Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $\mathrm { a } _ { n } = \frac { 1 } { 22 } e ^ { n }$

A hyperbola has eccentricity less than 1.

Write the binomial expansion of the expression. - $( 2 x + 3 ) ^ { 5 }$

Graph the equation. Give the domain and range. Identify whether the equation is a function. - $3 y=\sqrt{3 x^{2}-48}$

Provide an appropriate response. -Consider the arrangements of sixteen students in a line. Is this a combination, a permutation, or neither?

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } + \frac { ( y - 5 ) ^ { 2 } } { 49 } = 1$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 25.2 \text {, a5 } = 69.15$

A rectangular board is 2 feet by 12 feet. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 128$

Find the eccentricity $e$ of the hyperbola. - $8 x ^ { 2 } - 9 y ^ { 2 } = 72$

Give the focus, directrix, and axis for the parabola. - $( y + 3 ) ^ { 2 } = 8 ( x + 4 )$

A student thinks that the graphs of the equations $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 36 } = 1 \text { and } \frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 36 } = 1$ are identical. Is the student correct? Explain.

Evaluate the expression. - $\left( \begin{array} { c } 293 \\ 2 \end{array} \right)$

Find the common ratio r for the given infinite geometric sequence. - $1 , - 3,9 , - 27,81 , \ldots$

Find the eccentricity $e$ of the ellipse. - $4 x ^ { 2 } + y ^ { 2 } = 36$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 5 } = - 15 , a _ { 5 } = - 7$

How many ways can a president, vice-president, and secretary be chosen from a club with 12 members? Assume that no member can hold more than one office.

Give the focus, directrix, and axis for the parabola. - $( x - 2 ) ^ { 2 } = 20 ( y + 4 )$

When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite's velocity $V$ in meters per second. It will be hyperbolic if $V > \frac { k } { \sqrt { D } }$ , parabolic if $\mathrm { V } = \frac { \mathrm { k } } { \sqrt { \mathrm { D } } }$ , and elliptical if $\mathrm { V } < \frac { \mathrm { k } } { \sqrt { \mathrm { D } } }$ , where $\mathrm { k } = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem. -When a certain satellite was at a maximum distance of $57.6 \times 10 ^ { 6 }$ m from Earth's center, it had a velocity of 4873 m per sec. Determine the shape of its trajectory.

Write an equation for the hyperbola. -vertices at $( 0 , \pm 6 )$ , asymptotes at $y = \pm \frac { 3 } { 5 } x$