Find the volume (in units3) generated when the region between the curves is rotated around the given axis. y = x3, y = 0, and y = 27 rotated around the y-axis
The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46
Volume of the curves:
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π ∫dc [f(y)]2dy.
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).
Given,
y = x³
Here we have to find the volume along to the y axis.
With limit as y = 0 and y = 27.
When we apply the values it can be written as,
=>[tex]V=\pi \int\limits^0_{27} {(x^3)^2} \, dx[/tex]
[tex]\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx[/tex]
Apply the limits then we get,
[tex]\implies V = \pi [0^6 - (27)^6][/tex]
=> V = π [0 - 387420489]
=> V = π x 387420489
=> V = 1216500335.46
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16x + 9 = 9y - 2x
need the step and answer.
The solution for x and y for the given expression are :
x =1/2y + −1/2 and y=2x+1 respectively.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, the given equation is : 16x + 9 = 9y - 2x
Now,
solving for x :
16x+9=9y−2x (Add 2x to both sides.)
16x+9+2x=−2x+9y+2x
18x+9=9y
18x+9+−9=9y+−9 (Add -9 to both sides)
18x=9y−9
18x/18 = 9y−9/18 (Divide both sides by 18.)
x =1/2y + −1/2
solving for y :
16x+9=9y−2x
−2x+9y=16x+9 (Flip the equation.)
−2x+9y+2x=16x+9+2x (Add 2x to both sides.)
9y=18x+9
9y/9=18x+9/9 ( Divide both sides by 9.)
y=2x+1
Therefore, the solution for x and y for the given expression are :
x =1/2y + −1/2 and y=2x+1 respectively.
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A side of the triangle below has been extended to form an exterior angle of 147°. Find
the value of x
Answer:
X+90 = 147 ( sum of two interior angles equals opposite/adjacent exterior angle)
X = 147 - 90
X = 57
Answer:b
eez nuts srry
Step-by-step explanation:
Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
5=3x-1/4
Answer:
1 3/4
Step-by-step explanation:
so the question will be done like this
5 =3x-1/4
The (-1/4) will go to the other side where 5 is and the equation becomes
5+1/4=3x which will be
7/4=3x hence you divide both sides by 3 to get the value of x as 1 as the whole number and 3/4 as the remainder
Answer:
x = 7
Step-by-step explanation:
[tex]5=\frac{3x-1}{4}[/tex]
multiply both sides by 4 (Multiplication property of equality)
[tex]20=3x-1[/tex]
add both sides by 1 (Addition property of equality)
[tex]21=3x[/tex]
divide both sides by 3 (Division property of equality)
[tex]7 = x[/tex]
switch sides (Symmetric property of equality)
[tex]x=7[/tex]
Lashondra's playlist has 9 times as many songs as Harriette's playlist.-Velora-has 7 times as many songs on her playlist as Harriette does. If they combined their playlists, they would have 986 songs
Harriette has 58 songs in her playlist.
No of the songs in Lashondra's playlist = Nine times Harriette's playlist
No of the songs in Velora's playlist = Seven times Harriette's playlist
Total number of songs combined by all = 986
Let the number of songs in Harriette's playlist be x.
According to the problem,
9x + 7x + x = 986
⇒ 17x = 986
⇒ x = 58
Answer) Harriette's playlist has 58 songs.
We have taken the number of songs in Harriette's playlist as x as the other numbers were given in relation to this playlist. Thus, the variable is used to create a generalized formula.
Since the total number of songs is given, we can carry out simple algebraic addition and simplification to find out the answer.
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The entire question is given below:
Lashondra's playlist has 9 times as many songs as Harriette's playlist.-Velora-has 7 times as many songs on her playlist as Harriette does. If they combined their playlists, they would have 986 songs. How many questions does Harriette have in her playlist?
in a recent study investigating a link between walking and improved health, researchers reported that adults walked an average of 6.4 days in the past month for the purpose of health or recreation. specify the null and alternative hypotheses for testing whether the true average number of days in the past month that adults walked for the purpose of health or recreation is higher than 6.4 days.
As per the question, the study investigated the link between walking and the improved health. The researchers reported that the adults walked at an average of [tex]6.4[/tex] days that means [tex]9216[/tex] minutes in the past month for the purpose of health or recreation.
Now to claim for the null hypothesis, the true average number of days as well as minutes in the past months that the adults walked for the purpose of health or recreation is lower than the [tex]6.4[/tex] days as well as [tex]9216[/tex] minutes. That means [tex]u < 9216.[/tex]
And as per the standard theory of the null hypotheses which contains equal sign. And it can be represented as:
[tex]H(0):u = 9216[/tex] but [tex]H(0):u < 9216[/tex]
What are null hypotheses and alternative hypotheses?
The two hypotheses that is null hypotheses and alternative hypotheses are used in statistical testing. The test prediction based on the null hypotheses has no effect as well as no relationships between the variables. And the alternative hypotheses has both a relationship with the variables as well as effect on the variables.
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The school newspaper wants to find the opinions of students on availability of campus parking. They send a staff member to stand outside a busy dorm and interview students as they walk in or out of the building. What type of sampling process did the paper use?.
Answer: single random sample
Step-by-step explanation:
Solve inequality.
y-13<2
To solve the inequality, add 13 to both sides. The solution is y < 15 or (∞, 15)
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
y-13 < 2
Add 13 to both sides. Adding a number to both sides will not change the inequality. Hence,
y -13 + 13 < 2 + 13
y < 15
Using the interval notation, the solution is (∞, 15)
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PLEASE HELP!!!!!!!!!!
Answer:
< DGB = 101
Step-by-step explanation:
< CGB is equal to 79
< CGB is another name for < 1
We want to find < DGB which is another name for <2
< 1 and < 2 are a linear pair
<1 + <2 = 180
79 + <2 = 180
<2 = 180-79
<2 = 101
< DGB = 101
Answer:
The answer is 101
Step-by-step explanation:
Since a line has an angle of 180°
To know DGB we will just subtract 79 from 180
hence DGB=180°-79°
=101°
cynthia besch wants to buy a rug for a room that is 19 ft wide and 29 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 299 square feet of carpeting. what dimensions should the rug have?
The dimension which this rug should have is 23 feet × 13 feet.
How to calculate the dimensions of this rug?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.Let x represent the width of this rug.
Also, the dimension of this rug is given by:
299 = (29 - 2x) × (19 - 2x)
299 = (29 - 2x)(19 - 2x)
Evaluating the equation, we have:
299 = 551 - 58x - 38x + 4x²
4x² - 58x - 38x + 551 - 299 = 0
4x² - 96x + 252 = 0
Dividing all through by 4, we have:
x² - 24x + 63 = 0
x² - 21x - 3x + 63 = 0
x(x - 21) - 3(x - 21) = 0
(x - 3)(x - 21) = 0
x = 3 or 21 feet.
Note: The plausible solution is x = 3.
Therefore, the width and length of this rug is given by:
Length = 29 - 2(3)
Length = 29 - 6
Length = 23 feet.
Width = 19 - 2(3)
Width = 19 - 6
Width = 13 feet.
In conclusion, the dimension of this rug is 23 feet × 13 feet.
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There are 100 centimeters in 1 meter. How many square centimeters are there in
1 square meter? Explain how you found your answer.
if the length of a rectangle is (x-6) the width is (x-2) and the height (x-1), write a polynomial that is the volume of the rectangle. what if the volume is 60?
Answer: x3+5x2+6x
Hope this helps
What is the population variance of the following set of numbers: 3, 5, 8, 9, 10? 29 6.8 7 8.5?
The population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
For given question,
We need to find the population variance of the following set of numbers: 3, 5, 8, 9, 10
The formula for the Population variance is,
[tex]\sigma = \frac{\sum (x-\bar x)^2}{N}[/tex]
Here,
[tex]\bar x[/tex] = sample average
x = individual values in sample
N = count of values in the sample.
For given question,
[tex]\bar x=\frac{3+ 5+ 8+ 9+ 10}{5} \\\\\bar x=7[/tex]
Using the formula for variance,
[tex]\sigma = \frac{1}{5} [(3-7)^2 + (5 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (10 - 7)^2]\\\\\sigma = \frac{1}{5} \times 34\\\\\sigma = 6.8[/tex]
Therefore, the population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8
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Fill in the blanks of the number line
Step-by-step explanation:
The line should go: 0, 1/3, 2/3, 1, 1 1/3, 1 2/3, 2 or 0, 0.33, 0.66, 1, 1.33, 1.66, 2 depending on how it's needed (decimals repeating)
Convert 0.000 000425 to Standard form
Answer: 4.25
x
10
−
4
Step-by-step explanation:
Answer:
4.25x10^-9
Step-by-step explanation:
HELP 50 PTS AND BRAINLY!!!
Answer:
1 1/2
1/2
2 hours
Step-by-step explanation:
Answer: 1/2 hour and 1/2 hour and 1 hour
Step-by-step explanation:
Hope this helps you! :) Have an Amazing day! ^-^
Select the correct answer.
What is the ratio of the length of DE to the length of BC?
A. 1/4
B. 1/3
C. 2/5
D. 1/5
Taylor bought a watch on sale for 60% off the original price, and another 10% off the discounted price. If the watch originally cost $82, What was the final sale price?
Answer: $29.52
Step-by-step explanation: 82x0.6=49.2 82-49.2=32.8 32.8x0.1=3.28
32.80-3.28=29.52
Write an equation of the line with the given slope, m, and y-intercept (0,b), m=7, b=5
Answer: y = 7x + 5 (maybe, please make sure, I'm very doubtful of myself sometimes)
Step-by-step explanation:
1. With the given numbers, m is slope, so 7 is the slope and b is y-intercept, and 5 is the y-int in this case.
2. This is hinting that the equation is in slope intercept form, which is y = mx + b.
3. Since y = mx + b is the formula, then it means y = 7x + 5 is the likely answer
What is the product of 2 2/3⋅4 1/3?
Answer:
11.5
Step-by-step explanation:
there is no prior information about the proportion of americans who support gun control in 2019. if we want to estimate 97% confidence interval for the true proportion of americans who support gun control in 2019 with a 0.27 margin of error, how many randomly selected americans must be surveyed?
If we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.
Given,
The confidence level =97%
Critical z value of 97% confidence interval =2.170
Margin error E= 0.27
We know,
Sample size n= [tex]0.25(\frac{z}{E})^{2}[/tex]
Substitute the values in the equation
[tex]n=0.25(\frac{2.170}{0.27})^{2}\\ n=0.25( 8.03)^{2}[/tex]
n=16.12
n≈16
Hence, if we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.
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in a recent study on the effects of sleep and test results, volunteers took a math test. the volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were sleep-deprived volunteers. complete parts a through d.
The test results of the study's subjects serve as the sample.
The portion of the population from which data was actually gathered is known as a sample.
Sample = Hours of sleep and maths test score of the volunteers that were included in the study.
How is a sample related to a population?A population is the total group about which you want to draw conclusions. A sample is the specific group from which you will collect data. Always, the sample size is less than the whole population.
A population in research doesn't usually refer to humans. It can refer to a collection of whatever you desire to study, including things, occasions, groups, nations, species, and animals.
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.
(d² + 14d + 5) + (d - 4)
Answer:
d^2+15d+1
Step-by-step explanation:
group like terms
d^2+14d+d-4+5
simply like terms
d^2+15d+1
however, the answer is d^2+15d+1
what is 33 divided by 50
Answer:0.66
Step-by-step explanation:
hope this helps
Answer:0.66
Step-by-step explanation:33%50=0.66
Find the value of x.
15
X
36
Answer:
x = 39
Step-by-step explanation:
As we can see in the diagram, the triangle is a right-angled triangle, meaning that one of the angles inside the triangle has a measure of 90°.
Whenever we have a right-angled triangle and are given the lengths of two of its sides, and we are asked for the length of the third side, we must use the Pythagorean theorem, which states that:
[tex]\boxed{\mathrm{a^2 + b^2 = c^2}}[/tex],
where:
c = hypotenuse (longest side, opposite to 90° angle)
a, b = the two other sides of the triangle.
In this question, we are asked for the value of x, which is the hypotenuse of the given triangle, while the lengths of the other two sides are 15 and 36.
Therefore, using the Pythagorean theorem, we get:
[tex]15^2 + 36^2 = x^2[/tex]
⇒ [tex]x = \sqrt{36^2 + 15^2}[/tex]
⇒ [tex]x = \sqrt{1296 + 225}[/tex]
⇒ [tex]x = \sqrt{1521}[/tex]
⇒ [tex]x = \bf 39[/tex]
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Answer:
39
Step-by-step explanation:
This is called the Pythagorean Theorem. You are trying to find x or the hypotenuse. The a and b side are the two shorter side of the triangle(the a and b side can be interchangeable), these are the legs. The c side is the hypotenuse the long side. Plug in the numbers to the formula and get your answer.
The water depth in a harbor rises and falls over time. the function f(t) = 4.1 sine (startfraction pi over 6 endfraction t minus startfraction pi over 3 endfraction) 19.7 models the water depth, in feet, after t hours. during the first 24 hours, at what times does the water depth reach a maximum? at 5 and 17 hours at 11 and 23 hours at 2, 8, 14, and 20 hours at 5, 11, 17, and 23 hours
Answer:
Step-by-step explanation:
A function assigns the value of each element of one set to the other s/p
hile traveling across flat land, you notice a mountain directly in front of you. its angle of elevation (to the peak) is 4.5°. after you drive 13 miles closer to the mountain, the angle of elevation is 8°. approximate the height of the mountain. (round your answer to three decimal places.)
The height of the mountain using the angles of elevation is 2.346 miles
How to find the height of the mountain using angle of elevation?let
x = distance from the mountain to your current position
h = height of the mountain
Therefore, using trigonometric ratios,
angle of elevation of the current position to the mountain = 8°
angle of elevation of the former position to the mountain = 4.5°
Therefore,
tan ∅ = opposite / adjacent
where
∅ = angle of elevation
tan 8 = h / x
tan 4.5 = h / x + 13
Hence,
x tan 8 = h
(x + 13) tan 4.5 = h
using substitution,
x tan 8 = (x + 13) tan 4.5
x tan 8 = x tan 4.5 + 13 tan 4.5
0.1405408347x = 0.07870170682x + 1.02312218872
0.1405408347x - 0.07870170682x = 1.02312218872
0.0613x = 1.02312218872
x = 1.02312218872 / 0.0613
x = 16.6900489396
x = 16.690 miles
Therefore,
h = 16.6900489396 × tan 8
h = 16.6900489396 × 0.1405408347
h = 2.34561947798
h = 2.346 miles.
Therefore, the height of the mountain using the angles of elevation is 2.346 miles
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Solve by Elimination Algebra 2 A park charges $10 for adults and $5 for kids. How many adult tickets and kid tickets were sold, if a total of 524 tickets were sold for a total of $3860 There were _ adults and _ kids tickets sold
Answer:
There were 248 adult tickets and 248 kid tickets.
Step-by-step explanation:
a = number of adult tickets
k = number of kid tickets
a + k = 524 10a + 5k = 3860
Multiply the equation on the right all the way through by -5 so that we can eliminate the k's when we add the equations together.
-5(a+ K) = 524(-5)
-5a - 5k = -2620
Add the two equations together:
-5a - 5k = -2620
10a + 5K = 3860
5a = 1240 Divide both sides by 5
a = 248 There are 248 adult tickets. Plug in 248 for a in either of the original equations.
a + k = 524
248 + k = 524 Subtract 248 from 524 to find the number of kid tickets.
There are 276 kid tickets.
Check:
Plug in 276 for k and 248 for adult to both equations to see if they work
a + k = 524
248 + 276 = 524
524 = 524
10a + 5k = 3860
10(248) + 5(276) = 3860
2480 + 1380 = 3860
38060 = 3860
A student ran a distance of 3 miles each day for 5 days. Then the student ran a distance of
4 miles each day for the next 5 days.
What was the total distance in miles the student ran during these 10 days?
4
th
Answer:
40
Step-by-step explanation:
If the student ran 4 miles for 5 days multiply 4 by 5 and you get 20. Then just do the same thing for 5 more days. Also, 20. Then add 20 + 20 and you get 40
How many numbers between two and fifty are
divisible by three?
Answer:
18
Step-by-step explanation:
because i smart it's will be 18