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Let me put the times 2nd, insert, times just to make sure it understands that. T is measured in hours. That blockage just affects the rate the water comes out. So if you have your rate, this is the rate at which things are flowing into it, they give it in cubic feet per hour. 20 Gilligan C 1984 New Maps of Development New Visions of Maturity In S Chess A. The rate at which rainwater flows into a drainpipe of the pacific. Let me draw a little rainwater pipe here just so that we can visualize what's going on.
And I'm assuming that things are in radians here. And then close the parentheses and let the calculator munch on it a little bit. 09 and D of 3 is going to be approximately, let me get the calculator back out. The rate at which rainwater flows into a drainpipe youtube. And lucky for us we can use calculators in this section of the AP exam, so let's bring out a graphing calculator where we can evaluate definite integrals. So they're asking how many cubic feet of water flow into, so enter into the pipe, during the 8-hour time interval. So I'm gonna write 20sin of and just cuz it's easier for me to input x than t, I'm gonna use x, but if you just do this as sin of x squared over 35 dx you're gonna get the same value so you're going to get x squared divided by 35. Voiceover] The rate at which rainwater flows into a drainpipe is modeled by the function R, where R of t is equal to 20sin of t squared over 35 cubic feet per hour. In part one, wouldn't you need to account for the water blockage not letting water flow into the top because its already full?
Well, what would make it increasing? So this is approximately 5. For part b, since the d(t) and r(t) indicates the rate of flow, why can't we just calc r(3) - d(3) to see the whether the answer is positive or negative? Let me be clear, so amount, if R of t greater than, actually let me write it this way, if R of 3, t equals 3 cuz t is given in hour. 96t cubic feet per hour. Then water in pipe decreasing. 6. layer is significantly affected by these changes Other repositories that store. Well if the rate at which things are going in is larger than the rate of things going out, then the amount of water would be increasing. I don't think I can recall a time when I was asked to use degree mode in calc class, except for maybe with some problems involving finding lengths of sides using tangent, cosines and sine. In part A, why didn't you add the initial variable of 30 to your final answer? The rate at which rainwater flows into a drainpipe edinburgh news. So D of 3 is greater than R of 3, so water decreasing. Provide step-by-step explanations. So I already put my calculator in radian mode. But if it's the other way around, if we're draining faster at t equals 3, then things are flowing into the pipe, well then the amount of water would be decreasing.
You can tell the difference between radians and degrees by looking for the. So that is my function there. Alright, so we know the rate, the rate that things flow into the rainwater pipe. Then you say what variable is the variable that you're integrating with respect to.
Is the amount of water in the pipe increasing or decreasing at time t is equal to 3 hours? °, it will be degrees. But these are the rates of entry and the rates of exiting.
That is why there are 2 different equations, I'm assuming the blockage is somewhere inside the pipe. Gauth Tutor Solution. It does not specifically say that the top is blocked, it just says its blocked somewhere. So that means that water in pipe, let me right then, then water in pipe Increasing. AP®︎/College Calculus AB. Check the full answer on App Gauthmath. 1 Which of the following are examples of out of band device management Choose. Crop a question and search for answer. Close that parentheses. At4:30, you calculated the answer in radians. R of 3 is equal to, well let me get my calculator out. When in doubt, assume radians.
I would really be grateful if someone could post a solution to this question. And the way that you do it is you first define the function, then you put a comma. After teaching a group of nurses working at the womens health clinic about the. If you multiply times some change in time, even an infinitesimally small change in time, so Dt, this is the amount that flows in over that very small change in time. 89 Quantum Statistics in Classical Limit The preceding analysis regarding the. We're draining faster than we're getting water into it so water is decreasing.
Gauthmath helper for Chrome. Does the answer help you? For the same interval right over here, there are 30 cubic feet of water in the pipe at time t equals 0. So we just have to evaluate these functions at 3. And so what we wanna do is we wanna sum up these amounts over very small changes in time to go from time is equal to 0, all the way to time is equal to 8. The result of question a should be 76. Is there a way to merge these two different functions into one single function? T is measured in hours and 0 is less than or equal to t, which is less than or equal to 8, so t is gonna go between 0 and 8.
Good Question ( 148). Usually for AP calculus classes you can assume that your calculator needs to be in radian mode unless otherwise stated or if all of the angle measurements are in degrees. Otherwise it will always be radians. Sorry for nitpicking but stating what is the unit is very important. If the numbers of an angle measure are followed by a. Grade 11 · 2023-01-29.
Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e. g., in search results, to enrich docs, and more. So if that is the pipe right over there, things are flowing in at a rate of R of t, and things are flowing out at a rate of D of t. And they even tell us that there is 30 cubic feet of water right in the beginning. Actually, I don't know if it's going to understand. Still have questions? Almost all mathematicians use radians by default.