Answer all correctly, hurry! this is worth half my grade! you (: the lengths of two sides of a triangle are shown below: side 1: 3x2 − 2x − 1 side 2: 9x + 2x2 − 3 the perimeter of the triangle is 5x3 + 4x2 − x − 3. part a: what is the total length of the two sides, 1 and 2, of the triangle? (4 points) part b: what is the length of the third side of the triangle? (4 points) part c: do the answers for part a and part b show that the polynomials are closed under addition and subtraction? justify your answer. (2 points)

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

  or  

sin y = 7/q

7 is the opposite side length, q is the hypotenuse

tan y = 7/r

7 is the opposite side length, r is the adjacent side length

using sohcahtoa ^^^^

cos y = adjacent/hypotenuse

cos y = r/q