The amounts y (in millions of dollars) the U.S. Department of Energy spent for research and development from 2005 through 2010 can be approximated by the model

$$y = 56.77t^2-366.8t+8916$$

, 5 ≤ t ≤ 10 where t represents the year, with t = 5 corresponding to 2005. Use a graphing utility to graph the model.

Simplify, then use a calculator to check your answer: $-(-2)^{6}$

For $f(x)=4x$ and $g(x)=4x^2+6$, find the following expressions. (a) (f∘g)(4) (b) (g∘f)(2) (c) (f∘f)(1) (d) (g∘g)(0)

Two angles of a triangle each measure

$$45 ^ { \circ }$$

. Make a rough sketch of the triangle.

In Exercise, solve for $x$.

$$\left| \frac { x - 3 } { x + 4 } \right| = 5$$

Choose the correct letter. What is the solution of -(-5 - 6x) = 4(5x + 3)? F. -2 G. -1/2 H. 1/2 I. 2

18. An architect is hired to design a skyscraper in the Indonesian city of Jakarta, which is near the Ring of Fire. The architect must follow special building cades that the city has writ- ten. What might those codes be for and why are they important in Jakarta?

Why did the U.S. government impose regulations on industrial and food production during the war? What was the impact of the regulation for the Allies?

Find the errors in the following calculations. Explain why you think the error occurs and how you would help someone see the error of his or her thinking. a.

$$\log (12+17)=\log 12+\log 17$$

b.

$$\log 0=0$$

c.

$$\log 5^{3}=\log 15$$

d.

$$\log (7 \times 5)=(\log 7)(\log 5)$$

e.

$$\frac{\log 20}{\log 2}=\log {10}$$

Why do you often have to round off answers to math problems that involve measured quantities?

find the sum of the finite geometric sequence. 4∑i=1 (1/2)^i

The number of times x an adult human breathes per minute when at rest has a probability distribution that is approximately normal, with the mean equal to 16 and the standard deviation equal to 4. If a person is selected at random and the number x of breaths per minute while at rest is recorded, what is the probability that x will exceed 22?

Graph the polynomial function.

$$f(x)=x^4-2$$

A cylindrical volume of radius a is filled with charge of uniform density $\rho$. We want to know the potential energy per unit length of this cylinder of charge, that is, the work done per unit length in assembling it. Calculate this by building up the cylinder layer by layer, making use of the fact that the field outside a cylindrical distribution of charge is the same as if all the charge were located on the axis. You will find that the energy per unit length is infinite if the charges are brought in from infinity, so instead assume that they are initially distributed uniformly over a hollow cylinder with large radius R. Write your answer in terms of the charge per unit length of the cylinder, which is $\lambda=\rho \pi a^{2}$.