Use the arc length formula to find the length of the curve y = 4x - 1, -3 lessthanorequalto x lessthanorequalto 2. check your answer by noting that the curve is a line segment and calculating its length by the distance formula. 4 squareroot 17

5 is the answer.

Step-by-step explanation:

y= 4x-1

taking derivative with respect to x ,we get

Using distance formula

we have points

at x =-3 the value of y = 4(-3)-1= -12-1 = -13

at x =2 the value of y = 4(2)-1 =7

points are ( -3,-13) and (2,7)

distance formula =

                             =

                             =

                             =

                             =5

whatvare the choices

step-by-step explanation:

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