.<br><br> What is the dimension of $\omega$?
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="T$^{-1}$" id="drill-Dimensions-18-1" w="29" name="drill-Dimensions-18" hint="Nice. A common unit of frequency is Hertz (Hz), sometimes called "cycles per second."" show_hints="TRUE"/>
T$^{-1}$
<input type="radio" class="devoirs-mcq" value="T" id="drill-Dimensions-18-2" w="19" name="drill-Dimensions-18" hint="This would mean the input to $\sin()$ has dimension T$^2$. But $\sin()$ only makes sense for a dimensionless input." show_hints="TRUE"/>
T
<input type="radio" class="devoirs-mcq" value="T$^2$" id="drill-Dimensions-18-3" w="87" name="drill-Dimensions-18" hint="This would mean the input to $\sin()$ has dimension T$^3$. But $\sin()$ only makes sense for a dimensionless input." show_hints="TRUE"/>
T$^2$
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-18" id="drill-Dimensions-18.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-18-hintarea">question id: drill-Dimensions-18</small>
</div>
:::
12. Suppose $t$ is measured in hours and $x$ in yards. What will be the dimension of $P$ in $$\sin(2\pi t x/P)\ ?$$
::: {.cell show_hints='true'}
<p>
<input type="radio" class="devoirs-mcq" value="There is n ... $\sin()$ " id="drill-Dimensions-19-1" w="3" name="drill-Dimensions-19" hint="Untrue!" show_hints="TRUE"/>
There is no such $P$ that will make a valid input to $\sin()$
</p>
<p>
<input type="radio" class="devoirs-mcq" value="L T" id="drill-Dimensions-19-2" w="20" name="drill-Dimensions-19" hint="Yes." show_hints="TRUE"/>
L T
</p>
<p>
<input type="radio" class="devoirs-mcq" value="L / T " id="drill-Dimensions-19-3" w="3" name="drill-Dimensions-19" hint="Not quite." show_hints="TRUE"/>
L / T
</p>
<p>
<input type="radio" class="devoirs-mcq" value="T / L " id="drill-Dimensions-19-4" w="3" name="drill-Dimensions-19" hint="This is wide of the mark." show_hints="TRUE"/>
T / L
</p>
<input type="radio" class="devoirs-mcq" name="drill-Dimensions-19" id="drill-Dimensions-19.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-Dimensions-19-hintarea">question id: drill-Dimensions-19</small>
</div>
:::
:::
::: {#exr-drill-M04-24}
1. In mathematics/trigonometry, what is the value of $\sin(180^\circ)$.
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="0" id="drill-04-24-1-1" w="35" name="drill-04-24-1" hint="Right!" show_hints="TRUE"/>
0
<input type="radio" class="devoirs-mcq" value="$\sqrt{2}$" id="drill-04-24-1-2" w="3" name="drill-04-24-1" hint="Impossible. The output of the sinusoid is always within the range -1 to 1. $\sqrt(2) \gt 1$." show_hints="TRUE"/>
$\sqrt{2}$
<input type="radio" class="devoirs-mcq" value="1" id="drill-04-24-1-3" w="3" name="drill-04-24-1" hint="Better luck next time." show_hints="TRUE"/>
1
<input type="radio" class="devoirs-mcq" value="-1" id="drill-04-24-1-4" w="7" name="drill-04-24-1" hint="Not quite." show_hints="TRUE"/>
-1
<input type="radio" class="devoirs-mcq" name="drill-04-24-1" id="drill-04-24-1.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-04-24-1-hintarea">question id: drill-04-24-1</small>
</div>
:::
:::
2. In R/mosaic, what is the value of `sin(180)`?
::: {.cell show_hints='true' inline='true'}
<input type="radio" class="devoirs-mcq" value="-0.80" id="drill-M04-24-2-1" w="8" name="drill-M04-24-2" hint="Correct The argument to trigonometric functions is interpreted by R to be in **radians**." show_hints="TRUE"/>
-0.80
<input type="radio" class="devoirs-mcq" value="0" id="drill-M04-24-2-2" w="19" name="drill-M04-24-2" hint="This would be right if sine interpreted its argument in *degrees*. But arguments to the trigonometric functions in R and most other languages are in **radians**." $\sin(\pi) = 0$." show_hints="TRUE"/>
0
<input type="radio" class="devoirs-mcq" value="0.80" id="drill-M04-24-2-3" w="3" name="drill-M04-24-2" hint="You've got the sign incorrect." show_hints="TRUE"/>
0.80
<input type="radio" class="devoirs-mcq" value="1" id="drill-M04-24-2-4" w="3" name="drill-M04-24-2" hint="The argument to `sin()` is in radians." show_hints="TRUE"/>
1
<input type="radio" class="devoirs-mcq" name="drill-M04-24-2" id="drill-M04-24-2.null" style="display: none;" w="skipped" checked=""/>
<div class="hintarea">
<small style="color: grey;" id="drill-M04-24-2-hintarea">question id: drill-M04-24-2</small>
</div>
:::
:::
<span id="devoirs-docID" style="display: none;">15-review.rmarkdown</span>
<button onclick="devoirsSubmit()">Collect your answers</button>
<div id="devoirs_summary">No answers yet collected</div>
::: {.cell}
::: {.cell-output-display}
```{=html}
<script type='text/javascript'>
console.log("In devoirs.js")
function devoirsCollectEssays() {
var essay_answers = [];
var items = document.getElementsByClassName("devoirs-text");
for (i = 0; i < items.length; i++) {
//console.log("text entry" + i + "being handled");
essay_answers[i] = {itemid: items[i].id, contents: items[i].value}
}
return essay_answers;
}
function devoirsGetDocID() {
return document.getElementById("devoirs-docID").innerHTML
}
function devoirsCollectMC() {
let mc_answers = [] // Hold the information
var ele = document.getElementsByClassName("devoirs-mcq");
var count = 0;
for (i = 0; i < ele.length; i++) {
if (ele[i].checked) {
//console.log("Entering conditional.");
let checked_one = ele[i];
mc_answers[count++] = {itemid: checked_one.id, w: checked_one.getAttribute("w"), contents: checked_one.text};
}
}
return mc_answers;
}
console.log("About to define WebR")
function devoirsCollectWebR() {
var chunk_contents = []; // placeholder for collecting webr items
if (typeof qwebrCellDetails == "undefined") {
// There aren't any webr chunks
return chunk_contents;
}
var chunks = qwebrCellDetails;
for (i = 0; i < chunks.length; i++) {
chunk_contents[i] = {itemid: chunks[i].options["label"], contents: chunks[i].code};
}
return chunk_contents;
}
console.log("About to define devoirsSubmit")
function devoirsSubmit() {
console.log("About to collect history")
// check if there is any sign of a webr entry
// If not, don't try to collect webr entries
if (typeof qwebrRCommandHistory === 'undefined') {
items = {docid: devoirsGetDocID(), MC: devoirsCollectMC(), Essays: devoirsCollectEssays(), WebR: {}, R: {}}
} else {
console.log("Getting R commands.")
var Rhistory = qwebrRCommandHistory.map((x) => x.replace(/Ran code in (.*) at (.*[AP]M).{5}(.*)/, "[chunk: $1, time: $2, code: $3]"))
items = {docid: devoirsGetDocID(), MC: devoirsCollectMC(), Essays: devoirsCollectEssays(), WebR: devoirsCollectWebR(), R: Rhistory}
}
navigator.clipboard.writeText(JSON.stringify(items));
// summarize what's being collected
var my_summary = "Answers copied to clipboard. Fixed choice: " + items.MC.length + " Essays: " + items.Essays.length + " WebR chunks: " + items.WebR.length
document.getElementById("devoirs_summary").innerHTML = my_summary;
}
console.log("Read devoirsSubmit()")
// Hint handling in Multiple choice
// Still have to add an on/off switch from options
function devoirs_setup_hintarea() {
answers = document.getElementsByClassName("devoirs-mcq")
for (i=0; i<answers.length; i++) answers[i].addEventListener('click', function(e){document.getElementById(e.target.name + "-hintarea").innerHTML = e.target.getAttribute("hint")})
}
window.addEventListener("load", function() {
answers = document.getElementsByClassName("devoirs-mcq")
for (i=0; i<answers.length; i++) {
if (answers[i].getAttribute("show_hints") == "TRUE") {
answers[i].addEventListener('click', function(e){
document.getElementById(e.target.name + "-hintarea").innerText = e.target.getAttribute("hint")
})
}
}
})
console.log("Added hint summary.")
</script>
::: :::