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

Answer 1

Answer:

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

Step-by-step 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;

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

$\frac{\mathrm{d} h(t)}{\mathrm{d} t} = - 4 \times sin(t) = 0$

∴ 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;

$Tan \theta = \frac{Distance \ moved \ along \ y \ coordinate}{Distance \ moved \ along \ x \ coordinate} = \frac{-4}{3}$

$\therefore \theta = Tan^{-1}(\frac{-4}{3}) = -53.13^{\circ}$

Sinθ = sin(-53.13) = -0.799≈ -0.8.