Sketch the graph of the height of a particle against time if velocity is positive and acceleration is negative.

$\angle A B D$ and $\angle B D C$ are complementary. Find the measures of both angles. $\mathrm { m } \angle A B D = ( 5 y + 1 ) ^ { \circ } , \mathrm { m } \angle B D C = ( 3 y - 7 ) ^ { \circ }$

Raul is explaining how he and his family are preparing for his siter´s birthday party. Read his description and answer the questions that follow in complete sentences.
¿Con que decora Raul?

What happens to the speaker's mother in "A Voice"?

Two orthogonal vectors $u$ and $v$ are given. Compute the quantities $||u||^2$, $||v||^2$, and $||u+v||^2$. Use your results to illustrate the Pythagorean theorem.

$$\begin{equation*} u=\begin{bmatrix}1\\3\\2\end{bmatrix}\text{ and } v=\begin{bmatrix}-1\\1\\-1\end{bmatrix} \end{equation*}$$

In April 2015 in the US, there was one birth every 8 seconds, one death every 12 seconds, and one new international migrant every 32 seconds. (a) Let f(t) be the population of the US, where t is time in seconds measured from the start of April 2015. Find f'(0). Give units. (b) To the nearest second, how long did it take for the US population to add one person in April 2015?

Suppose R is the region bounded by y=f(x) and y=g(x) on the interval [a, b], where f(x)

$$\geq g ( x ) \geq 0$$

. How is this formula changed if the line

$$y=y_0$$

lies above R?

In living things, energy is stored in the molecule adenosine triphosphate, called ATP for short. ATP is said to act like a battery, storing energy when it is not needed and instantly releasing energy when it is required. Investigate how energy is stored and the role of ATP in biological processes. Write a report including at least three references.

Graph the relation {(-2, 2), (-1, 1), (0, 1), (1, 1), (2, 0)}. Is the relation a function?

Sketch the graph of a function whose first derivative is everywhere negative and whose second derivative is positive for some x-values and negative for other x-values.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I have two points to work with, I use the formula for slope

$$\frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } }$$

to find the slope of the tangent line to the graph of a function

$$y = f ( x ) \text { at } ( a , f ( a ) ).$$

The cost, C (in dollars), to produce g gallons of a chemical can be expressed as C = f(g). Using units, explain the meaning of the following statements in terms of the chemical: (a) f(200) = 1300 (b) f'(200) = 6

Consider the following reactions: $\mathrm { H } _ { 2 } ( g ) + \mathrm { I } _ { 2 } ( g ) \rightleftharpoons 2 \mathrm { HI } ( g ) \quad \text { and } \quad \mathrm { H } _ { 2 } ( g ) + \mathrm { I } _ { 2 } ( s ) \rightleftharpoons 2 \mathrm { HI } ( g )$ List two property differences between these two reactions that relate to equilibrium.

Graph the functions described in parts (a)-(d). (a) First and second derivatives everywhere positive. (b) Second derivative everywhere negative; first derivative everywhere positive. (c) Second derivative everywhere positive; first derivative everywhere negative. (d) First and second derivatives everywhere negative.