Solve the equation. Check your solution. 44 = t - 72

Evaluate the limit of the following sequences or state that the limit does not exist.

$$a _ { n } = \cos \left( 0.99 ^ { n } \right) + \frac { 7 ^ { n } + 9 ^ { n } } { 63 ^ { n } }$$

Describe why it is important to take measurements that are both accurate and precise:

Evaluate the expression. -10 + (20)

What multiple of the energy needed to escape from Earth gives the energy needed to escape from (a) a moon of mass

$$1.472 \times 10 ^ { 23 } \mathrm { kg }$$

and radius

$$3.480 \times 10 ^ { 6 } \mathrm { m }$$

and (b) Jupiter?

By graphing $y = ( 1 + 1 / x ) ^ { x },$ estimate $\lim _ { x \rightarrow \infty } ( 1 + 1 / x ) ^ { x }.$ You should recognize the answer you get.

Find the limits.

$$\lim _ { x \rightarrow \pi ^ { + } } \frac { \sin x } { x - \pi }$$

You are given information about a network. Choose one of the following three options: (A) the network is definitely a tree; (B) the network is definitely not a tree; (C) the network may or may not be a tree (more information is needed). Accompany your answer with a brief explanation for your choice. The network has five vertices, no loops, and no multiple edges, and every vertex has degree 2.

Does Newton’s second law hold true for an observer in a van as it speeds up, slows down, or rounds a corner? Explain.

In an hour, David can wash 2 cars or mow 1 lawn, and Ron can wash 3 cars or mow 1 lawn. Who has the absolute advantage in car washing, and who has the absolute advantage in lawn mowing? a. David in washing, Ron in mowing. b. Ron in washing, David in mowing. c. David in washing, neither in mowing. d. Ron in washing, neither in mowing.

A football team gained 15 yards on the first play and lost 8 yards on the second. Use + and - numbers to show the team's progress.

Find an equation of the circle with center (6, -3) that passes through (-4, 1).

Use the approximate operation count $2 n ^ { 3 } / 3$ for Gaussian elimination to estimate how much longer it takes to solve n equations in n unknowns if n is tripled.

In your own words. define the following terms. kinetic energy.