Need some i get some for my finals

m∠A = 42°

Step-by-step explanation:

* Lets revise some facts in the circle

- If the vertex of an angle on the circle and the two sides of the

 angle are chords in the circle, then this angle is called

 an inscribed angle

- Each inscribed angle subtended by the opposite arc, the arc name

 is the starting point and the ending point of the angle

# Ex: ∠CAB is subtended by arc CB

- There is a relation between the inscribed angle and its

  subtended arc, the measure of the inscribed angle equals half

  the measure of its subtended arc

* Now lets solve the problem

- ∠CAB is an inscribed angle subtended by arc CB

∴ m∠CAB = (1/2) measure of arc CB

∵ The measure of arc CB = 84°

∴ The measure of ∠A = 1/2 × 84° = 42°

* m∠A = 42°

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