Answer:
dr/dt = -2 cm/s.
Explanation:
The volume of a cone is given by:
(1)
- r is the radius
- h is the height
Let's take the derivative with respect to time in each side of (1).
(2)
We know that:
- dh/dt = 10 cm / s (rate increasing of height)
- dV/dt = 0 (constant volume means no variation with respect of time)
- r = 4 cm
- h = 10 cm
We can calculate how fast is the radius changing using the above information.
Therefore dr/dt will be:
The minus signs means that r is decreasing.
I hope it helps you!
Answer:
The answer is below
Explanation:
The amplitude decreases by 2% during each oscillation. Hence the decrease in amplitude can be represented by an exponential decay in the form:
y = abˣ; where x ad y are variables, a is the initial value and b is the factor.
Let y represent the amplitude after x oscillations. Since the initial amplitude is 10 cm, hence:
a = 10 cm, b = 2% = 0.02.
Therefore:
y = 10(0.02)ˣ
The amplitude after 25 oscillations is gotten by substituting x = 25 into the equation. Hence:
y = 10(0.02)²⁵
y= 3.355 * 10⁻⁴² cm
The amplitude after 25 oscillations is 3.355 * 10⁻⁴² cm
It mainly depends on the season of the year
It is the instantaneous speed of the bike rider.
Explanation:
At the mile marker, the measured speed gives the instantaneous speed of the bike rider.
The instantaneous speed is speed measured at a precise or instance of time.
Speed is the rate of change of distance with time. It is a scalar quantity that only shows magnitude with no reference to direction.
Velocity is the displacement divided by time. It has both magnitude and directions.
Average speed is measured over a period of time as the distance increases from the starting point.
From this, we can see that 13.5mph is the instantaneous speed of the bike rider.
learn more:
Instantaneous velocity brainly.com/question/2234298
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Speed=30 m/s - 1.5 m/s = 28.5 m/s forward
