use a computer to provide a portrait of the given function g(x, y). To do this, (a) use the computer to help you understand some of the level curves of the function, and (b) use the computer to graph (a portion of) the surface z = g(x, y). In addition, mark on your surface some of the contour curves corresponding to the level curves you obtained in part (a).

$$g(x, y) = x^2 − xy$$

Find four solutions of the equation. Write the solution as ordered pairs. x + y = -1

Write a chemical equation that illustrates the autoionization of water.

What did the following people do in their youth? Modelo: Alicia (molestar a sus hermanos menores): Alicia molestaba a sus hermanos menores.

Luis y Sergio (coleccionar monedas): __________________

Graph the function.

$$f ( x ) = \left( \frac { 1 } { 8 } \right) ^ { x }$$

Give the structure for each of the following aromatic hydrocarbons. 1-phenyl-2-butene

When viewing a piece of art that is behind glass, one often is affected by the light that is reflected off the front of the glass (called glare), which can make it difficult to see the art clearly. One solution is to coat the outer surface of the glass with a film to cancel part of the glare. (a) If the glass has a refractive index of 1.62 and you use $\mathrm{TiO}_{2}$, which has an index of refraction of 2.62, as the coating, what is the minimum film thickness that will cancel light of wavelength 505 nm? (b) If this coating is too thin to stand up to wear, what other thickness would also work? Find only the three thinnest ones.

Find the opposite of each number. 16

Determine whether the statement is true or false. If a linear transformation is one-to-one, then it is invertible.

The surface area of a rectangular prism is 35 square inches. What is the surface area of a similar solid that has been enlarged by a scale factor of 7?

The charge inside a closed surface is proportional to the flux through that surface. To illustrate why the surface must be closed, draw an example of a charge distribution and a surface for which the flux through the surface would be considerably altered if the surface had any holes (unclosed regions of the surface through which flux is not counted).

Solve each quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators.

$$y^2=144$$

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval fo is not specified, assume that

$$- \infty < t < \infty$$

$$x = 1 + 3 \cos t , y = 2 + 3 \sin t ; 0 \leq t < 2 \pi$$

Find a vector parametrization for the line with the given description. Passes through (-2, 0, -2) and (4, 3, 7)