Use integration by parts to find the integrals. $\int_{0}^{3} \frac{3-x}{3 e^{x}} d x$

Johanna is planting tomatoes in the school garden this year. Tomato plants come in packs of six. She needs 80 plants in the garden and already has 28. How many packs of plants will she need?

(a) Write a structural formula for a sulfide having the molecular formula $\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{S}$. (b) What two thiols have the molecular formula $\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{S}$?

In Springfield the population P grows at the rate of 2% per year. The equation $P=1,500,000(1.02)^{t}$ gives the population t years after 2015. Find the value of t for which the tenth of a year.

Find each integral. Each integral contains a term of the form $\sqrt{a^{2}-x^{2}}$. $\int \sqrt{4-x^{2}} d x$.

At what wavelength does a cavity at $6000^{\circ} \mathrm{K}$ radiate most per unit wavelength?

Determine whether the system has infinitely many solutions or only the trivial solution. Do not solve the systems.

$$\left\{\begin{array}{l}{3 x+2 y+z=0} \\ {2 x+2 y+z=0} \\ {4 x+y+z=0}\end{array}\right.$$

For what values of does the function $y=e^{r x}$ satisfy the equation

Rationalize the denominators. $\frac{6}{\sqrt{5}}$

Find each definite integral. $\int_{3}^{0}(-\pi) d t$.

You read on a financial website that the nominal interest rate is 12 percent per year in Canada and 8 percent per year in the United States. Suppose that international capital flows equalize the real interest rates in the two countries and that purchasing-power parity holds.

Using the Fisher equation, what can you infer about expected inflation in Canada and in the United States?

What can you infer about the expected change in the exchange rate between the Canadian dollar and the U.S. dollar?

Find the derivative of each function. $f(x)=x^{4}(x+5)$

Write the product using exponents. $-(7 \cdot 7 \cdot 7 \cdot 7 \cdot 7)$

A solution made up with calcium carbonate is initially supersaturated with $\mathrm{Ca}^{2+}$ and $\mathrm{CO}_{3}^{2-}$ ions, such that the concentrations of each are both $1.35 \times 10^{-3}$ M. When equilibrium is finally reached, what is the final concentration of calcium? (Use the $pK_s$ for aragonite.)