Tristin is attempting to dive from an 8 foot diving board into a tube that is located 12 feet from the base of the diving board. what should be his angle of depression to ensure he hits the tube

The angle of depression is 33.7°.

Step-by-step explanation:

To find the angle of depression, you need to form a triangle based on the given measurements and use trigonometric functions to solve for the angle.  In this case, the triangle is formed from a base of 12 feet (the horiontal distance from the tube to the base of the diving board) and a height of 8 feet (the height of the diving board).  The angle of depression is formed from the angle made from the tube in the water to the top of the diving board.  To find the measure of the angle, we get:

tan y = or tan y =

In order to find 'y', or the angle of depression, we need to take the inverse tangent of the fraction:

y = or y = 33.7°.

- (2, -7)

- lines r and s and lines t and u must be parallel

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