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

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

Use a calculator to evaluate the expression. - ${ } _ { 17 } \mathrm { P } _ { 4 }$

A tunnel is in the shape of a parabola. The maximum height is 29 m and it is 19 m wide at the base. What is the vertical clearance 2 m from the edge of the tunnel?

Find the future value of the annuity. -There are payments of $100 at the end of each year for 10 years at 2% interest compounded annually

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether a parabola opens up or down or whether it opens left or right.

Write out the first five terms of the sequence. - $a _ { n } = 2 ^n$

Use mathematical induction to prove that the statement is true for every positive integer n. - $\text { If } 0 < a < 1 \text {, then } a n < a n - 1$ (Assume that a is a constant.)

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { k = 5 } ^ { 12 } ( 1.79 ) ^ { k }$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } - y ^ { 2 } = 25$

The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 58$ , where $x$ and $y$ are in meters. Determine the distance, w, between the outside walls. $A = 12 m$

Find the common ratio r for the given infinite geometric sequence. - $1 , \frac { 1 } { 4 } , \frac { 1 } { 16 } , \frac { 1 } { 64 } , \frac { 1 } { 256 } , \ldots$

How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O?

Evaluate the sum. - $\sum _ { j = 4 } ^ { 15 } ( 7 j + 8 )$

Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having exactly two girls and three boys?

A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 2 m down from the top of the dome the ceiling is 28 m wide, find the best location for the Light source.

Identify the type of graph. - $( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + 12 = 0$

Find the eccentricity of the conic section shown in the graph. - $x=-4 \sqrt{3}$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. - $a _ { 1 } = 42 , d = - 8$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x - 4 = ( y - 7 ) ^ { 2 }$

A sequence of yearly payments of $2000 is invested at the end of every compounding period, where interest is compounded semi-annually at 2%. What is the total amount of the annuity at the end of 6 years?