Evaluate the expressions. a. 30 div 2 b. 30 mod 2

Fill in the blanks. A vector that has a magnitude of 1 is called a ________ ________ .

True or False. The graph of a rational function may intersect a horizontal asymptote.

Simplify. Check your work. $\frac { - ( r - 12 ) } { \left( r ^ { 2 } - 24 r + 144 \right) }$

If ${x < 0}$, use the substitution

$$\begin{gather*} t = \ln(-x) \end{gather*}$$

to show that the general solutions of the Cauchy–Euler equation (i) in ${x < 0}$ are

$$\begin{gather*} y = c_{1} e^{\lambda_{1}t} + c_{2} e^{\lambda_{2}t} = -c_{1}x^{\lambda_{1}} - c_{2}x^{\lambda_{2}} , \end{gather*}$$

if $\lambda_{1}$ and $\lambda_{2}$ are real and $\lambda_{1}$ $\neq$ $\lambda_{1}$,

$$\begin{gather*} y = c_{1} e^{\lambda_{1}t} + c_{2} e^{\lambda_{1}t} = -c_{1}x^{\lambda_{1}} - c_{2}x^{\lambda_{1}} \ \ln (-x), \end{gather*}$$

if $\lambda_{1}$ = $\lambda_{2}$,

$$\begin{align*} y & = e^{\mu t} [c_{1} \cos(vt) + c_{2} \sin(vt)] \\ & = -x^\mu [c_{1} \cos(v \ln (-x)) + c2 sin(v \ln (-x))] \end{align*}$$

if $\lambda_{1}$ = $\mu$ + iv and $\lambda_{2}$ = $\mu$ - iv.

If an average American composted 1.5 pounds of trash every day, how many people would it take to compost 114 pounds of trash in a day? Define a variable and write an equation. Solve the equation and check your solution.

A city has 7,204 recycle bins. The city gives half of the recycle bins to its citizens. The rest of the recycle bins are divided into 23 equal groups for city parks. How many recycle bins are left over?

For a recent period of 100 years, there were 93 major earthquakes (at least 6.0 on the Richter scale) in the world (based on data from the World Almanac and Book of Facts). Assuming that the Poisson distribution is a suitable model, find the mean number of major earthquakes per year, then find the probability that the number of earthquakes in a randomly selected year is 7.

Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables.

$$\frac { \partial f } { \partial \theta } ; f ( x , y , z ) = x y - z ^ { 2 } , x = r \cos \theta , y = \cos ^ { 2 } \theta,$$

z = r

Contesta. ¿Te vistes antes o después de desayunar?

25m=25

Evaluate the product. Express the result in scientific notation.

$$(7.5 \times 10^6)(2.5 \times 10^{-2})$$

For each of the values of n and d given, find integers q and r such that n=dq+r and

$$0 \leq r < d$$

. n=3, d=11

Which situation is a better match with the word "exploit"? A or B?