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.

Determine whether the graph of each function is symmetric with respect to the $y$-axis or the origin.

$$f(x)=x^4-9 x^2$$

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

Suppose that a merchant buys a patio set from the wholesaler for $180. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant a 40% profit on his$180 investment.

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

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

Quand il sera en Europe

faire du ski

For this item, draw a cone with a height of 12 cm and a radius of 5 cm. Find the volume.

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]

The horny scales that cover the skin of reptiles prevent them from

a. using their skin as an organ of gas exchange.

b. sustaining high levels of metabolic activity.

c. laying their eggs in water.

d. flying.

e. crawling into small spaces.

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.

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

Delia wants to enclose a rectangular plot of land that adjoins a straight brick wall. If she has only 200 yards of fence, what should the dimensions of the rectangular plot be so that the area enclosed is a maximum?

Determine whether the graph of the function is symmetric about the y-axis, the origin, or neither.

$$y = e ^ { - x ^ { 2 } }$$