Answer:
2
Step-by-step explanation:
All you do is substitute x.
Add.
|-12 + 10|
Find the absolute value of |-2|.
|-2|
2
If you notice the terms, they're
7, -21, 63, -189 and so forth.
7*-3 = -21 and -21 * -3 is 63 and so forth, meaning the "common ratio" is -3.
now, for a common ratio say "r", which is a fraction, namely less than ±1 and more than 0, or |r| < 1 , you do have a convergent sequence.
however this one notice, |-3| is 3, and that's greater than 1 clearly, therefore is divergent, meaning the summation has no finite value.
The equation that we can create from this situation is:
i = (190 – 5 x) * (29 + x)
where i is the income and x is the increase in daily rate
Expanding the equation:
i = 5510 + 190x – 145x - 5x^2
i = -5x^2 + 45x + 5510
Taking the 1st derivative:
di/dx = -10x +45
Set to zero to get the maxima:
-10x + 45 = 0
x = 4.5
So the cars should be rented at:
29 + x = 33.5 dollars per day
The maximum income is:
i = (190 – 5*4.5) * (33.5)
i = 5,611.25 dollars
All we need to do to find the correct answer is to double the prize for a night. I'll "cut" it into pieces so you can see exactly how I calculated it:
$91.35 * 2 =
= $90.00 * 2 + $1.00 * 2 + $0.35 * 2 =
= $180.00 + $2.00 + $0.70 =
= <u>$182.70</u>
Answer: They will pay $182.70 for two nights at the hotel.