Aparabola is given by the equation y2 = -24x. the equation of the directrix of the parabola is

Step-by-step explanation:

We have been given an equation of a parabola . We are asked to find the equation of directrix of the given parabola.

First of all, we will convert our given equation in standard form of right-left opening parabola: , where, represents focal length and (h,k) is vertex of parabola.

We can rewrite our given equation as:

Since our given parabola has a term, so it will be symmetric about x-axis.

The vertex of parabola is (0,0) and focal length is 6.

We know that equation of directrix of right-left opening parabola is .

Therefore, the equation of the directrix of our given parabola is .

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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