Q2 Question 2 - Combining Functions 1On most state highways, the fine for speeding depends on the speed of the car. On a certain state highway, the fine for driving 70 mph is $25 and the fine for driving 85 mph is $100. On this particular road, when a car brakes suddenly, the function S(d) = √ (under the square root) 40d can be used to approximate the speed of a car (in mph) when it leaves a skid mark of length d feet on the road.
a) Using the information provided, write a linear equation that represents the fine for speeding, F,
as a function of the speed in mph on the state highway.
Part b) Find (F x S)(d) and explain what this function can be used for in context of the problem.

here is a big fat

false

step-by-step explanation:

the meaning of changing is to edit or make something different.

but transmitting means cause (something) to pass on from one place or person to another.

there 2 different things

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt