6. A college student who is looking for a data plan for her cell phone found a third option, which also offers a 2 gigabyte monthly
allowance for data.
The monthly cost of this option can be represented by function C.
defined by: C(x) - 25x +8, where x is the gigabytes of data used over
the monthly allowance.
a. Find the value of C(1.5) and EXPLAIN what it means in this
situation. Show All of your work.
b. Her budget is $100 a month. To find out how many gigabytes
of data she could use if she chose this plan, she writes
C(.) - 100 and solves for x. What value of x makes this
equation true? Show All of your work.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation:

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation: