Answer: 1200pi cubic cm per sec
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Work Shown:
dr/dt = 3 is the rate of change of the radius
V = (4/3)pi*r^3 ..... volume of a sphere
dV/dt = (4/3)*3*pi*r^2*dr/dt ... chain rule
dV/dt = 4*pi*r^2*dr/dt
dV/dt = 4*pi*r^2*3
dV/dt = 12*pi*r^2
dV/dt = 12*pi*10^2 ... plug in r = 10
dV/dt = 1200pi
Answer:
The solutions of the equation are -41.8° , 0.0° , 41.8°
Step-by-step explanation:
∵ 3 sin²Ф - 2 sinФ = 0 is a quadratic function
∵ The domain of the function is -90° ≤ Ф ≤ 90°
- Lets take sinФ as a common factor
∴ sinФ (3 sinФ - 2) = 0
- Two terms multiplied by each other = 0
∴ One of them must be equal zero
∴ sinФ = 0 or 3 sinФ - 2 = 0
- If sinФ = 0 ⇒ Ф = 0.0°
- If 3 sinФ - 2 = 0 ⇒ 3 sinФ = 2 ⇒ sin Ф = 2/3
∵ sinФ 2/3
∴ Ф = 41.8° ⇒ Ф ≤ 90° (in first quadrant)
∵ -90° ≤ Ф ≤ 90°
∴ Ф = -41.8° ⇒ Ф ≥ -90° (in fourth quadrant)
∴ The solutions of the equation are -41.8° , 0.0° , 41.8°
Y = -1/2x + 4
2y = -x + 8
x + 2y = 8: the standard form
