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A tank is full of water. Find the work required t…

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Problem 25 Hard Difficulty

A tank is full of water. Find the work required to pump the water out of the spout. In Exercises 25 and 26 use the fact that water weighs $ 62.5 lb/ft^3 $.

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 4

Work

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Video Transcript

because the first we need a familiar with us before me with the judge of the problem, we're gonna set about the coordinates. This is old waxes and access. I will sketch the shape of the ting from from a site B. So the highest age and, uh, the length of three. And the other thing is six. So have shaped here. That's the head of tank from the sudden. Well, suddenly you and we need to fund the equation of this The segments here when winds have fun, This equation here. So call this point it's 11 So Wyman's where wanted his toe m, which is Thea Slope comes experts extra and the plug in other values when they have it's equals three plus three wait times tops work. That's all the equation of this line called El The same ones segment. Phil, that's unreasonable. Okay, so the nothing next thing is to calculate to representing everything in a room is some. So if you did that divided volume by in hordes of the slices a thin slice and that why I be the height from the bond I flies of the water with thickness the other way so the volume off the knife slice the very things less isn't the pious square time step away and plugging this equation from over junction, and that equals two. Pi Got away times a two or three times Y plus three squares This part and the fours equals two volume times the weight per unit volume. It's a clock G. And there were given J equals two sensitive 15 pounds over Fit Cube. So the Force two, the Force exerting only life think slice is the item street, and that equals two senators quote. I didn't simplify the number, though, but we're going to check with the final result. Okay, so it's 562.5 or 64 pieds rather long times why I squared Woz. So here is actually what, plus eight What I plus eight square times that way. So that's the Force and the Force. The work equals to force. Thomas did this instead. It the things lice in the travel and for each thing for the items things slice, the business is gonna travel equals toe a minus y by. So now we have everything for a room. In some ways, this thing, and setting up over within seven equals two limits and goes to Infinity Force times. This isn't travel times Dad away, and we convert some to a ninja girl, which is from 0 to 8. That's a total recall. Visited the height of the of the tank and plan your battle here, which is a very lengthy expression. 462 on five over 64 times High times y plus Ace Wired Times A minus. Why? Because it's over d D. What? And after a long calculation, we're gonna have It's ah approximates 1.4 times 10 to the five, and the unit is feet.

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