Answer:
Step-by-step explanation:
Let “a” be the first term and ”r” the common ratio of the GP. Then,
f(n) = ar^(n - 1).
f(2) + f(3) = 6f(4). (given)
ar + ar^2 = 6ar^3, or
1 + r = 6r^2, or
6r^2 - r - 1 = 0,
(3r + 1)(2r - 1) = 0.
r = -1/3, or 1/2.
If the common ratio is positive and the second term is 8 we have,
ar = 8, or
a*1/2 = 8, or a = 16.
f(n) = 16*(1/2)^(n - 1) = 2^4*2^(1 - n), or
f(n) = 2^(5 - n).
The first six terms of the GP are : 16, 8, 4, 2, 1, 1/2,…
××××××××××
Checking : f(2) + f(3) = 6f(4), (given).
LHS = 8 + 4 = 12.
RHS = 6* 2 = 12.
LHS = RHS.
You can always match 4 points using a cubic polynomial. A graphing calculator can find a cubic regression equation for you. This set of points is matched by
.. y = x^3 +3x^2 +5x +3
To find the final amount, you would have to multiply her rate per hour (10) by how many hours she tutored (h). Then, you need to add her flat rate of 8.
10h + 8 = 48, where h is how many hours she tutored.
We know that, in the US, the average mile per gallon was 25 mpg in 2015. Since we don't have the mile per gallon of the car in our problem, we are going to use that average.
For our first situation, <span>drive 0.3 miles to fill up for $3.59 per gallon:
</span>




<span>We just proved that in our trip, we used 0.012 gallon, and at $3.59 per gallon; we will pay (0.012)(3.59)=$0.04 for that gasoline.
For our second situation, </span><span>drive 1.2 miles to fill up for $3.41 per gallon:
</span>




We just proved that in our trip, we used 0.048 gallon, and at $3.41 per gallon; we will pay (0.048)(3.41)=$0.16 for that gasoline.
We can conclude that is much better to drive 0.3 miles to fill up for $3.59 per gallon than drive <span>1.2 miles to fill up for $3.41 per gallon.</span>