V = t^2 - 9t + 18
position, s
s = t^3 /3 - 4.5t^2 +18t + C
t = 0, s = 1 => 1=C => s = t^3/3 -4.5t^2 + 18t + 1
Average velocity: distance / time
distance: t = 8 => s = 8^3 / 3 - 4.5 (8)^2 + 18(8) + 1 = 27.67 m
Average velocity = 27.67 / 8 = 3.46 m/s
t = 5 s
v = t^2 - 9t + 18 = 5^2 - 9(5) + 18 = -2 m/s
speed = |-2| m/s = 2 m/s
Moving right
V > 0 => t^2 - 9t + 18 > 0
(t - 6)(t - 3) > 0
=> t > 6 and t > 3 => t > 6 s => Interval (6,8)
=> t < 6 and t <3 => t <3 s => interval (0,3)
Going faster and slowing dowm
acceleration, a = v' = 2t - 9
a > 0 => 2t - 9 > 0 => 2t > 9 => t > 4.5 s
Then, going faster in the interval (4.5 , 8) and slowing down in (0, 4.5)
Answer:
dV/dt = 9 cubic inches per second
Explanation:
Let the height of the cylinder is h
Diameter of cylinder = height of the cylinder = h
Radius of cylinder, r = h/2
dh/dt = 3 inches /s
Volume of cylinder is given by

put r = h/2 so,

Differentiate both sides with respect to t.

Substitute the values, h = 2 inches, dh/dt = 3 inches / s

dV/dt = 9 cubic inches per second
Thus, the volume of cylinder increases by the rate of 9 cubic inches per second.
c.charge due to the reaction process between the two
Answer:
1 Ampere.
Explanation:
From the question given above, the following data were obtained:
Resistor 1 (R₁) = 20 ohm
Resistor (R₂) = 20 ohm
Voltage (V) = 10 V
Current (I) =?
Next, we shall determine the equivalent resistance in the circuit. This can be obtained as follow:
Resistor 1 (R₁) = 20 ohm
Resistor (R₂) = 20 ohm
Equivalent Resistance (R) =?
Since the resistors are in parallel connection, the equivalent resistance can be obtained as follow:
R = (R₁ × R₂) / (R₁ + R₂)
R = (20 × 20) / (20 + 20)
R = 400 / 40
R = 10 ohm
Finally, we shall determine the total current in the circuit. This can be obtained as illustrated below:
Voltage (V) = 10 V
Equivalent Resistance (R) = 10 ohm
Current (I) =?
V = IR
10 = I × 10
Divide both side by 10
I = 10 / 10
I = 1 Ampere
Therefore, the total current in the circuit is 1 Ampere.