Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

An oil storage tank ruptures at time $ t = 0 $ and oil leaks from the tank at a rate of $ r(t) = 100e^{-0.01t} $ liters per minute. How much oil leaks out during the first hour?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

4512 liters

02:14

Frank Lin

01:15

Amrita Bhasin

04:26

Jacquelyn Trost

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

0:00

An oil storage tank ruptur…

02:46

00:52

01:12

02:35

06:16

Oil is leaking out of a ru…

04:45

Oil is leaking at the rate…

02:11

If oil leaks from a tank a…

have a question ah in this it is given that the oil is tourist tank ruptures at equal to zero. That is People to zero. It starts leaking an oil leak from the tank at a rate of so rate of oil leaking is equal to 100 Areas to the Power -0.01 T Letters. But a minute. So how much I like it. This is the rate of our licking. So let us write it as D. V. By DT. That is volume because volumizing leaders. So that is this is the rate of decreasing, decreasing of volume for tv by DT equal to it is given it like this but Dave ability should be negative as it is leaking so volume will be decreasing. So we should write D by D. T. Equal to minus 100 areas of the power -0.01. The so D. B will be equal to minus and did areas to the power minus 0.0 and T. D. T. Now we have to integrate to get all the values. So integrating that went equal to zero Like it had just started. So it should be zero Went equal to first hour, that is 16 minutes. This is the which means volume will be called to minus hinted From limited 0 to 60. Areas of the Power -0.01 T. Mhm. So this is mine is ended. Here is the power -0.01. T divide by minus 0.01 from limit 0 to 60. This will be minus and minus will become place hunted by 0.01. and areas to the power -0.01 T from 0 to 60. Okay, This will become 10,000. And let us start plugging in the limits -0.01 into 60- It is to the power -0.01 in 20. Okay, so 10,000 and it is the power it would become it is really power uh -0.6 you have to use and collected. It is the power the he used to be published minus blind stick and minus one -15 into 1000 king. Yeah. Okay let's do it again. It is the bottom line is sick and then it is to the farmers minus but I'm sick minus one into and tell him this is 4000 500 11 point aided with negative side later 10 shoulder. This much volume is lost or leaked during the first star approximately it is 4511 point 88 liters. Thank you

View More Answers From This Book

Find Another Textbook

02:18

Atmospheric pressure P in pounds per square inch is represented by …

01:44

Find the y-intercept for this function. Explain what this value mean…

01:20

If a loading ramp is placed next to a truck, at a height of 7feet, and t…