Use the following steps. Choose a number. Multiply by 5. Add 2. Multiply by 3. Subtract 8. a. Choose the number 4. What ending number did you get?
b. Choose the variable $x$. What ending expression did you get?

Determine whether each argument is valid or invalid. All A are B, no C are B, and all D are C. Thus , no A are D.

Sparks will occur between the plates of an air-filled capacitor at a lower voltage when the air is humid than when it is dry. Discuss why, considering the polar character of water molecules

In each part, is the given function continuous on the interval

$$[ 0 , \pi / 2 )$$

? (a) sin x, (b) cos x, (c) tan x, (d) csc x

Differentiate the series

$$E(x)=\sum_{n=0}^{\infty} \frac{x^{n}}{n !}$$

term-by-term to show that E(x) is equal to its derivative.

You are an engineer in an electric-generation station. You know that the flames in the boiler reach a temperature of 1200 K and that cooling water at 300 K is available from a nearby river. You also know that the metalurgical temperature limit for the blades in the turbine is 1000 K before they will incur excessive creep. What is the maximum efficiency for this plant?

Complete statement by writing the correct word or words. In a(n) _____ reaction, a compound breaks down into two or more products.

Find the unit tangent vector for the following parameterized curves. $\mathbf { r } ( t ) = 6 \mathbf { i } + \cos ( 3 t ) \mathbf { j } + 3 \sin ( 4 t ) \mathbf { k } , \quad 0 \leq t < 2 \pi$

The temperature at 6 A.M. is

$$- 10 ^ { \circ }$$

Fahrenheit. During the day, the temperature rises

$$6 ^ { \circ } \mathrm { F }$$

, drops

$$3 ^ { \circ } \mathrm { F }$$

, and drops

$$8 ^ { \circ } \mathrm { F }$$

. Write an integer to represent each value. What is the temperature after these changes?

Rationalize the numerator:

$$\frac { \sqrt { x + 3 } - \sqrt { x } } { 3 }.$$

Use the dot product to find the angle between u and v. u=2i-j, v=i+3j

solve the system graphically. { 2x - y + 3 = 0 , x^2 + y^2 - 4x = 0

Write the word or phrase from the list that completes the sentence correctly. A person with a condition that limits their normal daily activities for a limited time is said to have a(n) _____. aggressive driving, carbon monoxide, central vision, chronic illness, color blindness, depth perception, disability, emotion, field of vision, fringe vision, glare recovery time, glare resistance, night blindness, peripheral vision, permanent disability, road rage, speed smear, temporary disability, tunnel vision, visual acuity.

Solve each inequality and graph the solution set.

$$5 - 3 x \geq - 1$$