Answer:
a. F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy
b. W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy
Step-by-step explanation:
(a) Write down an integral for the total fluid force on the side of the tank.
We know force, F = ∫PdA where P = pressure and dA = differential area element in tank surface.
Let the position of the bottom of the tank be y = -h where h = height of tank and y = 0 be the top of the tank. So, the height of any point y of the tank H is y - (-h) = y + h = y + 10
The pressure P = ρgH where ρ = density of oil in tank = 51.2 lb/ft³ and g = acceleration due to gravity = 32 ft/s²
P = ρgH
P = ρg(y + 10)
The differential area element of a point on the side of the tank is dA = 2πrdy
So, F = ∫PdA
F = ∫ρg(y + 10)2πrdy
we integrate y from y = -h = -10 to y = 0
So, F = ∫₋₁₀⁰ρg(y + 10)2πrdy
F = ∫₋₁₀⁰2πrρg(y + 10)dy
F = ∫₋₁₀⁰2π(8 ft)(51.2 lb/ft³)(32 ft/s²)(y + 10)dy
F = ∫₋₁₀⁰26214.4π lb/ft-s²(y + 10)dy
F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy
(b) Suppose all the kerosene is pumped to ground level. Write down an integral for the work required to pump the oil.
The work done W = ∫F.dy
W = ∫F.dy
F = ρgV where V = volume of tank = πr²H = πr²(y + 10)
F = ρgπr²(y + 10)
So, W = ∫F.dy
W = ∫ρgπr²(y + 10).dy
Since the water is pumped to ground level, we integrate y from y = -h = -10 to y = 0
W = ∫₋₁₀⁰ρgπr²(y + 10).dy
W = ∫₋₁₀⁰π(51.2 lb/ft³)(32 ft/s²)(8 ft)²(y + 10).dy
W = ∫₋₁₀⁰104857.6π lb-ft/s²(y + 10).dy
W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy
Robin has a rectangular picture frame that is 8 1/2 by 11 inches. What is the
approximate perimeter of the picture frame in centimeters?
Answer: 99.06cm
Step-by-step explanation:
Note that 1 inch = 2.54cm
Therefore, we'll convert the sides of the frame in inches to cm. This will be:
8 1/2 inch = 8.5 × 2.54cm = 21.59cm
11inches = 11 × 2.54cm = 27.94cm
Therefore, the perimeter of a rectangle will be:
= 2(length + width)
= 2(27.94 + 21.59)
= 2(49.53)
= 99.06cm
what is the estamate 1/4 of 16
Answer:
4
Step-by-step explanation:
1/4 of 16 is the same as 16 divided by 4. 16 divided by four is 4.
Give the coordinates of point D.
A. (-2,-4)
B. (-4,2)
C. (-4,-2)
D. (4, -2)
What is the change in y?
Answer:
+4
Step-by-step explanation:
Answer:
-4.
Step-by-step explanation:
Change in y is 11 - 15 = -4 ( 7 - 11 = -4)
The owner of a restaurant wants to collect data to find out the customers' opinions on the variety of appetizers offered on the menu. Which group should she survey to collect the best data? ANSWERRR QUCIKK A.
thirty customers who asked to share their opinions of the appetizers with the chef
B.
fifty randomly selected customers who dined at the restaurant
C.
sixty members of the local community
D.
the first fifty customers who dine at the restaurant without ordering an appetizer
Fifty randomly selected customers who dined at the restaurant will be best to collect the data thus, option (B) is correct.
What is sampling?Sampling is collecting some items in a lot randomly to predict opinions about the lot.
For example; the Selection of goods, selection of people
Sampling is a useful technique because if we do it for all samples then it will take time and cost as well.
As per the given,
To find out the customers' opinions on the variety of appetizers offered on the menu we need to take randomly customers and the customers who dine at the restaurant because if they did not dine then they didn't know the verities.
The random selection gives the exact results.
Hence "Fifty randomly selected customers who dined at the restaurant will be best to collect the data".
To learn more about sampling,
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Match the equation below with the following graph.
a) What fraction is equal to 50% of
1/3
?
b) What fraction is equal to 75% of 1
?
In the figure, WM = MY = 11 in, and XM = MZ = 8 in. Is quadrilateral WXYZ a parallelogram? Why or why not?
Question 15 options:
A)
No, because the diagonals aren't congruent.
B)
No, because both diagonals bisect each other.
C)
There isn't enough information.
D)
Yes, because both diagonals bisect each other.
Answer:
Yes, because both diagonals bisect each other.
Step-by-step explanation:
correct on test
Answer:
yes
Step-by-step explanation:
help again asap thanks
Answer:
simplify
[tex] \frac{ - 168}{4} = - 42[/tex]
Escribe una operacion numérica para este modelo.
A. 4-(-2)
B. -4 - (-2)
C. -2 + 4
D. -2 + (-4)
Answer:
A. 4- (-2)
Step-by-step explanation:
suerte!!!!!!!
Help plz:)))I’ll mark u Brainliest
Answer:
4/5
Step-by-step explanation:
Given :
A right angled triangle with sides 24 , 3 and 40 .And we need to find the value of sinZ .
We know that , sine is the ratio of perpendicular and Hypotenuse. So that ,
[tex]:\implies[/tex] sinZ = p/h
[tex]:\implies[/tex] sin Z = 32/40
[tex]:\implies[/tex] sin Z = 4/5
Hence the renquired answer is 4/5.
write a function rule for the statement. The output is five times the input.
Answer:
y=5x
Step-by-step explanation:
If the input is x, then the out put is 5x. So y=5x
increased in price by 1/4. After the increase it was priced at £85 what was the original price of the tshirt?
Find the volume of the cylinder.
Round to the nearest tenth.
r = 5 cm
5 cm
V = [?] cm3
Enter the number that goes in the green box.
Enter
Answer:
392.7
Step-by-step explanation:
The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2} h[/tex]
It is given that the radius of the cylinder is 5 cm and the height of the cylinder is 5 cm also.
So, The volume of the cylinder = [tex]\pi r^{2} h[/tex]
= 3.14 x 5^2 x 5
= 3.14 x 125
= 392.7 cubics cm
Thus, The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm.
Learn more about volume;
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Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n rectangles. Calculate the approximation for each of the given function and interval below. (You may use calculator and keep the final numerical answer in decimals for this question) (a) (3 pts) R5, f(x) = x 2 + x on the interval [−1, 1]
Answer:
[tex]R_5=1.12[/tex]
Step-by-step explanation:
We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:
[tex]f(x)=x^2+x[/tex]
On the interval [-1, 1] using five equal rectangles.
Find the width of each rectangle:
[tex]\displaystyle \Delta x=\frac{1-(-1)}{5}=\frac{2}{5}[/tex]
List the x-coordinates starting with -1 and ending with 1 with increments of 2/5:
-1, -3/5, -1/5, 1/5, 3/5, 1.
Since we are find the right-hand approximation, we use the five coordinates on the right.
Evaluate the function for each value. This is shown in the table below.
Each area of each rectangle is its area (the y-value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function f(x) over the interval [-1, 1] using five equal rectangles is:
[tex]\displaystyle R_5=\frac{2}{5}\left(-0.24+-0.16+0.24+0.96+2)= 1.12[/tex]
Milton purchases a 5-gallon aquarium for his bedroom. To fill the aquarium with water, he uses a container with a capacity of 1 quart.How many times will Milton fill and empty the container before the
aquarium is full?
Answer:
5-gallon = 20 quarts
4 quarts is a gallon 4 x 5 = 20 quarts
A rectangle has the length of (3x + 4) cm with a width of (2x - 2) cm. What is the perimeter of the rectangle?
Answer:
Step-by-step explanation:
The table shows the depths of four plants.
Order the numbers from least to greatest.
Answer:
-20 3/4, - 15 1/2, - 14 3/4, - 1/4
Step-by-step explanation:
Given the depths :
-14 3/4, - 15 1/2, - 1/4, - 20 3/4
Ordering from least to greatest :
Since the numbers are negative; arranging the numbers as it would appear on a number line ; Large whole number negative values are always the least.
-20 3/4, - 15 1/2, - 14 3/4, - 1/4
6 friends share 10 pizzas equally plz help
Answer:
6/10 of the pizza.
Find the value of x.
Answer:
143
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
Answer:
A
Step-by-step explanation:
What is the area of the shape.
If a speedboat can travel 34 nautical miles in 2 hours, how far can it travel in 3 hours? Round your answer to the nearest tenth.
Answer:
(34 / 2) * 3 = 51 nautical miles
Step-by-step explanation:
(34/2) => Finds miles per hour
* 3 => Finds total miles traveled in 3 hours
Answer:
51
Step-by-step explanation:
1 hour= 17 nautical miles
2 hour= 34 nautical miles
3 hour= 51 nautical miles
12222222222222222222222222222
Answer:
what's the question
Step-by-step explanation:
is it multiplied divide add subtract
1. The shape shown below is dilated by a scale factor of 2.6. It is in the attachment that was included.
(a) Calculate the length of each side of the dilated image.
(b) Draw the new image and label it .
Answer:
L' = 26cm
W' = 39cm
Step-by-step explanation:
a) Given the dimension of the shape;
length L = 10cm
Width W = 15cm
After dilating by a scale factor os 2.6
New length L' = 2.6(10) = 26cm
New width = W' = 2.6(15) = 39cm
Hence the length of each sides of the dilated image are 26cm and 39cm
b) The new image will be similar to the given image but of with the resulting length gotten in (a).
Can someone please help?
Answer:
The one all the way to the right
Step-by-step explanation:
30 ÷ X = 6
30 ÷ 5 = 6
Consider point P(4, 2) and line l with equation −3x+4y=6 .
The equation of the line that passes through P and is parallel to l
Step-by-step explanation:
all working is above
hope that helps
daniel’s print shop purchased a new printer for 35,000 each year it depreciates at a rate of 5% how much will the printer be worth in 8 years
Answer:
$23,219.72
Step-by-step explanation:
ab^x
a: initial value
b: value remaining after depreciation per year (in percentage)
x: number of years that have passed
35000(0.95)^8= 23219.7151
Round to the nearest hundredth value:
About $23219.72
selecting a marble from a bag containing 50 marbles and 45 orange marbles
find 3 rational numbers between 1/3 and 1/2
