An aquarium 4 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3). Show how to approximate the required work by a Riemann sum.
Express the work as an integral.
Evaluate the integral.

Answers

Answer 1

Answer:

Workdone = 4900joules

Step-by-step explanation:

Work-done = force x distance

Force = mass x acceleration

If we suppose that the aquarium is at height 0 at the top and height 1 at the bottom (since it's 1m deep), then we need to lift the slide at height x by x metres.

Mass = Density x Volume, therefore force needed to lift the slice is given is

F = density*volume*∆x*acceleration

Since we the mass changes as we take out water then there will be a change in height, for this reason we have ∆x.

Acceleration is due to gravity, therefore g=9.8m/s²

Density = 1000kg/m³

Volume = 4*1*1 = 4m³

F = 1000*4*∆x*9.8 = 39200∆x

Since our distance from the top of the aquarium to the bottom is x metres, then

Work-done = 39200x∆x

To find the total workdone, we find the integral of 39200xdx and the limit will be from 0 to 0.5 since we are to pump halfway of the aquarium. Integrating that we have

19600*x² limit from 0 to 0.5

19600(0.5² – 0²) = 19600(0.25 – 0) = 19600(0.25) = 4900joules


Related Questions

Answer please 10 points

Answers

Answer:

3/4 to 9/6

Step-by-step explanation:

Plot points on the number line to represent all whole numbers that round to 200 to the nearest hundred and 250 when rounded to the nearest ten.

Answers

Answer:

To round a number to the nearest hundred, you make it into the hundred that is closest. Take the number 246, for example, which is between 200 and 300. It is closer to 200. So 246 rounded to the nearest hundred is 200.

explain C = 15 + 0.6Yd

Answers

explain what exactly ? are we solving for a variable ?

What are the solution(s) to the quadratic equation 40 - x2 = 0?
O x = +2/10
O x = +4/10
O x = +2/5
x = +4V5

Answers

Answer:

±2sqrt(10)

Step-by-step explanation:

40 - x^2 = 0

Add x^2 to each side

40 -x^2 + x^2 = x^2

40 =x^2

Take the square root of each side

±sqrt(40) =sqrt(x^2)

±sqrt(4)sqrt(10) =x

±2sqrt(10) =x

What is -3v = 15 like I need this answer!!

Answers

Answer:

v = -5

Step-by-step explanation:

Answer:

v=-5

Step-by-step explanation:

-3 times -5= 15


Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term
is two times the fifth term. Find the common difference and the first term.


Answers

Answer:

The first term is -6 and common difference is 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

Tn = a + (n-1)d

T3 = a+2d

T4 = a + 3d

If the third term of an arithmetic sequence less than the fourth term by three

T3 = T4 - 3

a+2d = a+3d - 3

2d - 3d = -3

-d  = -3

d = 3

Similarly;

T7 = a+6d

T5 = a+4d

If the seventh term  is two times the fifth term, the;

T7 = 2T5

a+6d = 2(a+4d)

a+6d = 2a+8d

Since d = 3

a + 6(3) = 2a + 8(3)

a+18 = 2a + 24

a-2a = 24 - 18

-a = 6

a = -6

Hence the first term is -6 and common difference is 3

What is the length of side 'y'?

Answers

Answer:

B

Step-by-step explanation:

You are a plumber who needs to replace a broken pipe that is 12.5 feet long. You have 2 pipes, A and B, that are
3.75 meters and 4.25 meters long, respectively. A pipe longer than the broken pipe can be cut to fit.
Which pipe can be used to complete the task, and why?

Answers

Answer:

the 4.25 m pipe because it is longer than 12.5 feet. The 3.75 m pipe is too short

Step-by-step explanation:

In which choice do all three points lie on the same straight line?
A. (0, 1), (-1, 3), (1, 3)
B. (4, 2), (2, 1), (4, -2)
C. (0, 0), (8, 0), (0, 8)
D. (1, 2), (2, 4), (4, 8)

Answers

I think the answer is D

Find the circumference of the circle to the nearest tenth.
C
6 cm

Answers

I assume the radius is 6 cm.

Diameter = 2 times the radius.

D = 12 cm.

We now use C = pi•D.

C = pi•12cm

C = 12pi cm

Done!

Count the units from (2,4) to (-2,-6).How many blocks are between Jenna’s apartment and Zac’s house

Answers

Answer:

Distance = 10.77 unit (Approx.

Step-by-step explanation:

Given:

Coordinate of Jenna's house = (2,4)

Coordinate of Zac's house = (-2,-6)

Find:

Distance

Computation:

Distance = √(X1 - X2)² + (Y1 - Y2)²

Distance = √(2 + 2)² + (4 + 6)²

Distance = √(2 + 2)² + (10)²

Distance = √16 + 100

Distance = √116

Distance = 10.77 unit (Approx.

Find the quadratic root of 3 x² - 4x + 2​

Answers

Answer:

it has no real roots.

and the 2nd answer is correct.

Step-by-step explanation:

Answer:

this quadratic equation has two roots:

x = (2+i√(2))/3 , (2-i√(2))/3

Steps:

3x²-4x+2​=0

x = (4±√((-4)²-4×3×2))/2×3

x = (4±√(16-24))/6

x = (4±√(-8))/6

x = (4±√(-2×4))/6

x = (4±√(-2)×√(4))/6

x = (4±i√(2)×2)/6

x = (2±i√(2))/3

x = (2+i√(2))/3 , (2-i√(2))/3

4.
What equation has the missing number?
50/5=
?
a. 50 x 5 =
b. 50-5=
c. 5+) = 50
d. 5x = 50

Answers

I believe it’s B, i may be wrong. I’m not entirely sure what this question is asking

I need help on this!!

Answers

Answer:

C and A

Step-by-step explanation:

Part 1.

The area of a trapezoid is base 1 + base 2 divided by 2 times height.

Base 1 is 38, base 2 is 14, and the height is 16.

38 + 14 = 52, 52 / 2 = 26, and 26 x 16 = 416.

The answer is C, 416.

Part 2.

The area of a kite is diagonal 1 times diagonal 2 divided by 2. The length of diagonal 1 is 12 (on the left) + 12 (on the right) = 24. The length of diagonal 2 is 10 (on the top) + 18 (on the bottom) = 28.

28 x 24 / 2 = 336.

The answer is A, 336

Answer:

336

Step-by-step explanation:

In the figure, there are four triangles

Total Area = sum of four triangles areas

0.5(12*18)*2+0.5(12*10)*2=336

You have $2,000 on a credit card that charges a 17% interest rate. If you want to pay off the credit card in 4 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? Disclaimer: this is treating credit cards as an amortized loan, which they are not.

Answers

Answer:

$65?

Step-by-step explanation:

You work as a residential painter. A customer wants two tables and eight chairs painted using one coat of the same color paint. Each table requires 15858 quarts of paint, and each chair requires 2323 quarts of paint. How many total quarts of paint should you bring to paint this furniture?

Answers

Step-by-step explanation:

Let t be the number of tables

Let c be the number of chairs

Total paint needed = 15858t + 2323c

Given t = 2 and c = 8, substitute t and c into expression to find total paint needed

Total Paint needed = 15858(2) + 2323(8)

= 31716 + 18584

= 50300 quarts of paint

A 2-ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 74 ft. How much farther does a wheel on the outer travel than a wheel on the inner rail of the track in one turn ?

Answers

Answer:

As we know the formula for "Circumference of circle": Since we have also mentioned that there is 2 feet wide circular track for a camera dolly. Therefore, A wheel on the outer rail travel 12.57 ft more than a wheel on the inner rail of the track.

Step-by-step explanation:

i hope it helped

please help me I will give a brainlist​

Answers

Answer:

I think this is helpful .

Simplify the expression:
[tex] ({2x + 5y})^{2} - ({3x + 4y})^{2} [/tex]

Answers

Step-by-step explanation:

the answer is in the picture

Answer:

3x+18y

Step-by-step explanation:

2x+5y+2x+5y-3x+4y+3x+4y

2x+2x-3x+3x+5y+5y+4y+4y

4x-x+10y+8y

3x+18y

Which of the given numbers is not a Pythagorean triplets. *

1 point

8,15,17

9,40,41

4,7,8​

Answers

Step-by-step explanation:

By Pythagoras' Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is always the largest number.

a and b can be interchangeable between the 2nd largest and the 3rd largest numbers.

Given a = 8, b = 15 and c = 17,

[tex] {a}^{2} + b {}^{2} = {8}^{2} + {15}^{2} \\ = 64 + 225 \\ = 289 \\ \\ {c}^{2} = {17}^{2} \\ = 289[/tex]

Since c^2 = a^2 + b^2 , 8 , 15 and 17 are pythagorean triplets.

Now let's move on to 9, 40 and 41.

[tex] {a}^{2} + {b}^{2} = {9}^{2} + {40}^{2} \\ = 81 + 1600 \\ = 1681 \\ \\ {c}^{2} = {41}^{2} \\ = 1681[/tex]

Since c^2 = a^2 + b^2 , 9 , 40 and 41 are pythagorean triplets.

Last let's move on to 4,7 and 8.

[tex] {a}^{2} + {b}^{2} = {4}^{2} + {7}^{2} \\ = 16 + 49 \\ = 65 \\ \\ {c}^{2} = {8}^{2} \\ = 64 [/tex]

Since a^2+b^2 IS NOT EQUAL to c^2, 4,7 and 8 ARE NOT pythagorean triplets.

The probability that lucy will do. The drawing is 0.125. What is the probability that she will not win

Answers

Answer:

probability is alway 1 or less than 1

therefore the probability is 0.125/1

"Fifty-seven more than two times j"

Answers

Answer:

2j+57

Step-by-step explanation:

Two times a umber j is expressed as 2j

if Fifty-seven is more than two times j", this means we will have to add 57 to 2j as shown;

f(j) = 2j + 57

Hence the statement written as a function is expressed as 2j+57

the co-terminal angle of -120°​

Answers

Answer:

-480°, 240° (among others)

Step-by-step explanation:

± 360

Find the area of a parallelogram with vertices (-7, 2), (6, 2), (6, -5), and (-7, -5). Use the coordinate grid below to help you find your answer.

Answers

Answer:91

Step-by-step explanation:

w + what - s = w
help plz help helppp i want help

Answers

Answer: S

Step-by-step explanation:

w + ? - s = w

w + s - s = w

w = w

Which sequence is modeled by the graph below? (6 points)

Answers

Answer:

Step-by-step explanation:

if you help me you are a sweet sweet sweet angel

Answers

Answer:

the last option

option four or D

Step-by-step explanation:

have a great day :)


Dylan is creating clay at home for an art project. The recipe calls for 6 cups of water and 5.5 cups of flour. Dylan would like to make more clay than the recipe calls for and so he puts 44 cups of flour in the bowl instead. How many cups of water should he use?

Answers

Answer:

48 cups of water

Step-by-step explanation:

Using the provided ratio of 6:5.5...

if 6:5.5

then

48:44

This is relative frequency tables. Can someone help ?

Answers

Answer:

87 is the answer

Hope it helps!!!

Step-by-step explanation:

Below is the graph of f(x) = 3 log10^ x. How would you describe the graph of
g(x) = 9 log10^x?
A. g(x) shifts f(x) to the right 3 units.
B. g(x) shifts f(x) up 3 units.
C. g(x) compresses f(x) by a factor of 3.
O
D. g(x) stretches f(x) vertically by a factor of 3

Answers

Answer:c

Step-by-step explanation:

Answer:D g(x) stretches f(x) vertically by a factor of 3.

Step-by-step explanation: ape3

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