You can access this page in I-Learn. It's the third bullet (Class Activities) on the home page.
Pre-Class Chatter
Feel free to turn on your mic and chat with people, or use the zoom chat if you prefer. You can also use Jamboards to chat with your group members.
9:00 AM Jamboard Links
| G1 | G2 | G3 | G4 | G5 | G6 | G7 |
|
|
|
|
|
|
|
12:45 PM Jamboard Links
| G1 | G2 | G3 | G4 | G5 | G6 |
|
|
|
|
|
|
- Alternate Possible Theme Song : The Power of Yet
Rapid Recall
- Compute the derivative of the following functions:
- $f(x) = \pi^2$
- $\displaystyle g(x) = \frac{22}{7} x $
- $p(x) = x^3-2x^2+x+5$
Answer:
- $\displaystyle \frac{df}{dx} = 0$
- $\displaystyle g'(x) = \frac{22}{7}$
- $p'(x) = 3x^2-4x+1$
Where can I go for practice if my derivative skills are lacking? Thomas's calculus sections 3.3-3.6 are a great place to practice. You can use any calc text, if you had calculus at another school.
- If a rover's motion on flat ground is described by $(x,y)=(3,4)t+(-2,5)$, what is its speed? Assume $x$ and $y$ are measured in meters and $t$ is given in minutes. (Hint: the rover's speed is constant in this situation.)
Answer:
When $t=0$, $(x,y) = (-2,5)$. When $t=1$, it is at $(1,9)$, so its position has changed by $\Delta x = 3$ and $\Delta y=4$. This means the rover has moved a total of $\sqrt{3^2+4^2}=5$ meters, so its speed is 5 meters/minute.
- Using the vectors on the screen, draw $\vec u+\vec v$ and $\vec u-\vec v$.
Answer:
We'll discuss this one.
- Give the component form of a vector of length 2 that is parallel to $\left<3,4\right>$.
Answer:
A unit vector is $\frac{1}{5}(3,4)$, so the desired vector is twice this, namely $$\frac{2}{5}(3,4) = \left(\frac{6}{5},\frac{8}{5}\right).$$
- Draw and shade the region in space satisfying $0\leq z\leq 5$ with $x=2$.
Answer:
The region is an infinitely long sheet with $0\leq z\leq 5$, located 2 units out on $x$-axis, with the $y$ value taking on all possible values. The most common error here is to not let $y$ take on all possible values, in which case you'll end up with a short line segment at $y=0$ and $x=2$ running from 0 to 5 in the $z$ direction.
Group Problems
9:00 AM Jamboard Links
| G1 | G2 | G3 | G4 | G5 | G6 | G7 |
|
|
|
|
|
|
|
12:45 PM Jamboard Links
| G1 | G2 | G3 | G4 | G5 | G6 |
|
|
|
|
|
|
Remember to take turns annotating on the screen, and use the Jamboards to show key bits of your work.
- Give the component form of a vector that points from $(1,2,3)$ to $(-2,4,9)$.
- Give a vector equation of the line that passes through the point $(1,2,3)$ and $(-2,4,9)$ (all distances are in meters).
- An object starts at $P=(1,2,3)$ and each unit of time its displacement is $\vec v=(-4,5,1)$. Give an equation for the position $(x,y,z)$ at any time $t$.
- What is the speed of an object that follows the path describe above?
- Use the law of cosines ($c^2=a^2+b^2-2ab\cos\theta$) to find the angle between the vectors $(-2,1)$ and $(1,3)$.
- Use the law of cosines to find the angle between the vectors $(1,2,3)$ and $(-2,4,9)$.
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |