Y=1/4x+3 through (4,1) perpendicular

y + 4x = 17

Step-by-step explanation:

Y= mX + C

y = 1/4x + 3

m= gradient= 1/4

The perpendicular gradient should be the negative reciprocal of the gradient we have now.

which is : -1÷(1/4) = - 4

Now for the perpendicular line equation, we have:

y = 1

x= 4

m= -4

y - y1 = m ( x - x1 )

y - 1 = -4 ( x - 4 )

y - 1 = -4x + 16

y +4x = 17

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