Let S be the graph of

$$x ^ { 2 } + z ^ { 2 } + 6 z = 16$$

in 3-space. (a) The intersection of S with the xz-plane is a circle with center ___ and radius . (b) The intersection of S with the xy-plane is two lines, x= and x=___. (c)

Select the representations that do not change the location of the given point.

$$\left( 7,140 ^ { \circ } \right)$$

$$a. \ \left( - 7,320 ^ { \circ } \right) \\ b. \ \left( - 7 , - 40 ^ { \circ } \right) \\ c. \ \left( - 7,220 ^ { \circ } \right) \\ d. \ \left( 7 , - 220 ^ { \circ } \right)$$

Solve each compound inequality.

$$2 t \leq - 4 \text { or } 7 t \geq 49$$

Simplify each expression. State any excluded values.

$$\frac { 2 s ^ { 2 } + s } { s ^ { 3 } }$$

An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. About 40% break in the kiln during firing. Hoping to solve this problem, she buys some more expensive clay from another supplier. She plans to make and fire 10 pieces and will decide to use the new clay if at most one of them breaks. If she decides to switch to the new clay and it is no better, what kind of error did she commit?

Simplify the expression. Write your answer using exponents.

$$\left( - \frac { 5 } { 4 } \right) ^ { 4 }$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.

$$( x - 4 ) ^ { 2 } = 4 ( y + 1 )$$

Bank loans often are arranged under existing lines of credit. What is a line of credit? How does a noncommitted line of credit differ from a committed line?

Sketch the line. Also, find a Cartesian equation for each line.

$$r = 2 \sec \theta$$

Determine whether the following statements are true and give an explanation or counterexample.

If $m$ is a positive integer, then $\int _ { 0 } ^ { \pi } \cos ^ { 2 m + 1 } x d x = 0$.

Una universidad desea conocerte y saber algo más sobre tu vida escolar. Contesta. Generalmente, ¿Cuántas horas duermes?

Solve the equation. 32. (8x³ - 9)³ = 5832

Solve each absolute value inequality.

$$1 < | 2 - 3 x |$$

Design a capacitor whose capacitance can be varied mechanically over the range of 50 nF and 100 nF by rotating a knob $90^\circ .$