91Ó°ÊÓ

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used a formula to find the sum of the infinite geometric series \(3+1+\frac{1}{3}+\frac{1}{9}+\dots\) and then checked my answer by actually adding all the terms.

$$\text { Solve: } x^{4}-6 x^{3}+4 x^{2}+15 x+4=0$$.

Determine the amplitude, period, and phase shift of \(y=\frac{1}{2} \cos \left(3 x+\frac{\pi}{2}\right) .\) Then graph one period of the function.

Will help you prepare for the material covered in the next section. Consider the sequence \(8,3,-2,-7,-12, \ldots .\) Find \(a_{2}-a_{1}\) \(a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4} .\) What do you observe?

Will help you prepare for the material covered in the next section. Consider the sequence whose \(n\) th term is \(a_{n}=4 n-3\) Find \(a_{2}-a_{1}, a_{3}-a_{2}, a_{4}-a_{3},\) and \(a_{5}-a_{4} .\) What do you observe?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the \(n\) th term of a geometric sequence is \(a_{n}=3(0.5)^{n-1}\) the common ratio is \(\frac{1}{2}\).

Will help you prepare for the material covered in the next section. Use the formula \(a_{n}=4+(n-1)(-7)\) to find the eighth term of the sequence \(4,-3,-10, \ldots\)

You are now 25 years old and would like to retire at age 55 with a retirement fund of \(\$ 1,000,000 .\) How much should you deposit at the end of each month for the next 30 years in an IRA paying \(10 \%\) annual interest compounded monthly to achieve your goal? Round up to the nearest dollar.

Find the dimensions of a rectangle whose perimeter is 22 feet and whose area is 24 square feet. (Section 7.4, Example 5)

Solve using matrices. Use Gaussian elimination with back. substitution or Gauss-Jordan elimination. $$ \left\\{\begin{aligned} x-2 y+z &=-4 \\ 2 x+2 y-z &=10 \\ 4 x-y+2 z &=-1 \end{aligned}\right. $$ (Section 8.1, Examples 3 and 5).