What is the sum of two complementary angles in degrees? in radians?

Which expression shows the prime factorization of 100?

$$A. 2 ^ { 2 } \times 5 ^ { 2 }$$

$$B. 10 \times 10$$

$$C. 10 ^ { 10 }$$

$$D. 2 \times 5 \times 10$$

Suppose an automobile has 2000 J of kinetic energy. When it moves at twice the speed, what will be its kinetic energy? What’s its kinetic energy at three times the speed?

The integral

$$\vec{a}=\int_Sd\vec{a}$$

is sometimes called the vector area of the surface S.If S happens to be flat, then $|\vec{a}|$ is the ordinary (scalar) area, obviously. Find the vector area of a hemispherical bowl of radius R. Show that $\vec{a}=0$ for any closed surface. Show that $\vec{a}$ is the same for all surfaces sharing the same boundary. Show that

$$\vec{a}=\dfrac{1}{2}\oint \vec{r}\times d\vec{l}$$

where the integral is around the boundary line. [Hint: One way to do it is to draw the cone subtended by the loop at the origin. Divide the conical surface up into infitesimal triangular wedges, each with vertex at the origin and opposite side $d\vec{l}$, and exploit the geometrical interpretation of the cross product.] Show that

$$\oint(\vec{c}\cdot\vec{r})d\vec{l}=\vec{a}\times\vec{c}$$

for any constant vector $\vec{c}$.

Tell whether the function represents exponential growth or exponential decay. Then graph the function.

$$y = 0.5 e ^ { x }$$

How much more power is required to pedal a bicycle at 15 mph into a 20-mph headwind than at 15 mph through still air? Assume a frontal area of $3.9 \mathrm{ft}^{2}$ and a drag coefficient of $C_{D}=0.88$.

To find the polar equation of the orbit of the planet and the perihelion and aphelion distances. Mars $a \approx 1.4164 \times 10^{8}$ miles, $e \approx 0.0934$

Scientist can make plans to photograph a solar eclipse because most astronomical events are (1) cyclic and predictable (2) cyclic and unpredictable (3) random and predictable (4) random and unpredictable

Make a table of values that includes the vertex.

$$f(x)=-3x^2+5$$

Ms. Chen's fifth-grade class held bake sales on Tuesday and Thursday during lunch to raise money to buy science equipment for the classroom.

They raised $20.55 more on Thursday than on Tuesday. Use this information to fill in the data that are missing from the table.

$$\begin{array}{|c|c|c|c|c|} \hline {} & \text{1st lunch}& \text{2nd lunch}& \text{3rd lunch}& \text{TOTAL}\\ \hline \text{Tuesday} & \$21.45 & {} & \$25.90 & {}\\ \hline \text{Thursday} & {} & \$26.35 & {} & \$86.70\\ \hline \text{TOTAL} & \$50.55 & {} & \$57.15 & {} \\ \hline \end{array}$$

How many of the 32 households, in the graph on page 223, own only two TVs? Why is that number noteworthy?

Graph the function and its parent function. Then describe the transformation. f(x) = -|x| - 3

Consider a cylindrical cavity of diameter D=100mm and depth L=50 mm whose sidewall and bottom are diffuse and gray with an emissivity of 0.6 and are at a uniform temperature of 1500 K. The top of the cavity is open and exposed to surroundings that are large and at 300 K. (a) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as one surface $\left(q_{A}\right)$. (b) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as two separate surfaces $\left(q_{B}\right)$. (c) Plot the percentage difference between $q_{A}$ and $q_{B}$ as a function of L over the range $5 \mathrm{mm} \leq L \leq 100 \mathrm{mm}$.

Find a set of parametric equations for the line or conic. Circle: center: (−2, −5); radius: 7