Use the alternative form of the derivative to find the derivative at x=c (if it exists).f(x) = 3/x, c=4

Use the fundamental identities to simplify the expression. Use the table feature of a graphing utility to check your result numerically. $\cos x\left(1+\tan ^{2} x\right)$

A car is 2.0 km west of a traffic light at t = 0 and 5.0 km east of the light at t = 6.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) What are the car's position vectors at these two times? (b) What is the car's displacement between 0 min and 6.0 min?

There are 198 students in the soccer league. There are 11 players on each soccer team. How many soccer teams are there?

Perform the indicated operation. 5.85 - 9.47

A survey asks 60 teachers and 48 parents whether school uniforms reduce distractions in school. Of these, 49 teachers and 18 parents say uniform reduce distractions in school. Organize these results in a two-way table. Then find and interpret the marginal frequencies.

In an ideal gas-turbine cycle with intercooling, reheating, and regeneration, as the number of compression and expansion stages is increased, the cycle thermal efficiency approaches (a) 100 percent, (b) the Otto cycle efficiency, or (c) the Carnot cycle efficiency.

Prove that every integer greater than $27$ can be written as $5a+8b$, where $a,b\in\mathbb Z^+$

Find the product. Write the product in simplest form.

$$\frac { 3 } { 5 } \times 11$$

Hydrogen at a pressure of 2 atm flows within a tube of diameter 40 mm and wall thickness 0.5 mm. The outer surface is exposed to a gas stream for which the hydrogen partial pressure is 0.1 atm. The mass diffusivity and solubility of hydrogen in the tube material are $1.8 \times 10^{-11} \mathrm{m}^{2} / \mathrm{s}$ and $160 \mathrm{kmol} / \mathrm{m}^{3} \cdot \mathrm{atm}$, respectively. When the system is at 500 K, what is the rate of hydrogen transfer through the tube per unit length $(\mathrm{kg} / \mathrm{s} \cdot \mathrm{m})$?

A(n) _____ is a signal to which an organism responds.

Simplify each expression. (a) $\sqrt[3]{16 x^{5}}$ (b) $\sqrt{75 x^{2} y^{-4}}$

Use technology to graph the derivative of the given function. In each case, choose a range of x-values and y-values that shows the interesting features of the graph. $f(x)=3 x^{3}+3 \sqrt[3]{x}$

The band leader wants to line up the 92 band members in 4 rows so that each row has two more members than the row before. How many members should be in the shortest row?