A single force acts on a $3.0 \mathrm{~kg}$ body that moves along an $x$ axis. Figure $7.36$ gives the velocity $v$ versus time $t$ due to the motion. What is the work done on the body (sign included) for the time intervals (a) 0 to $2.0 \mathrm{~ms}$, (b) $2.0$ to $5.0 \mathrm{~ms}$, (c) $5.0$ to $8.0 \mathrm{~ms}$, and (d) $8.0$ to $11 \mathrm{~ms}$ ? What is the average power supplied to the body (sign included) for the time intervals (e) 0 to $2.0 \mathrm{~ms}$, (f) $2.0$ to $5.0 \mathrm{~ms}$, (g) $5.0$ to $8.0 \mathrm{~ms}$, and (h) $8.0$ to $11 \mathrm{~ms}$ ?

Suppose that $f(x)=x^{2}$ and g(x) = |x|. Then the compositions $(f \circ g)(x)=|x|^{2}=x^{2}$ and $(g \circ f)(x)=\left|x^{2}\right|=x^{2}$ are both differentiable at x = 0 even though g itself is not differentiable at x = 0. Does this contradict the Chain Rule? Explain.

In this exercise, let $\mathcal{D}$ be the annular region

$$-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}, \quad a \leq r \leq b$$

where b>a>0. Assume that $\mathcal{D}$ has a uniform charge distribution of $\rho$ coulombs per square meter. Let F be the net force on a charged particle of charge Q coulombs located at the origin (by symmetry, F acts along the x-axis).

(a) Argue as in the previous exercise to show that

$$F=k \rho Q \int_{\theta=-\pi / 2}^{\pi / 2} \int_{r=a}^b\left(\frac{\cos \theta}{r^2}\right) r d r d \theta$$

(b) Compute F.

Write an equation for the ellipse with each set of characteristics. foci (1, 2), (9, 2); length of minor axis equals 6

Write a program to play a variation of the game, as follows: Roll two dice. Each die has six faces representing values 1, 2, . . ., and 6, respectively. Check the sum of the two dice. If the sum is 2, 3, or 12 (called craps), you lose; if the sum is 7 or 11 (called natural), you win; if the sum is another value (i.e., 4, 5, 6, 8, 9, or 10), a point is established. Continue to roll the dice until either a 7 or the same point value is rolled. If 7 is rolled, you lose. Otherwise, you win. Your program acts as a single player.

Three concentric spherical shells r-1, r=2, and r=3 m, respectively, have charge distributions 2,-4, and $5 \mu \mathrm{C} / \mathrm{m}^2$.

(a) Calculate the flux through $r=1.5 \mathrm{~m}$ and $r=2.5 \mathrm{~m}$.

(b) Find $\mathbf{D}$ at r=0.5, r=2.5, and $r=3.5 \mathrm{~m}$.

Solve each matrix equation for X, where

$$A = \left[ \begin{array} { r r r } { 2 } & { 3 } & { - 1 } \\ { 1 } & { - 2 } & { 4 } \end{array} \right]$$

and

$$B = \left[ \begin{array} { r r r } { - 2 } & { 1 } & { 0 } \\ { 2 } & { 3 } & { 4 } \end{array} \right]$$

2X - A = B

Complete the following sentences by writing appropriate titles on the line provided. Use correct capitalization.

Example 1. Last weekend, I read $\underline{\color{#c34632}\text{“To Build a Fire”}}$ .

The next production of the drama club will be _____________________________________________ .

What is the posterior lobe of the cerebrum called?

Find the volume of the following. If necessary, round to the nearest tenth. }

Triangular prism: base of triangle 22 yards, height of triangle 14 yards, height of prism 30 yar

Which of the following is the most correct interpretation of the figure?

A. Energy from food sources can be used directly for performing cellular work.

B. ADP + Pi are a set of molecules that store energy.

C. ATP is a molecule that acts as an intermediary to store energy for cellular work.

D. Pi acts as a shuttle molecule to move energy from ATP to ADP.

When hydrazine is dissolved in water it acts like a base. $\mathrm{N}_{2} \mathrm{H}_{4}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{N}_{2} \mathrm{H}_{5}^{+}(a q)+\mathrm{OH}^{-}(a q)$ $K_{\mathrm{b}_{1}}=8.5 \times 10^{-7}$, $\mathrm{N}_{2} \mathrm{H}_{5}^{+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{N}_{2} \mathrm{H}_{6}^{2+}(a q)+\mathrm{OH}^{-}(a q)$ $K_{\mathrm{b}_{2}}=8.9 \times 10^{-16}$ a. Calculate the $K_b$ for the overall reaction of hydrazine forming $\mathrm{N}_{2} \mathrm{H}_{6}^{2+}$. b. Calculate $K_{a_1}$, for $N_2H_5 ^+$. c. Calculate the concentration of hydrazine and both cations in a solution buffered at a pH of 8.5 for a solution that was made by dissolving 0.012 mo! of hydra zine in 1 L of water.

Use the Chain Rule to find $d z / d t$ or $d w / d t$.

$$w=x e^{y / z}, \quad x=t^2, \quad y=1-t, \quad z=1+2 t$$

Sketch the ellipse, and label the foci, vertices, and ends of the minor axis.

$$9x^2+4y^2-18x+24y+9=0$$