Join the IDNLearn.com community and start finding the answers you need today. Discover comprehensive answers from knowledgeable members of our community, covering a wide range of topics to meet all your informational needs.
Sagot :
To find the rate at which the water level is rising, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height of the water.
Given that the radius is 1 and the length is 2, the volume V = π(1)^2(2) = 2π.
Since water is being pumped in at a rate of m^3 per minute, the rate of change of volume with respect to time is dm/dt = m.
To find the rate at which the water level is rising when the water is m deep, we can differentiate the volume formula with respect to time t: dV/dt = πr^2 dh/dt.
Substitute the known values:
2π = π(1)^2 dh/dt,
2 = dh/dt.
Therefore, the rate at which the water level is rising when the water is m deep is 2 units per minute.
Given that the radius is 1 and the length is 2, the volume V = π(1)^2(2) = 2π.
Since water is being pumped in at a rate of m^3 per minute, the rate of change of volume with respect to time is dm/dt = m.
To find the rate at which the water level is rising when the water is m deep, we can differentiate the volume formula with respect to time t: dV/dt = πr^2 dh/dt.
Substitute the known values:
2π = π(1)^2 dh/dt,
2 = dh/dt.
Therefore, the rate at which the water level is rising when the water is m deep is 2 units per minute.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.
