a. What is the formula used to calculate the acceleration of an object moving in a straight line? b. A cyclist's speed changes from 0 m/s to 15 m/s in 10 seconds. What is the cyclist's average acceleration?

a. Identifying What formula do you use to calculate the acceleration of an object moving in a straight line? b. Calculating The velocity of a cyclist moving in a straight line changes from 0 m/s to 15 m/s in 10 seconds. What is the cyclist's acceleration?

Show that a. $\sec ^ { - 1 } x \neq \frac { 1 } { \cos ^ { - 1 } x }$ b. $\sec ^ { - 1 } x = \cos ^ { - 1 } \frac { 1 } { x }$

a. What is a formula unit? b. What are the components of one formula unit of

$$\mathrm { CaF } _ { 2 } ?$$

Two balloons of different mass hang from strings near each other. You charge them about the same amount by rubbing each balloon with wool. Draw a force diagram for each of the balloons. Compare the angles of the threads with the vertical. How do your answers depend on whether the balloons have the same or different magnitude charge?

Determine whether the statement is true or false. If $T:R^2\to R^2$ is a linear transformation, then det$[T(u)$ $T(v)]$= det$[u$ $v]$ for any vectors $u$ and $v$ in $R^2$.

Let a, b, c, and d be positive. Prove the following properties of the proportion

$$\frac { a } { b } = \frac { c } { d }$$

.

$$\frac { a - b } { b } = \frac { c - d } { d }$$

(Hint: Add -1 to each side of

$$\frac { a } { b } = \frac { c } { d }$$

.)

In Exercise, use Formula $\frac { d y } { d x } = \lim _ { \Delta x \rightarrow 0 } \frac { \Delta y } { \Delta x } = \lim _ { \Delta x \rightarrow 0 } \frac { f ( x + \Delta x ) - f ( x ) } { \Delta x }$ to find $d y / d x$

$$y = \frac { 1 } { \sqrt { x } }$$

Consider the following steady, three-dimensional velocity field: $egin{aligned} ec{V} &=(u, v, w) \ &=(3.0+2.0 x-y) ec{i}+(2.0 x-2.0 y) ec{j}+(0.5 x y) ec{k} \end{aligned}$. Calculate the vorticity vector as a function of space (x, y, z).

Explain what is wrong with the statement. If $\lim _{n \rightarrow \infty}\left|C_{n+1} / C_{n}\right|=0,$ then the radius of convergence for $\sum C_{n} x^{n}$ is 0.

In allocating congressional seats, how does Hamilton’s method choose some states over others for preferential treatment? Explain how this is avoided in Jefferson’s and Adams’s methods.

A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence did the pollsters use?

Figure JKLM has as its vertices the points J(4, 4), K(2, 1), L(-3, 2), and M(-1, 5). Find the slope. $\overline{M J}$

Determine whether the statements that follow are true or false, and justify your answer: rank

$$\begin{bmatrix} 2&2&2\\2&2&2\\2&2&2\end{bmatrix}=2$$