Show that the graph of the given equation is an ellipse. Find its foci, vertices, and the ends of its minor axis.

$$288 x ^ { 2 } - 168 x y + 337 y ^ { 2 } - 3600 = 0$$

On

$$\mathbb { R } ^ { + },$$

the set of positive real numbers, define the operations of addition,

$$\oplus,$$

and scalar multiplication,

$$\odot,$$

as follows:

$$\left. \begin{array} { l } { \mathscr { x } \oplus y = x y } \\ { c \odot x = x ^ { c } } \end{array} \right.$$

A 10.00-g sample consisting of a mixture of sodium chloride and potassium sulfate is dissolved in water. This aqueous mixture then reacts with excess aqueous lead(II) nitrate to form 21.75 g of solid. Determine the mass percent of sodium chloride in the original mixture.

Simplify by combining similar terms. (-2r+s+5)+2(r-3s+2)

In 1920 veteran suffragist Anna Howard Shaw stated that equality in the workplace would be harder for women to achieve than the vote. "You younger women will have a harder task than ours. You will want equality in business, and it will be even harder to get than the vote." Why do you think Shaw held this belief? Support your answer with evidence from the text.

Use Logarithmic differentiation to find $y^{\prime}$ Assume that variable is restricted so that all arguments of logarithm functions are positive

$$y=\frac{x \cos x}{\left(x^{2}+1\right)^{3} \sin x}$$

The decayed organic material in soil is called (a) bedrock (b) humus (c) silt (d) subsoil

Graph the equation using a graphing utility.

$x=\cot y, 0<y<\pi$

Graph the equation using a graphing utility.

$$x=\tan y, - \pi / 2 < y < \pi / 2$$

Find an equation for the ellipse that satisfies the given conditions. Foci (−1, 1) and (−1, 3); minor axis of length 4.

What can you say about the arc length of the portion of the curve

$$r=1 / \theta$$

for

$$\pi / 4 \leq \theta \leq \pi / 2$$

that lies inside the circle r=1?

Graph the equation using a graphing utility.

$$x=y-3 y^3+y^5$$

Find the arc length of the polar curve

$$r=1 / \theta$$

for

$$\pi / 4 \leq \theta \leq \pi / 2$$

.

Graph the equation using a graphing utility.

$$x=y+2 y ^ { 3 } - y ^ { 5 }$$