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
If f(x) = 3x - 2 and g(x) = -x + 4, find (g o f)(x).
Answer:
-3x + 6
Step-by-step explanation:
(gof) = -(3x-2)+4
= -3x + 2 + 4
= -3x + 6
Help with #9 pleaseeee
Answer:
9' - 1.29"
Step-by-step explanation:
Total rise = 5' - 2"
Total run = 7' - 6"
1' = 12" = 1 feet = 12 inches
5' = 5 * 12 = 60"
3' = 7 * 12 = 84"
Total rise = 60" + 72" = 62"
Total run = 84" + 6" = 90"
Length of stringer = hypotenus
Hypotenus = √(total rise² + total run²)
Hypotenus = √(62² + 90²)
Hypotenus = 109.28860"
Convwrting back to feet and inches
= 9' - 1.29"
A UW Madison professor is interested in learning about the variance of grades for university students. The professor gathers the sample variance for a random sample of 50 students. From past experience, the professor knows that the population of students is normally distributed. The sample variance that is collected is equal to 80. The professor would like to infer at the 1% significance level that the population variance is less than 100.
a. State the appropriate null and alternative hypothesis.
b. What is the correct test statistic?
c. What is the conclusion of the test?
d. What would be the effect if the professor increased the sample size?
Answer:
A) H0 : μ = 100
H1 : μ < 100
B) 39.2
C) We fail to reject null hypothesis
D) If the professor increases the sample size the value of the test statistic will increase .
Step-by-step explanation:
sample variance ( s ) = 80
sample size = 50
At ∝ = 0.01 population variance ( σ ) < 100
a) Hypothesis
H0 : μ = 100 ( Null hypothesis )
H1 : μ < 100 ( Alternate hypothesis )
b) Determine The correct test statistic
x^2 = ( n-1 ) * s^2/σ^2
= ( 49 ) * 80^2 / 100^2
= 39.2
C) Determine the conclusion of the test
The P-value = 0.1596 ( calculated )
The conclusion of the test is that we fail to reject null hypothesis given that
P-value ( 0.1596 ) > ∝ ( 0.01 )
D) If the professor increases the sample size the value of the test statistic will increase .
Which series is convergent? Check all that apply.
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction 2 n Over n + 1 EndFraction
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction n squared minus 1 Over n minus 2 EndFraction
Sigma-summation Underscript n = 1 Overscript infinity EndScripts (one-fifth) Superscript n
Sigma-summation Underscript n = 1 Overscript infinity EndScripts 3 (StartFraction 1 Over 10 EndFraction) Superscript n
Sigma-summation Underscript n = 1 Overscript infinity EndScripts StartFraction 1 Over 10 EndFraction (3) Superscript n
There are 2 correct answers
Answer:
Step-by-step explanation:
c
Answer choices)
A. (2/3x, 2/3y)
B. (3/2x, 3/2y)
C. (1/2x, 1/2y)
D. (2x, 2y)
Please help me :((
9514 1404 393
Answer:
B. (3/2x, 3/2y)
Step-by-step explanation:
It is perhaps easiest to see that B' is 3 grid squares from the origin while B is 2 grid squares from the origin. The scale factor is the ratio of these distances:
3/2
Dilation about the origin multiplies each coordinate value by the scale factor:
(x, y) ⇒ (3/2x, 3/2y)
Domain and range
What is the Domain and Range of the Relation
y = -5
Answer:
D: {all reals}
R: {-5}
Step-by-step explanation:
PLEASE ANSWER WHOEVER ANSWERS CORRECT I WILL GIVE 60 POINTS! Graph using as many points as needed y=|x-3|+5
Answer:
---
Step-by-step explanation:
hope it helps
Answer:
Transition:
1) The vertex point moves 3 steps to the right
2) Then, it goes up 5 steps
This equation is positive so the graph will face upwards.
The vertex will end up as: (3, 5)
The two other points will be:
Point 1 - (2,6)
Point 2 - (4,6)
Find the value of x
Answer:
Hello! answer: x = 4
Step-by-step explanation:
Because this is a 180 degree angle it will add up to 180 so 8 × 4 = 32 and 32 + 120 = 152 and 7 × 4 = 28 and 28 + 152 = 180 so 4 is x HOPE THAT HELPS!!
180 degree line-
180 = (8x + 120)
-120
60 = 8x
/8
7.5
x = 7.5
7(7.5) = 52.5
A company has machinery calibrated for a certain widget to manufacture the product so that all of the products will average out to a mean weight of 7 grams and a standard deviation of 2 grams. What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?
Answer:
By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 7 grams and a standard deviation of 2 grams.
This means that [tex]\mu = 7, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?
By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.
Order the numbers from least to greatest 41/50, 0.83, 80%
Answer:
80%, 41/50, 0.83
Step-by-step explanation:
80% = 0.80
41/50 = 0.82
0.83 = 0.83
An airline flying to a Midwest destination can sell 20 coach-class tickets per day at a price of $250 and ten business-class tickets per day at a price of $750. It finds that for each $10 decrease in the price of the coach ticket, it will sell four more per day, and for each $50 decrease in the business-class price, it will sell two more per day. What prices should the airline charge for the coach and business-class tickets to maximize revenue? [Hint: Let x be the number of $10 price decreases for coach tickets and y be the number of $50 price decreases for business-class tickets, and use the methods in this example and this example for each type of car.]
Solution :
Let x = number of coach class tickets sold per day on $ 10 reduced price
y = number of the business class tickets sold per day on $ 50 reduced per price.
Number of the coach class tickets sold = 20 per day at a price of $ 250
Number of the business class tickets sold = 10 per day at a price of $ 750
Decrease in the price of coach class tickets by $ 10 increases the number of tickets sold by 4 per day
Decrease in the price of business class tickets by $ 50 increases the number of tickets sold by 2 per day.
Therefore, the coach price, p(x) = 250 - 10x
Business class price, p(y) = 750 - 50y
Coach tickets, q(x) = 2 + 4x
Business class tickets, q(y) = 6 + 2y
Revenue R(x, y) = p(x) q(x) + q(y) q(y)
R(x, y) = (250-10x)(20+4x)+(750-50y)(6+2y)
R(x) = (250-10x)(0.4)+(20+4x)(-10)+0 = 0
1000-40x-200-40x=0
80x = 800
x = 10
R(y) = 0 + (750 - 50y)(0.2) + (6+2y)(-50) = 0
1500 - 100y+(-300-100y) = 0
200 y = 1200
y = 6
P(x) = 250 - 10(10) = $ 150
P(y) = 780-50(6) = $450
q(x) = 20 + 4(10) = 60
q(y) = 6 + 2(6) = 18
Maximum revenue = 150 x 60 + 450 x 18
= 9000 + 8100
= $ 17100
Must show work, please helppp
i can't see the photo.
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Answer:
1/2
Step-by-step explanation:
The base of the exponent tells us the common ratio of this geometric series is 1/2. The start value of n=7 tells us the first term in the series we're evaluating is ...
a1 = 2(1/2)^(7-4) = 2·(1/2)^3 = 2/8 = 1/4
The formula for the infinite sum of a geometric series is ...
S = a1(1/(1-r))
Filling in the values we know, this is ...
S = (1/4)(1/(1 -1/2)) = (1/4)(2) = 1/2
The infinite sum is 1/2.
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Answer:
y = (4/7)x + 3
Step-by-step explanation:
rise = 7 - 3 = 4
run = 7 - 0 = 7
slope = rise/run = 4/7
y-intercept = 3
---------------------
Slope intercept form is
y = mx + b
m is the slope = 4/7
b is the y-intercept = 3
the equation is
y = (4/7)x + 3
Convert:
5 pt 1 c= __c
ok heres the other one...
Step-by-step explanation:
Think of every surface as a 2D shape.
you know that
Area of a triangle is: A = 0.5 b h
Area of a square is: A = L x W
You add each area thats exposed
for example: the front and back of the triangle would be (0.5 x 3cm x 8cm) x 2 [since there are two faces]
Select the correct answer from each drop-down menu
The table shows the number of books Lucy borrowed from the library each month for a year
Month Number of Books
Month
Number of Books
January
14
6
February
8
July
August
September
19
March
16
12
April
14
October
May
8
November
7
June
7
December
Lucy bomowed the most books in
There were months in which she borowed fewer than 10 books
Answer:
6 Months where she borrowed less than 10,
and he borrowed the most books in August.
Step-by-step explanation:
How do your write a feaction with a denominator of 20 as a decimal?
Answer:
Step-by-step explanation:
What is 20 as a decimal? To write 20 as a decimal you have to divide numerator by the denominator of the fraction. 20 is not a fraction so it is a decimal already. And finally we have: 20 as a decimal equals 20
Plzzzzz help for a brainly
Answer:
20cmStep-by-step explanation:
120/6=20
Answer:
20cm
Step-by-step explanation:
120/6 = 20
How do we find the perimeter of a shape 20mm 10mm 20mm 60mm 20mm
Answer:
130mm
Step-by-step explanation:
I'm pretty sure you mean each of the sides is this length... so I'll go off of that. 20+10+20+60+20 is the addition for this problem.
20+10+20+60+20=130 is the answer.
Two parallel lines cut by a transversal are shown. What is the measure of X"?
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Answer:
x = 10
Step-by-step explanation:
The marked angles are "alternate interior" angles, so are congruent.
(x° +20°) = (4x° -10°)
30 = 3x . . . . . . . . . . . . . . . divide by °, add 10-x
10 = x . . . . . . divide by 3
A woman is thrice as old as her daughter. 12 years hence, she will be twice as old as her daughter find their present age.
help me
with explanation !!!
Answer:
Their present ages are:
Her daughter's age = 12 years Women's age = 36 yearsStep-by-step explanation:
Given that:
A woman is thrice as old as her daughter. 12 years hence, she will be twice as old as her daughter.To Find:
Their present ages.Let us assume:
Her daughter age be x. Women's age = 3xAfter 12 years:
Her daughter's age = x + 12Women's age = 3x + 12Finding their present ages:
According to the question.
⇒ 3x + 12 = 2(x + 12)
⇒ 3x + 12 = 2x + 24
⇒ 3x - 2x = 24 - 12
⇒ x = 12
Their present ages:
Her daughter's age = x = 12 years Women's age = 3x = (3 × 12) = 36 yearsHELP ASAP I WILL MARK BRANLIEST!!!
This probability distribution shows the
number of times a group of people takes
selfies before liking them.
Retakes
o
1
2
3
4
Frequency
27
29
18
14
12
Using this distribution, find the probability that a
person will retake their sexfie exactly 3 times.
p = [?]
Answer:
0.14
Step-by-step explanation:
0.14 is the probability that a person will retake their sexfie exactly 3 times.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
Total frequency = 27+29+18+14+12 = 100
frequency of 3 retakes = 14
p(r) = frequency of 3 retakes/ Total frequency
p(r) = 14/100 = 0.14
To learn more about probability refer to:
https://brainly.com/question/13604758
#SPJ2
What is the sum? Complete the equation.
-15 + (-15)
Answer:
-30
Hope this helps!
you made a batch of 24 cookies for school your brother ate 7 of them without asking you. What fraction of your cookies are left?
You take out a simple interest loan with a principal of $1500. Your interest rate is
5.6% and your loan term is 4 years.
What is the total interest you will pay?
What is the total you will pay including your principal and interest?
Answer: See explanation
Step-by-step explanation:
Interest = Principal × Rate × Time
Interest = $1500 × 5.6% × 4
= $1500 × 0.056 × 4
= $336
The total amount that will be paid will be:
= Principal + Interest
= $1500 + $336
= $1836
Is it possible to construct a triangle with the given side lengths?
1 ft, 6 ft, 9 ft
Yes or no?
dau coroana
daca il faceti
Answer:
I give the crown
if you do
Step-by-step explanation:
Answer:
what does that mean?
Step-by-step explanation:
help me please i need a lot of help
Answer: 3 or 9/12
Step-by-step explanation:
3/4 to 0.75
0.75 * 4 = 3
How so i slove 9z-63=0
What number is the best prediction! Please help :(
Answer:
28
Step-by-step explanation: