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2 years ago

How to find the derivative of an integral with bounds.

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

3 0

Answer:

The statement of the fundamental theorem of calculus shows the upper limit of the integral as exactly the variable of differentiation. Using the chain rule in combination with the fundamental theorem of calculus we may find derivatives of integrals for which one or the other limit of integration is a function of the variable of differentiation.

Step-by-step explanation:

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A tank can be filled by one pump in 3.2 hours and by another pump in 80 minutes. A third pump can drain the tank in 2 hours and

Mademuasel [1]

Answer:

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.

Step-by-step explanation:

Let's convert each time to minutes:

3.2 hours = 192 minutes

80 minutes = 80 minutes

2 hr 20 min = 140 minutes

Next, let's find the least common multiple:

LCM(192, 80, 140) = 6720

So let's say the volume of the tank is 6720 units. The speed of each pump is therefore:

Pump 1 = 6720 units / 192 minutes = 35 units/minute

Pump 2 = 6720 units / 80 minutes = 84 units/minute

Pump 3 = -6720 units / 140 minutes = -48 units/minute

Their combined speed is:

35 + 84 − 48 = 71 units/minute

So the time to fill the tank is:

6720 units / (71 units/minute) = 94.65 minutes

Rounding to the nearest minute, it would take 95 minutes, or 1 hour and 35 minutes.

6 0

3 years ago

A steel worker dropped his wrench off the top of a new high rise building. How far will the wrench fall in 3 seconds?

rosijanka [135]

Using S = ut + 1/2gt², from rest, u = 0

S = 1/2gt², g ≈ 9.8 m/s²

S = 1/2 *9.8*3²

S = 0.5 *9.8*3*3

S ≈ 44.1 m

6 0

3 years ago

The graphs below are based on government data on unemployment for 2017.

lord [1]

You already got the first two questions right: the group with the highest number of people unemployed / unemployment rate is the one with the highest bar in the respective histogram.

The two graph are related in this sense: take the first age group as reference. We know that 700 people from 16 to 19 are unemployed, and that those people represent 14% of the population, then we know that the 14% of the population between 16 and 19 is 700.

We can deduce that, if x is the number of people between 16 and 19, we have

$\dfrac{14}{100}x=700 \iff \dfrac{7}{50}x=700 \iff \dfrac{x}{50}=100 \iff x=5000$

So, by the relation between the two graphs, we can deduce the total population for each age group.

3 0

3 years ago

Diego is solving this system of equations:

USPshnik [31]

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 = 10

Multiply the terms

4x + 6 = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

Learn more about elimination method here

brainly.com/question/14619835

#SPJ1

7 0

1 year ago

10/12 - 11/12=??? I just want to correct my homework.

tangare [24]

Answer:

-1/12

Step-by-step explanation:

you jus gotta substract and jawnt uerme! i know you got dis wrong, dont bluff cutie...

5 0

3 years ago

Read 2 more answers