Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x-axis. y=

$$\sqrt { 50 - 2 x ^ { 2 } }$$

, in the first quadrant

A 2.25-g sample of scandium metal is reacted with excess hydrochloric acid to produce 0.1502 g hydrogen gas. What is the formula of the scandium chloride produced in the reaction?

Test the series for convergence.

$$\sum_{k=1}^{\infty} \frac{1}{k \sqrt{k}}$$

Simplify, then use a calculator to check your answer: $-(-1)^{8}$

Define a biochemical pathway. How are the steps in a biochemical pathway controlled? What are three ways in which enzymes are regulated?

List the quantum numbers ($n, \ell, m_{l}, m_{s}$) for all the electrons in a carbon atom.

$a+\dfrac{1}{a}=2$, then prove that $a=1$

If $f(x)=\frac{1}{x}:$ find in simplest form: a. $f(-x)$ b. $f\left(\frac{1}{2} x\right)$ c. $2 f(x)+3$ d. $3 f(x-1)+2$

Why are coal, oil, and natural gas called fossil fuels?

According to Forrest Gump, "Life is like a box of chocolates. You never know what you're gonna get." Suppose a candy maker offers a special "Gump box" with 20 chocolate candies that look the same. In fact, 14 of the candies have soft centers and 6 have hard centers. Choose 2 of the candies from a Gump box at random. Find the probability that one of the chocolates has a soft center and the other one doesn't.

Suppose $f \geq 0, f$ is continuous on $[a, b],$ and $\int_{a}^{b} f(x) d x=0 .$ Prove that $f(x)=0$ for all $x \in[a, b]$ .

To prove that $\forall x\exists yP(x,y)$ is true, show that for all $x\in X$, there is at least one $y\in Y$ such that $P(x,y)$ is true, where the domain of discourse is $X\times Y$.

Why do you think the seafarer chose a life at sea in spite of its hardships? Think about the feelings he expresses in lines 58-64, the problems recounted in lines 81 – 102, the view of fate expressed in the final lines

Your 1000-m-long starship has warning lights at each end that, to you, flash simultaneously every minute. You are moving directly away from the planet Zerkon at $0.70 c$. To a Zerkonian,do the lights flash simultaneously? If not, which flashes first - the light at the front of your ship or the trailing one?