Traveling at an average speed of 50 miles per hour, the trip from point a to point b takes 2 hours. traveling at an average speed of 40 miles per hour, the same trip takes 2.5 hours. if time, y, varies inversely with speed, x, how long will the trip take traveling at 45 miles per hour?

Step-by-step explanation:

At a speed of 50m/h time taken is 2hours

At a speed of 45m/h time take is 2.5 hours

You can find the distance between A and B

Distance=speed × time

But time y varies inversely with speed x , hence

where k is a constant of proportionality and D is distance.

To find k

where y is time and x is speed

Given

x=45m/h  you should find time y. Apply the expression above

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

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