Find the volume under the surface $z=x^{2}+y^{2}$ and above the square region bounded by $|x| \leq 1$ and $|y| \leq 1$.

Let V be a vector space with subspaces U and W. Prove that

$$U \cap W$$

is a subspace of V.

Find the domain of each logarithmic function. $F(x)=\ln \left(x^{2}-9\right)$

What do the equations have in common? $y=x^{2} ; y=3 x^{2} ; y=-0.5 x^{2}$

For each topic, decide which type of association a scatterplot of the data would likely show. Explain your choice.

outdoor temperature and layers of clothing

True or false: Every ratio of polynomials has vertical asymptotes.

Determine the surface area in square meters of a rectangular prism that has a length of 13 m, a width of 10 m, and a height of 8 m.

How do you determine the surface area of a rectangular prism?

Solve the given problems using inequalities. (All data are accurate to at least two significant digits.)

A rectangular parking lot is to have a perimeter of 180 $\mathrm{m}$ and an area of at least 2000 $\mathrm{m}^{2} .$ What are the possible dimensions of the lot?

Seawater contains 3 mg of uranium per cubic meter. Estimate how long this uranium could supply the world’s energy needs at the current usage of $1.5 \times 10 ^ { 13 }$ J/s.

Evaluate each expression when $a=-3$ and $b=4$ $\quad a^{2}-b^{2}$

Find the value. Give answers in radians, rounded to the nearest ten-thousandth. $\tan ^{-1}(-38.2004)$

Determine whether the improper integral converges and, if so, evaluate it.

$$\int _ { 0 } ^ { \infty } \frac { d x } { ( x + 2 ) ^ { 2 } }$$

The wheels on a moving bicycle have both translational (or linear) and rotational motions. What is meant by the phrase "a rigid body, such as a bicycle wheel, is in equilibrium"? (a) The body cannot have translational or rotational motion of any kind. (b) The body can have translational motion, but it cannot have rotational motion. (c) The body cannot have translational motion, but it can have rotational motion. (d) The body can have translational and rotational motions, as long as its translational acceleration and angular acceleration are zero.

Graph the function and approximate any local maxima or minima to the nearest tenth. $P(x)=6+x-3 x^{2}$