The equations of parabolas, circles, ellipses, and hyperbolas are given. Graph the equation.

$$y^2/25-x^2/121=1$$

Draw a cone with a height of 9 inches and a diameter of 4 inches. Find the volume.

Give an example to illustrate each axiom of equality: a) Reflexive b) Symmetric c) Transitive d) Substitution

What were the motives behind European exploration in the 1400s? Explain

If a supersonic jet flies at Mach 3.2, what will be the cone angle (to the nearest degree)?

If the smell of gasoline is detectable at 3 parts per billion, what percent of the air is occupied by the gasoline?

$\odot Q$ and $\odot R$ both have a radius of $3 \mathrm{cm} .$ Therefore the circles are ____________. (concentric or congruent)

If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled? F. The x-intercept becomes four times as great. G. The x-intercept becomes twice as great. H. The x-intercept becomes one-fourth as great. J. The x-intercept remains the same.

Circles T and S intersect at points A and B. What is the relationship between

$$\overline{AB}\ and\ {\overleftrightarrow{TS}}?$$

Explain.

For those cases in which the Mean Value Theorem applies, make sketch of the function and the line that passes through (a, f(a)) and (b, f(b)). Mark the points P at which the slope of the function equals the slope of the secant line. Then sketch the tangent line at P. f(x)=x/(x+2); [-1, 2]

Let A be an n × n symmetric negative definite matrix. Show that the leading principal submatrices of A are negative definite.

If q is a quadratic form on $\mathbb{R}^{n}$ with symmetric matrix A and if $L(\vec{x})=R \vec{x}$ is a linear transformation from $\mathbb{R}^{m}$ to $\mathbb{R}^{n},$ show that the composite function $p(\vec{x})=q(L(\vec{x}))$ is a quadratic form on $\mathbb{R}^{m}.$ Express the symmetric matrix of p in terms of R and A.

Find the second Taylor polynomial of $x(x+1)^{3 / 2}$ at x=0.

A circle has a radius of x. Another circle has a radius of 3x.

Write equations for the areas of both circles.