(q8) Find the volume of the solid obtained by rotating the region bounded by
, and the x-axis about the y axis.
Answers
Rotating the area enclosed by, and the x-axis about the y axis yields the solid's volume, which is [tex]9\pi[/tex]. option C.
The cylindrical shell method can be used to determine the solid's volume after rotating the region enclosed by the curves x = 3y, x = 3, and the x-axis about the y-axis.
Let's begin by mapping the area:
The parabola that opens to the right and passes between the points (0,0) and (9,3) is represented by the curve x = 3y.
The volume element must be expressed in terms of y in order to set up the integral. Imagine rotating a narrow strip of material with width dy along the y-axis to create a cylindrical shell.
The tallness of theThe difference between the x-values of the curves x = 3 and x = 3y yields the cylindrical shell:
h = 3 - (3√y) = 3(1 - √y)
The distance between the y-axis and the curve x = 3y, denoted by the symbol r, and the circumference of the cylindrical shell is 2r. Here, r equals 3y.
The volume element is thus:
dV = 2π(3√y)(3(1 - √y)) dy
The integral may now be set up to determine the entire volume:
V = ∫[0,3] 2π(3√y)(3(1 - √y)) dy
This integral can be simplified to give us the solid's volume. After analysing the integral, we determine that is the right response. 9 cubed units.option C
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Related Questions
Determine the margin of error for a 90% confidence interval to estimate the population mean when s = 40 for the sample sizes below.
a) n=14
b) n = 28
c) n = 45
a) The margin of error for a 90% confidence interval when n = 14 is
(Round to two decimal places as needed.)
b) The margin of error for a 90% confidence interval when n=28 is
(Round to two decimal places as needed.)
c) The margin of error for a 90% confidence interval when n = 45 is
(Round to two decimal places as needed.)
Answers
Answer:
a) The margin of error for a 90% confidence interval when n = 14 is 18.93.
b) The margin of error for a 90% confidence interval when n=28 is 12.88.
c) The margin of error for a 90% confidence interval when n = 45 is 10.02.
Step-by-step explanation:
The t-distribution is used to solve this question:
a) n = 14
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 14 - 1 = 13
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7709
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for a 90% confidence interval when n = 14 is 18.93.
b) n = 28
27 df, T = 1.7033
[tex]M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88[/tex]
The margin of error for a 90% confidence interval when n=28 is 12.88.
c) The margin of error for a 90% confidence interval when n = 45 is
44 df, T = 1.6802
[tex]M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02[/tex]
The margin of error for a 90% confidence interval when n = 45 is 10.02.
What is the answer please help no links
Answers
Answer:
The answer is 432
Step-by-step explanation:
Multiply
Using compatible numbers, which is the best estimate of (28.5)(7.1)?
36
40
210
300
Answers
Answer:
210
Step-by-step explanation:
29*7 = 203, 203 is the closest number to 210!
Answer:
210
Step-by-step explanation:
Select ALL TRUE statements about Linear Functions:
Group of answer choices
The degree of the function is one.
The y values change by a common difference.
The graph is a straight line.
Vertex form is used for graphing.
Answers
Step-by-step explanation:
The degree of the function is one: Correct
The y values change by a common difference: incorrect
The graph is a straight line: Correct
Vertex form is used for graphing: Incorrect
Hope that helps :)
Please help! What's the perimeter of Trapezoid ABCD?
Answer and explanation please! <3
Answers
Answer:
Step-by-step explanation:
The formula is P= a+b+c+d
a=base
b=base
c=side
d=side
Please search perimeter of a trapezoid. It will provide the answer.
Answer:
Perimeter = 19.77 units
Step-by-step explanation:
Perimeter = AB + BC + CD + AD
BC = 5
AD = 8
AB² = 2² + 3² = 4 + 9 = 13
AB = √13 = 3.61
CD² = 1² + 3² = 1 + 9 = 10
CD = √10 = 3.16
Perimeter = 3.61 + 5 + 3.16 + 8 = 19.77
Cups are sold by 6 per package while plates are sold by 8 per package. If you want
to have the same number of each item for a party, what is the least number of
packages of cach item you need to buy?
A. 2 packages of cups and 3 packages of plates
3 packages of cups and 4 packages of plates
C. 4 packages of cups and 3 packages of plates
D. 5 packages of cups and 3 packages of plates
Answers
Answer:
C
Step-by-step explanation:
What is the lowest common multiple
6 = 2 * 3
8 = 2 * 2 * 2
LCM = 2 * 2 * 2 * 3
LCM = 24
So you just divide 6 and 8 into 24. The result will be the number of packages.
Cups: 24/6 = 4
Plates: 24/8 = 3
You need 4 packs of cups and 3 of plates
I had $370.00. My Mom gave $150.00. My Dad gave $150.00. My Aunt and Uncle gave me $100.00. I had another $30.00. How much did I have? I will delete the right answers.
Answers
Answer:400
Step-by-step explanation:
The quantity of a product demanded by consumers is a function of its price. The quantity of one product demanded may also depend on the price of other products. For example, if the only chocolate shop in town (a monopoly) sells milk and dark chocolates, the price it sets for each affects the demand of the other. The quantities demanded, q1​ and q2​, of two products depend on their prices, p1 and p2, as follows:
q1​=150−2p1​−p2
q2​=200−p1​−3p2​.​
If one manufacturer sells both products, how should the prices be set to generate the maximum possible revenue? What is that maximum possible revenue?
Answers
Answer:
Both prices should be set to #25.
The maximum revenue is #4375
Step-by-step explanation:
Given
[tex]q_1 = 150-2p_1-p_2[/tex]
[tex]q_2 = 200-p_1-3p_2[/tex]
Start by calculating the total revenue (R):
[tex]R = p_1q_1 + p_2q_2[/tex]
[tex]R = p_1(150-2p_1-p_2) + p_2(200-p_1-3p_2)[/tex]
[tex]R = 150p_1-2p_1^2-p_1p_2 + 200p_2-p_1p_2-3p_2^2[/tex]
Collect and solve like terms
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
Differentiate with respect to pi and to p2, respectively
[tex]\frac{dR}{dp_1} = 150 -4p_1 - 2p_2[/tex]
[tex]\frac{dR}{dp_2} = 200 -2p_1 - 6p_2[/tex]
Equate both to 0, to get the critical point
[tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]200 -2p_1 - 6p_2 = 0[/tex]
Solve for p1 in [tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]4p_1 = 150 - 2p_2[/tex]
[tex]p_1 = 37.5 - 0.5p_2[/tex]
Substitute [tex]p_1 = 37.5 - 0.5p_2[/tex] in [tex]200 -2p_1 - 6p_2 = 0[/tex]
[tex]200 - 2(37.5 - 0.5p_2) - 6p_2 = 0[/tex]
[tex]200 - 75 - p_2 - 6p_2 = 0[/tex]
[tex]125 - 7p_2 = 0[/tex]
[tex]-7p_2 =-125[/tex]
[tex]p_2 = 25[/tex]
Substitute [tex]p_2 = 25[/tex] in [tex]p_1 = 37.5 - 0.5p_2[/tex]
[tex]p_1 = 37.5 - 0.5 * 25[/tex]
[tex]p_1 = 37.5 - 12.5[/tex]
[tex]p_1 = 25[/tex]
So, we have:
[tex]p_1 = p_2 = 25[/tex]
This implies that the prices should be set to #25.
The maximum possible revenue is:
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
[tex]R = 150 * 25 + 200 * 25 -2 * 25^2 - 2 * 25 * 25 - 3 * 25^2[/tex]
[tex]R = 4375[/tex]
The maximum revenue is #4375
The maximum possible revenue is 4375.
How to calculate the revenue?From the information given, the following can be deduced:
Q₁ = 150 - 2P₁ - P₂
Q₁ = 150 - 2P₁ - P₂Q₂ = 200 - P₁ - 3P₂
The total revenue will be:
R = P₁Q₁+ P₂Q₂
R = P₁(150 - 2P₁ - P₂) + P₂(200 - P₁ - 3P₂)
R = 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
To maximize, differentiate it in both the direction of P₁ and P₂.
d/dP₁ = 150 - 4P₁ - 2P₂
d/dP₂ = 200 - 2P₁ - 6P₂.
Solving for P₁ goes thus:
4P₁ = 150 - 2P₂
Divide through by 4
P₁ = 37.5 - 0.5P₂
Since 200 - 2P₁ - 6P₂ = 0
200 - 2(37.5 - 0.5P₂) - 6P₂ = 0.
P₂ = 25
Therefore, the revenue will be:
= 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
= (150 × 25) + (200 × 25) - (2 × 25 × 25) - (3 × 25²)
= 4375
In conclusion, the revenue is 4375.
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Un tercio es menor que cuatro centésimos.?
Answers
Answer:
no por que 1/3 es menor que 4
Step-by-step explanation:
A quadrilateral has angles that measure 115, 97, and 68. What is the measure of the missing angle? Plz help me I don't know the answer!!!
A.45
B. 115
C.68
D.80
Answers
Answer:
Step-by-step explanation:
The sides of a quadrilateral always add up to 360°.
Missing angle = 360-115-97-68 = 80°
Answer:
D. 80°
Step-by-step explanation:
A quadrilateral always add up to 360°
To find the missing value we first have to add the given number up:
115 + 97 + 68 = 280°
Now we minus our value from 360° :
360° - 280° = 80°
Hope this helps!
PLSSSSSSSSSSS HELP ASAPPP
Answers
Answer:
C
Step-by-step explanation:
400*.035 = 14 *2 = 28
250*.0325 = 8.125 *2 = 16.25
28 + 16.25 = 44.24
44.25+650 = 694.25
PLEASE HELP AND EXPLAIN IT FOR ME :(
Answers
Answer:
15 x 10 x 20 =
Step-by-step explanation:
Answer:
1,100
Step-by-step explanation:
15*10*2=300
20*15*2=600
20*10=200
300+600+200=1,100
you need to find the surface area which means the area of all the sides except the top(bc i think its open???)
a shortcut i used was multiplying sides that have the same area by 2. for example, the side 15*10, there was another side like that, so i multiplied by two instead of having to solve for the other side individually, does that make sense?
check my math if im wrong
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.76 MPa. (a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.) MPa
Answers
Answer:
95% of the lower confidence interval for the true average proportional limit stress of all such joints
7.7829
95% of the confidence interval for the true average proportional limit stress of all such joints
(7.7829, 9.3171)
Step-by-step explanation:
Step(i):-
Given that the sample size 'n' = 12
Mean of the sample = 8.55
The standard deviation of the sample (S) = 0.76
Step(ii):-
95% of the confidence interval is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} })[/tex]
Degrees of freedom = n-1 = 12-1 = 11
t₀.₀₂₅ = 3.4966
[tex](8.55 - 3.4966\frac{0.76}{\sqrt{12} } , 8.55 + 3.4966 \frac{0.76}{\sqrt{12} })[/tex]
(8.55 - 0.7671 , 8.55+0.7671)
(7.7829, 9.3171)
Final answer:-
95% of the confidence interval for the true average proportional limit stress of all such joints
(7.7829, 9.3171)
Will give brainliest
Answers
Answer:
Perpendicular
Step-by-step explanation:
Answer:
Perpendicular
Step-by-step explanation:
They form a 90 degree angle.
A gumball machine contains gumballs in several different colors.
orange 26
yellow 2
green 3
purple 1
red 1
If you purchase one gumball from the machine, what is the probability it will be green?
Write your answer as a fraction or whole number.
Answers
5. A book of length 20 cm and breadth 5 cm is kept on a table, its area is
(a) 50 cm
(b) 100 cm
(c) 150 cm
(d) 200 cm
Answers
Area= length multiplied by width
Area= 20cm multiplied by 5cm and your area will be 100cm
Ella is solving the equation (x+5)2=0 . She writes that the solutions are x=5and−5 .
Anne looks at her work and disagrees. She says that only x=−5 is a solution. Who do you agree with? Explain your reasoning.
Answers
Answer:
Anne
Step-by-step explanation:
Let's solve it by replacing x by 5, then -5.
(5+5)2=0
10*2=0
20=0
(-5+5)2=0
-5 and 5 cancel each other out, and 0 times anything is 0.
0=0
So Anne is correct.
--
hope it helps
Pedro is building a playground in the shape of a right triangle. The base of the triangle is 18 yards. The height of the right triangle is 2 1/3 yards. Find the area of the triangular playground.
Answers
Answer:
area of right triangle = ab/2
base = 18yards
height = 2 1/3 = 7/3yards
area = (18 * 7/3) /2 = 42 /2 = 21[tex]yards^{2}[/tex]
hope this answer helps you.....
Solve the equation for solutions over the interval [0°, 360°). 7tanθ−7/3cotθ=0
Answers
Answer:
Step-by-step explanation:
[tex]7\tan \theta-\frac{7}{3}\cot \theta=0\\\tan \theta=\frac{1}{3} \cot \theta\\\tan^2\theta=\frac{1}{3}\\\tan \theta=\pm \frac{1}{\sqrt{3}}\\when ~\tan \theta=\frac{1}{\sqrt{3}}=tan 30,tan (180+30)\\\theta=30^\circ ,210^\circ\\when~ \tan \theta=-\frac{1}{\sqrt{3}}=\tan (180-30),tan(360-30)\\\theta=150^\circ,330^\circ[/tex]
solution set is {30,150,210,330}
Four boxes hold 36
apples. How many
apples are in 9 boxes?
Answers
Answer:
86 apples
Step-by-step explanation:
Hope this helps and have a great day!!!!
the nswer is 81 36/4=9
9x9=81
Help SOMEONE???? MATH IS SO HARD!!!
Answers
Answer:
16. 70%
17. 100%
Step-by-step explanation:
16. As seen here, there are 10 marbles in total. Out of those marbles, there are 7 green marbles.
We can set up a "part to whole" fraction such as 7/10
Then we just find the % value by finding an equivalent "x to 100" ratio (percentages go up to 100)
7/10 = x/100
1000 = 7x
70 = x
17. Fortunately, there doesn't seem to need too much math involved as the only possible marbles are red and green. Therefore, you have a 100% chance of getting a green or red marble.
Hope that helps a bit!
Given the following data, find the weight that represents the 28 percentile
Answers
Answer:
so I just tried to find the mean (average) and it was: 6.3
A hairstylist charges $15
Answers
Answer:
Ok.....
Step-by-step explanation:
Was that a question or was that the price you paid for getting a hair cut.
Five hundred students were asked whether they perfer apple juice or orange juice.
Answers
Answer:
Step-by-step explanation:
240 said apple juice and 340 said orange juice.
Solve for x. Show your work:
2x+17+3x = 4x+3x+3
Answers
Answer:
The answer is 7
Step-by-step explanation:
2x+17+3x=4x+3x+3
5x+17=7x+3
5x-7x=3-17
-2x=-14
x=7
The figure shows a gas tank in the form of a rectangular prism that is 40% full. How many more gallons of gas will it take to fill the tank? (1 gallon = 231 in.3)
Answers
Answer:
10.8 gallons
Step-by-step explanation:
First change everything to inches:
2.75 ft = 33 in
1.5 ft = 18 in
Volume of tank = lwh = (33)(18)(7) = 4158 in³
The tank is 40% full, so only 60% is need to fill it. To find 60%, multiply 4158 by 0.6 = 2494.8 in³
Now find out how much 2494.8 in³ is in gallons:
231 in³ = 1 gallon
1 in³ = 1/231 gallons
2494.8 = (1/231)(2494.8) gallons = 10.8 gallons
Emma drove 5 hours and 20 mins to her vacuum she left home at 10:15 am what time did she arrive
Answers
Answer: 3:35
Step-by-step explanation:
I don’t know what the answer for this
Answers
Answer:
isoceles and right
Step-by-step explanation:
Answer:
I think the answer us B........
What is the solution set for this inequality?
-8x + 32 -16
x < 6
x > 6
x > -2
x < -2
Answers
Answer:
x>-2
Step-by-step explanation:
-8x+32-16<0
-8x<16
divide both sides by -8
x>-2
that's because when you divide by a negative your inequality sign changes
1. Find
A) 35
B) 47.5
C) 67.5
D) 95
Answers
Answer:
i am pretty sure it is 95
Step-by-step explanation:
Answer:
B IS THE ANSWER.
Step-by-step explanation:
The angle is less than 50 degrees but more than 30.