Question

Question 1: The water level in a tank can be modeled by the function h(t)=4cos(+)+10, where t is the number of hours

since the water level is at its maximum height, h. How many hours pass between two consecutive times when
the water in the tank is at its maximum height?
Your answer...
Question 2: Point B has coordinates (3, -4) and lies on the circle whose equation is x + y = 25. If an angle is drawn in
standard position with its terminal ray extending through point B, what is the sine of the angle?
Your answer...

Answer 1

Question 1: The hours that will pass between two consecutive times, when the water is at its maximum height is π hours

Question 2: Sin of the angle is -0.8

Explanation:

Question 1: Here we have h(t) = 4·cos(t) + 10

The maximum water level can be found by differentiating h(t) and equating the result to zero as follows;

`\frac{\mathrm{d} h(t)}{\mathrm{d} t} = \frac{\mathrm{d} \left (4cos(t) + 10 \right )}{\mathrm{d} t} = 0`

`\frac{\mathrm{d} h(t)}{\mathrm{d} t} = - 4 * sin(t) = 0`

∴ sin(t) = 0

t = 0, π, 2π

Therefore, the hours that will pass between two consecutive times, when the water is at its maximum height = π hours.

Question 2:

B = (3, -4)

Equation of circle = x² + y² = 25

Here we have

Distance moved along x coordinate = 3

Distance moved along y coordinate = -4

Therefore, we have;

`Tan \theta = (Distance \ moved \ along \ y \ coordinate)/(Distance \ moved \ along \ x \ coordinate) = (-4)/(3)`

`\therefore \theta = Tan^(-1)((-4)/(3)) = -53.13^(\circ)`

Sinθ = sin(-53.13) = -0.799≈ -0.8.