Which is the complete factorization of

$$24 x ^ { 3 } - 12 x ^ { 2 }$$

? (A)

$$6 \left( 4 x ^ { 3 } - 2 x ^ { 2 } \right)$$

, (B)

$$12 \left( 2 x ^ { 3 } - x ^ { 2 } \right)$$

, (C)

$$12 x \left( 2 x ^ { 2 } - x \right)$$

, (D)

$$12 x ^ { 2 } ( 2 x - 1 )$$

Solve each system of inequalities by graphing.

$$\left. \begin{array} { l } { 6 x ^ { 2 } + 9 ( y - 2 ) ^ { 2 } \leq 36 } \\ { x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 25 } \end{array} \right.$$

What is the formula for the surface area of a right circular cylinder, $S=2 \pi r h+2 \pi r^{2},$ solved for h? $A. h=\frac{S}{4 \pi r}\ B. h=\frac{s}{2 \pi r^{2}}\ C. h=\frac{S}{2 \pi r}-r\ D. h=r-\frac{S}{2 \pi r}$

Find the area under the curve y=f(x) over the stated interval.

$$f ( x ) = \frac { 1 } { x } ; [ 1,5 ]$$

Use a graphing utility to graph the function. Find the domain and range of the function. $f(x)=\sqrt{16-x^{2}}$

A 500.0 kg module is attached to a 400.0 kg shuttle craft, which moves at 1000 m/s relative to the stationary main spaceship. Then a small explosion sends the module backward with speed 100.0 m/s relative to the new speed of the shuttle craft. As measured by someone on the main spaceship, by what fraction did the kinetic energy of the module and shuttle craft increase because of the explosion?

To receive a B in a course, you must have an average of at least 80% but less than 90% on five exams. Your grades on the first four exams were 95%, 79%, 91 %, and 86%. What range of grades on the fifth exam will result in a B for the course?

Graph and compare the two functions.

$$f ( x ) = | x - 1 | + 2 ; g ( x ) = 4 | x - 1 | + 8$$

Identify the following term or individuals and explain their significance. Theodore Roosevelt

A model airplane is built with a wing span of 23 inches. The actual wing span is 92 feet. Find the scale.

The position, P(d), of the Sun at sunset, in degrees north or south of due west, depends on the latitude and the day of the year, d. For a specific latitude, the position in terms of the day of the year can be modelled by the function

$$P ( d ) = 28 \sin \left( \frac { 360 } { 365 } d - 81 \right) ^ { \circ }$$

. a) Graph the function using a graphing calculator and adjust the WINDOW settings as required. b) What is the period of the function, and what does it represent in this situation? c) What is the equation of the axis of the function, and what does it represent in this situation? d) What is the amplitude of the function, and what does it represent in this situation? e) Determine the range of the function. f) What is the angle of sunset on February 15?

Simplify the factorial expression. $\frac{2 n !}{(n+1) !}$

Let f(x)=

$$x^8$$

-2x+3; find

$$\lim _ { w \rightarrow 2 } \frac { f ^ { \prime } ( w ) - f ^ { \prime } ( 2 ) } { w - 2 }$$

Write the quotient in scientific notation: (4 × 10^12)/(8 × 10^4)