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;
[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t} = \frac{\mathrm{d} \left (4cos(t) + 10 \right )}{\mathrm{d} t} = 0[/tex]
[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t} = - 4 \times sin(t) = 0[/tex]
∴ 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;
[tex]Tan \theta = \frac{Distance \ moved \ along \ y \ coordinate}{Distance \ moved \ along \ x \ coordinate} = \frac{-4}{3}[/tex]
[tex]\therefore \theta = Tan^{-1}(\frac{-4}{3}) = -53.13^{\circ}[/tex]
Sinθ = sin(-53.13) = -0.799≈ -0.8.
