100 points! a water tank is being drained. the table shows the number of gallons, g, of water left in the tank after h hours. the drainage rate will remain the same. table: h(hours); 1,2,3,4. g(gallons) ; 384,288,216,162. part a: what type of sequence can be used to model the number of gallons remaining? explain your answer. part b: write the recursive formula to express gh, the number of gallons left in the tank after h hours, in terms of the number of gallons left in the tank the previous hour, gh-1. part c: write the explicit formula to express gh, the number of gallons left in the tank after h hours. part d: use your explicit formula from part c to find the number of gallons of water left after 12 hours. show all your work, round your answer to the nearest gallon. part e: convert your final answer from part d into quarts, show all work. k

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

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc