True or False? The units for an integral of a function f(x) are the same as the units for f(x).

When the units molarity and liter are multiplied, what are the resulting units?

What is another name for a cube? Explain your reasoning.

Explain how eccentricity determines which conic section is given.

Graph the translation 3 units left and 9 units down.

Give conditions on a > 0, b > 0, and u so that

$$f_{X, Y}(x, y)=k e^{-\left(a x^{2}-2 u x y+b y^{2}\right)}$$

is the bivariate normal density of random variables X and Y each having expected value 0. Also, find Var(X), Var(Y), and $\rho(X, Y)$.

¿Qué clase de médica se solicita?

A 13.5-meter fire-truck ladder is leaning against a wall. Find the distance $d$ the ladler goes up dic wall (above the top of the fire truck) if the ladder makes an angle of $43^{\circ} 50^{\prime}$ with the horizontal.

A collage is a collection of images, words, or even objects pasted onto a flat surface. The aim is to create an impression-of a place or a person. The words in a collage can come from stories, poems, newspapers, or just your own head. Create a collage of Buddy's cousin, showing her in one of the settings described in the story: the kitchen, the field, Mr. Haha Jones's cafe, the house on Christmas morning, her bedroom. Be prepared to show your collage to the class and explain your choice of objects.

Two point charges of equal magnitude but of opposite sign are positioned with charge +q at z = +d/2 and charge -q at z = -d/2. The charges in this configuration form an electric dipole. (a) Find the electric field intensity E everywhere on the z axis. (b) Evaluate your part a result at the origin. (c) Find the electric field intensity everywhere on the xy plane, expressing your result as a function of radius $\rho$ in cylindrical coordinates. (d) Evaluate your part c result at the origin. (e) Simplify your part c result for the case in which $\rho>>d.$

Can the quadrilateral always be inscribed in a circle? Explain your reasoning. kite

Some worms swim by passing an undulatory wave along their bodies. The force that small worms apply to the water by passing this wave can be modeled using a formula derived by Lamb (1911)
F=$\frac{4 \pi L \mu U}{\left(-0.077-\ln \left(\frac{\rho U a}{4 \mu}\right)\right)}$
where U is the velocity of undulation, L is the length of the worm, a is the radius of the worm’s body, and $\mu$ and $\rho$ respectively the viscosity (or “stickiness”) and density of the water through which the worm swims. Calculate dF/dU, the rate of change of the force with increasing undulation velocity.

What is the perimeter of $\triangle$PQR with vertices P(-2, 9), Q(7, -3), and R(-2, -3) in the coordinate plane? (A) 21 units (B) 25 units (C) 34 units (D) 36 units

Determine if a triangle can be formed with the given side lengths. Explain your reasoning.

12 units, 4 units, 17 units