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
Which of the following rules represents the function shown in the table?
Answer:
I do not know
Step-by-step explanation:
23=5-2/3d then what is the value of 6d?
Answer:
-162
Step-by-step explanation:
23=5-2/3d
2/3d=-18
d= -27
6d= 6* -27
6d= -162
what are the factors of ×^2+4×+3
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
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?
Answer:
5 kg
Step-by-step explanation:
1 kg = 1000 g
4 kg = 4000 g
? kg = 5000 g
Need help on this please
Answer:
dff
Step-by-step explanation:
saf
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?
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.
The lines graphed below are parallel.The slope of the red line is-4/3. What is the slope of the green line?
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
I just need help with this question please
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)
I'm looking for the diagram related to question 5 ....pls if you can solve it correctly ,I will reward you as a brainlist ❤️
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
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.
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)
When 3 + 3x - 5 - 8x is simplified, the result is:
OOOO
-5X - 2.
-5x - 8.
- 11x - 15.
6x - 13x.
Answer:
A
Step-by-step explanation:
Austin Use the distributive property to overwrite 18 + 54 which expression could the student use
Answer:
18( 1 x 3 )
Step-by-step explanation:
find the greates common factor of 18 and 54
18
hope this helps
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answer:
24 miles per hour
Step-by-step explanation:
144/6
= 24
principal $2000 rate of interest 4% time 3 years
Answer:
principal =2000
rate of interest=4%
time=3 years
now,
P×T×R÷100
2000×4×3÷100
24000÷100
240....
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?
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:
The ratio of the vertical change to the horizontal change to any two points on a line is called _______ of the line
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!
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
Answer:
13
Step-by-step explanation:
3 + 5 + 5 = 13
that is the answer
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?
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
help please and thanks
Answer:
I'm pretty sure the answer is 21/20 or 1.05
What is the value of xwhen ik o h)(r)
-1?
OA.
2
OB.
-3
O C. 1
OD.
4
I NEED HELP ASAP
Answer:
4
Step-by-step explanation:
If 50% of a number is 60, find 5% of that number.
i need it rn
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:
help me pls. answer correct
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).
Answer:
32
Step-by-step explanation:
each line segment's distance is 8 (count them)
4 * 8 = 32
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%
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)}
Answer:
B
Step-by-step explanation:
Can somebody pls help me on this one?
Here's link to the answer:
tinyurl.com/wpazsebu
Can y’all help me on question 27?!
Answer:
B and D
Step-by-step explanation:
A would be:
57 + 2j
C would be:
13-t
victor has 8/12 of a tank of gasoline left in his car. which fraction is greater than 8/12?
Answer:
5/6
Step-by-step explanation:
last problem had the wrong photo so heres the right one
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.
Find the solution(s) to the system of equations below:
3x - 5y = 3 and y = 3x2 - 4x + 1
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