Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A spherical water tank, 24 ft in in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long

Answers

Answer 1

Answer:

The time it will take is approximately 104,128 seconds

Step-by-step explanation:

The given parameters are;

The diameter of the tank, D = 24 ft.

Therefore, the tank radius, R = D/2 = 24 ft./2 = 12 ft.

The height of the tower on which the tank sits, h = 60 ft.

The hose through which the tank is filled is attached at the bottom of the tank

The radius of a slice of sphere, r = √(R² - y²) = √(12² - y²)

The power of the pump which is used to deliver the water = 1.5 horsepower

The volume of a slice of water in the tank, V = π·r²·Δx = π·(√(12² - y²))²·Δx ft³ = (144 - y²)·π·Δx ft³

The force of the slice, F = V·g·ρ = (144 - x²)·π·Δx ft³ × 62.5 lb/ft³

Let '[tex]y_i[/tex]' represent the height to which each slice is pumped in  the tank, we have;

y = R - (√(R² - x²)) = 12 - (√(144 - x²)

[tex]\lim\limits_{n \to \infty}\ \sum\limits_{i=0}^n (144 - x^2) \cdot \pi \times 62.5 \cdot y_i\ \Delta x \ lb[/tex]

The work done is therefore;

[tex]W = 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \cdot(12-(\sqrt{144-x^2} ) \ } \, dx = 632044.366475 \ ft. \cdot lb[/tex]

The work done in filling the tank, W = 632,044.366475 ft·lb

The work done in lifting the water to the base of the tank, W₂ = V·ρ·g×h

[tex]\therefore W_2 = 60 \times 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \ } \, dx = 632044.366475 \ ft. \cdot lb = 85273382.0257[/tex]

Therefore, W₂ = 85,273,382.0257 ft.lb

The total work done by the pump,

W = 85,273,382.0257 ft.lb + 632,044.366475 ft·lb = 85,905,426.3922 ft.lb

The time it will take the pump to fill the tank, 't', is given as follows;

1

Power, P = Work, W/(Time, t)

∴ t = W/P

P = 1.5 HP = 550 × 1.5 ft·lb/s = 825 ft·lb/s

t = 85,905,426.3922 ft.lb/(825 ft·lb/s) = 104,127.789566 s

The time it will take, t ≈ 104,128 seconds


Related Questions

There were 20 boys and 26 girls in a chess club last year. This year the number of boys increased by 30% but the number of girls decreased by 15%. Was there an increase or
decrease in overall membership?

Answers

Step-by-step explanation:

Boys

[tex]20 + (20 \div 100)30 = \\ = 20 + 0.2 \times 30 = \\ = 20 + 6 = \\26[/tex]

Girls

[tex]26 - (26 \div 100)15 = \\ = 26 - 0.26 \times 15 = \\ = 26 - 3.9 = \\ = 22[/tex]

Total last year 46

Total this year 48

Increase

I'm looking for the diagram related to question 5 ....pls if you can solve it correctly ,I will reward you as a brainlist ❤️​

Answers

Answer:

a. A capital letter that have corresponding angles is the letter 'E'

b. A capital letter that have alternate angles is the letter 'N'

Step-by-step explanation:

The capital letter 'F' is made two horizontal parallel lines that touch a common transversal. Therefore, in the letter F, the two horizontal parallel lines form corresponding angles with the transversal below each parallel line

Similarly, the letter Z form alternate angles below the horizontal parallel lines and the inclined diagonal

a. Another capital letter that have corresponding angles is the letter 'E'

b. Another capital letter that have alternate angles is the letter 'N'

Answer:

A

Step-by-step explanation:

the answer is a

At an ice cream shop, a person can choose from 3 different
sizes of cones, 5 different flavors, and 5 different toppings. If
you want to buy an ice cream in a cone with a topping,
How many different options are there when you are buying
ice cream?
______ options

Answers

Answer:

13

Step-by-step explanation:

3 + 5 + 5 = 13

that is the answer

I just need help with this question please

Answers

Answer:

71.286

Step-by-step explanation:

60 x .09 = 65.4

65.4 x .09 = 71.286

Answer:

$71.29

Step-by-step explanation:

$60 x 1.09 = $65.40 (year one)

$65.40 x 1.09 = $71.286 (year two)

Can y’all help me on question 27?!

Answers

Answer:

B and D

Step-by-step explanation:

A would be:

57 + 2j

C would be:

13-t

Which set of ordered pairs does not represent a function?
O {(3,4),(-9,5 (-3,8),(-2,8)}
O {(5,5), (5, -9),(-1,-8), (-4, – 7)}
O{(-5, -8), (0, -4),(-8,-8), (6,6)}
o{(-1,7), (1,8), (0, -3), (-4, -3)}

Answers

Answer:

B

Step-by-step explanation:

help me pls. answer correct

Answers

Answer:

1st answer is

[tex](x.y) = ( \frac{38}{5} . \frac{2}{5} ) \\ [/tex]

2nd answer is (x, y) =(36, 45)

Find the perimeter of quadrilateral ABCD. The side lengths are A (-3, 4), B (5, 4), C (5,-4), and D (-3, -4).

Answers

Answer:

32

Step-by-step explanation:

each line segment's distance is 8 (count them)

4 * 8 = 32

Need help on this please

Answers

Answer:

dff

Step-by-step explanation:

saf

what are the factors of ×^2+4×+3​

Answers

Answer:

(x+3)(x+1)

Step-by-step explanation:

I'm assuming you need to factorise?

Answer:

(x+1)(x+3)

if u want me to explain how it works let me know

If 50% of a number is 60, find 5% of that number.
i need it rn

Answers

Answer:

6

Step-by-step explanation:

if something has 60 as it's 50 percent, then 100 percent would be 120

now we have to find 5 percent of 120:

5/100 × 120= 6

Answer:

6

Step-by-step explanation:

Austin Use the distributive property to overwrite 18 + 54 which expression could the student use​

Answers

Answer:

18( 1 x 3 )

Step-by-step explanation:

find the greates common factor of 18 and 54

18

hope this helps

victor has 8/12 of a tank of gasoline left in his car. which fraction is greater than 8/12?

Answers

Answer:

5/6

Step-by-step explanation:

What is the value of xwhen ik o h)(r)
-1?
OA.
2
OB.
-3
O C. 1
OD.
4
I NEED HELP ASAP

Answers

Answer:

4

Step-by-step explanation:

Bob has 4,000 grams of sand. If his brother has one kilogram more than Bob, how many kilograms of sand does Bob's brother have?

Answers

Answer:

5 kg

Step-by-step explanation:

1 kg = 1000 g

4 kg = 4000 g

? kg = 5000 g

Find the solution(s) to the system of equations below:
3x - 5y = 3 and y = 3x2 - 4x + 1

Answers

Answer:

1,0

8/15,-7/25

Step-by-step explanation:

3x - 5y = 3

5y = 3x-3

y = (3x-3)/5

y= 3x² -4x +1

or, (3x-3)/5 = 3x²-4x +1

or, 3x-3 = 15x²-20x+5

or, 15x² - 23x +8 =0

or, 15x² - (15+8)x +8 =0

or, 15x² - 15x -8x +8 = 0

or, 15x (x - 1) -8(x-1) =0

or, (x-1)(15x-8)=0

Either,

x-1=0

x = 1

when x=1,

y= 0

or,

15x-8=0

x=8/15

when x= 8/15,

y= -7/25

The ratio of the vertical change to the horizontal change to any two points on a line is called _______ of the line

Answers

Answer:

The ratio of the vertical change to the horizontal change to any two points on a line is called ___slope___ of the line

Step-by-step explanation:

Slope will be your answer, hope this helps!


A water container was 1/4 full. Two litres of water was added. The container was then 1/3 full. How much did the container hold?

Answers

Answer:

Bárbara come la tercera parte de una caja de bombones. Su papá luego compra 7 bombones más y los pone en la caja. ¿Cómo se representa la cantidad de bombones que hay ahora en la caja?

Step-by-step explanation:

When 3 + 3x - 5 - 8x is simplified, the result is:
OOOO
-5X - 2.
-5x - 8.
- 11x - 15.
6x - 13x.

Answers

Answer:

A

Step-by-step explanation:

Can somebody pls help me on this one?

Answers

Here's link to the answer:

tinyurl.com/wpazsebu

help please and thanks

Answers

Answer:

I'm pretty sure the answer is 21/20 or 1.05

Jackie Chan is reviewing the total accounts receivable of his new department store in Hong Kong customers who paid with credit totaled $85,000 this month this represents 40% of our receivables do what is mr. Chan's total account receivable?

Answers

Answer:

Mr. Chan's total account receivable is of $212,500.

Step-by-step explanation:

$85,000 this month this represents 40% of our receivables

This means that 85000 is 40% = 0.4 of the receivables, which is x.

What is mr. Chan's total account receivable?

We have to find x

[tex]0.4x = 85000[/tex]

[tex]x = \frac{85000}{0.4}[/tex]

[tex]x = 212500[/tex]

Mr. Chan's total account receivable is of $212,500.

PLEASE I NEED HELP CLICK ON THIS IMAGE

Answers

Answer:

24 miles per hour

Step-by-step explanation:

144/6

= 24

Its 24 miles per hour

= 144 / 6
= 24

I know someone answered this already, i just want points

A rectangle with an area of 61 units” is dilated by a scale factor of ;. Find the area of
the rectangle after dilation. Round your answer to the nearest lenth, if necessary.

Answers

Answer:

34 units

Step-by-step explanation:

I decided that one side is 61 units and the other is 1 unit, since that would make the area 61 units.

Then I multiplied 61 by 3/4, which equals a new length of 45.75 units, and I also multiplied 1 by 3/4, which equals a new length of 0.75 units.

Finally, I solve for the area of the rectangle:

45.75 x 0.75 ≈ 34 units (rounded to the nearest whole number)


After sales tax, a $96 watch costs
$101.28. What is the sales tax
percentage?

A:6.2%
B:5.5%
C:5.2%
D:8.5%

Answers

101.28-96 = 5.28
5.28/96 = 0.055
0.055 x 100% = 5.5%

principal $2000 rate of interest 4% time 3 years

Answers

Answer:

principal =2000

rate of interest=4%

time=3 years

now,

P×T×R÷100

2000×4×3÷100

24000÷100

240....

Which of the following rules represents the function shown in the table?

Answers

Answer:

I do not know

Step-by-step explanation:

last problem had the wrong photo so heres the right one

Answers

Answer:

J

Step-by-step explanation:

1. y = mx + c ( equation of a straight line,where "c" is the y intercept, i.e, the y co-oridnate of where it cuts the y-axis)

2. It is now clear to see that the value of "c", the y co-ordinate of the point of intercept is 3, eliminating F and G as options

3. Substitute a given point into the equation y = mx + 3 to solve for "m", the gradient. I chose (3; 1) as it is the only visible point that lies on the straight line

4. Solve for "m" algebraically and you'll find that the gradient is -2/3

5. Substitute "m" back into the equation and you'll find that your equation is y = -2/3x + 3 or J

ALTERNATIVELY:

You could just find the value of "c" as stipulated above, which would leave you with H and J as options. But since you know the coefficient of x in the equation is the gradient, you can just tell by looking at the line whether or not it will have a positive or negative gradient. The gradient is negative since the line is sloping downwards, so you're only option is J.

23=5-2/3d then what is the value of 6d?

Answers

Answer:

-162

Step-by-step explanation:

23=5-2/3d

2/3d=-18

d= -27

6d= 6* -27

6d= -162

The lines graphed below are parallel.The slope of the red line is-4/3. What is the slope of the green line?​

Answers

Answer:

-4/3

Step-by-step explanation:

You know that parallel lines have the same slope. So, if both lines are parallel, then they must have the same slope.

Answer:

-4/3

Step-by-step explanation:

A line thats parallel with a line with a slope -4/3 will have the same slope because it is parallel so it has the same the degree of tilt/slope

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