Simplify the expression.

$$\left(\frac{x^{2}}{y^{3}}\right)^{-5}$$

Use a calculator to rewrite the rational number as the ratio of two integers. $−7.5$

Find the solution for the equation. $6 b = 54$

The velocity of an ant running along the edge of a shelf is modeled by the function

$$v ( t ) = \left\{ \begin{array} { r l } { 5 t , } & { 0 \leq t < 1 } \\ { 6 \sqrt { t } - \frac { 1 } { t } , } & { 1 \leq t \leq 2 } \end{array} \right.$$

where t is in seconds and v is in centimeters per second. Estimate the time at which the ant is 4 cm from its starting position.

Consider a simple ideal Rankine cycle with fixed turbine inlet conditions. What is the effect of lowering the condenser pressure on

$$\begin{array}{ll} \text{Pump work input:} & \text{(a) increases, (b) decreases, (c) remains the same}\\ \text{Turbine work output:} & \text{(a) increases, (b) decreases, (c) remains the same}\\ \text{Heat supplied:} & \text{(a) increases, (b) decreases, (c) remains the same}\\ \text{Cycle efficiency:} & \text{(a) increases, (b) decreases, (c) remains the same}\\ \text{Moisture content at} & \text{(a) increases, (b) decreases, (c) remains the same}\\ \text{turbine exit:} & \text{ }\\ \end{array}$$

Simplify each expression. Use properties and combine like terms. 4c + 5cd - 4 (c + d)

Determine whether the number is divisible by each of the following numbers: 2, 3, 4, 5, 6, 8, 9, 10, and 12. If you are using a calculator, explain the divisibility shown by your calculator using one of the rules of divisibility.

$$238,632$$

What is the damping factor of the function $f(x)=e^{2 x} \sin x ?$

What is the sum of two complementary angles in degrees? in radians?

Find the exact value of each expression. $\sin \frac{\pi}{18} \cos \frac{5 \pi}{18}+\cos \frac{\pi}{18} \sin \frac{5 \pi}{18}$

Compare the graph of $y=\log _{3}(x+1)$ to the graph of its inverse $y=3^{x}-1 .$ How are the graphs alike? How are they different?

Use the graph of the function to determine whether the function is even, odd, or neither. $f(x)=\tan \left(x-\frac{\pi}{2}\right)$

Which expression shows the prime factorization of 100?

$$A. 2 ^ { 2 } \times 5 ^ { 2 }$$

$$B. 10 \times 10$$

$$C. 10 ^ { 10 }$$

$$D. 2 \times 5 \times 10$$

Suppose an automobile has 2000 J of kinetic energy. When it moves at twice the speed, what will be its kinetic energy? What’s its kinetic energy at three times the speed?