set up the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.y=x2/3+3,y=3,x=6
About the line y=16.
Answers
[tex]\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx[/tex] is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.
A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.
This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").
As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.
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Related Questions
how does the formula for the sample mean differ from the formula for population mean?
Answers
The sample mean is the average of selected observations taken from population, whereas the population mean averages of whole population Sample mean: [tex]\bar{x}[/tex] = ∑x / n
Population mean: μ = ∑x / N
Sample mean is the representation of average of selected number of observation which is one of the set of the population.It is represented by x bar ( [tex]\bar{x}[/tex] ).Here 'n' is the sample size which one of the set of population .Formula of sample mean is [tex]\bar{x}[/tex] = ∑x / nPopulation mean is the average of whole population.It is represented by 'μ' .Here sample size 'N' whole population.Formula of population mean is μ = ∑x / NTherefore, the sample mean is average of a sample selected from population whereas population mean is average of whole population.
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Please Answer will give 35 points
Answers
Answer:
D
Step-by-step explanation:
Raising a nonzero real number to the power of zero always gives you one.
Which is bigger -7/8 or -5/8
Answers
Answer:
-5/8
Step-by-step explanation:
-7/8 = -0.875
-5/8 = -0.625
The closer the negative number is to 0, the bigger that number.
-0.625 is closer to 0 than -0.875
So, -5/8 is bigger.
Select the correct answer.
The sum of the digits of a three-digit number is 13. The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits. Which system of equations can be used to find each digit?
Answers
System of equations can be used to find each digit is option A.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
Let's represent the hundreds, tens, and units digits as h, t, and u, respectively. Then we can use the given information to set up a system of equations:
A three-digit number has a digit sum of 13:
h + t + u = 13
One more than the hundreds digit (h) is the tens digit (t):
t = h + 1
The digit in the units, u, is 3 greater than the total of the digits in the tens and hundreds:
u = t + h + 3
Therefore, the correct system of equations is:
h + t + u = 13
t = h + 1
u = t + h + 3
Therefore, the answer is (A).
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An elevator travels directly up 36 floors in 108 seconds. How many floors can this elevator travel directly up in 80 seconds?
Answers
The number of floors can this elevator travel directly up in 80 seconds is, 26 2/3 floors
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
We are given that the elevator travels 36 floors in 108 seconds, so the rate can be calculated as follows:
rate = 36 floors / 108 seconds
= 1 floor / 3 seconds
To determine how many floors the elevator can travel in 80 seconds, we can use the rate and the formula: distance = rate x time:
distance = rate x time
distance = (1 floor / 3 seconds) x 80 seconds
distance = 80 / 3 floors
distance = 26 2/3 floors
So, the elevator can travel directly up 26 2/3 floors in 80 seconds.
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Erin withdrew $29.85 from her bank account. She plans to spend
$2.90 per day on lunch. Approximately how many days will her money
last?
Answers
Answer:
$2.90---1 day
$29.85----x days
x=29.85×1/2.90
x=10.29 days
Find the value of each variable, show proofs urgentttt
Answers
its a x, x, x√2 special triangle
so x and y are 19 <--- answer
2 angles are 90 & 45 so the third angle must be 45
that means x and y are equal
2x+2y as an equivalent expressions in factored form
Answers
Answer:
2(x + y)
Step-by-step explanation:
2x + 2y ← factor out the common factor of 2 from both terms
= 2(x + y)
You want to deliver a package to Japan. The FedEx delivery service charges a $10 flat fee plus $2 per pound. You can also use the USPS Priority Mail service which charges a $2 flat fee plus $4 per pound.
Write an equation for the cost for USPS Priority Mail to send the package.
Use x as the number of pounds and use y as the total cost.
Answers
Answer:5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
What is the difference between absolute and relative error?
Answers
Absolute error and relative error are two measures of the difference between an estimated or calculated value and the true or exact value of a quantity.
The main difference between absolute and relative error is that absolute error gives the magnitude of the difference between the estimated value and the true value, while relative error gives a measure of this difference relative to the size of the true value.
Absolute error is the magnitude of the difference between the estimated or calculated value and the true value.
It is calculated as the absolute value of the difference between the estimated value and the true value. Absolute error is expressed in the same units as the quantity being measured.
Relative error, on the other hand, is the absolute error expressed as a fraction or percentage of the true value. It is calculated as the absolute error divided by the true value, and is usually expressed as a percentage.
Relative error is a useful measure when the scale of the quantity being measured varies over a wide range, or when comparing the accuracy of measurements of different quantities.
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A rhombus has sides of length 8 m. It’s shorter diagonal is 10 m long. Find the length of the longer diagonal
Answers
Answer:
Step-by-step explanation:
Here's how you can find the length of the longer diagonal of a rhombus with sides of length 8 m and a shorter diagonal of length 10 m:
Step 1: Draw a diagram of the rhombus with the shorter diagonal labeled as 10 m.
Step 2: Draw a perpendicular bisector from one corner of the rhombus to the opposite corner, dividing the rhombus into two congruent right triangles.
Step 3: Label the longer diagonal as "d".
Step 4: Since the two congruent right triangles have sides that are half the length of the sides of the rhombus, the hypotenuse of each triangle must have length 4 m.
Step 5: Using the Pythagorean theorem, we can find the length of the other side of each triangle:
a^2 + b^2 = c^2
4^2 + b^2 = 10^2
16 + b^2 = 100
b^2 = 84
b = √84 = 2√21
Step 6: Now that we know the length of one side of each triangle, we can use it to find the length of the longer diagonal:
d^2 = 4^2 + (2√21)^2
d^2 = 16 + 168
d^2 = 184
d = √184 = 2√23
So, the length of the longer diagonal of the rhombus is 2√23 m.
12 Colin used 2 5/6 sheets of paper and completed 1/6 of his report. How many pages was the completed report?
Answers
Answer:
below
Step-by-step explanation:
He needs 6 times as many as 1/6 th to have a complete report
6 * 2 5/6 = 6 * 17/6 = 102/6 = 17 pages total
Let's start by finding out how many sheets of paper Colin used for each 1/6 of the report. We can divide the total number of sheets he used (2 5/6) by the fraction of the report he completed (1/6):
(2 5/6) ÷ (1/6) = (17/6) ÷ (1/6) = 17
So Colin used 17 sheets of paper to complete 1/6 of the report.
To find out how many pages the completed report will be, we need to multiply the number of sheets used to complete 1/6 of the report by the total number of 1/6ths in the completed report. Since 1/6 represents the fraction of the report that Colin has completed, there are 5/6 of the report left to complete:
1/6 + 5/6 = 6/6 = 1 (the completed report)
So there are a total of 6 1/6ths in the completed report. To find the total number of sheets, we can multiply the number of sheets used to complete 1/6 of the report by 6:
17 sheets x 6 = 102
Therefore, Colin will need a total of 102 sheets of paper to complete the entire report.
What is an outlier in statistics?
Answers
It is an observation that significantly differs from the other observations in a dataset is referred to as an outlier in statistics.
An observation that significantly differs from the other observations in a dataset is referred to as an outlier in statistics. A true abnormality in the data may be the cause of an outlier, but they can also happen by chance as a result of random variation in the data, or they might be a sign of a measurement or data entry error.By modifying the dataset's mean, variance, or correlation, outliers can alter the outcomes of statistical studies. In order to properly handle outliers, it is crucial to recognise them.
There are several techniques to identify outliers in a dataset, including graphical techniques like scatter plots or box plots, as well as numerical techniques like computing z-scores or utilising the interquartile range (IQR). Consider any observation more than once is a general rule of thumb.
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What is -2y = 6x - 8
Answers
Answer:
y= -3x+4
Step-by-step explanation:
You need to simplify down to y=mx+b by dividing -2 from both sides:
-2/-2= cancels out making y
6/-2= -3
-8/-2= 4
New equation:
y= -3x+4
Hope this helped!
4x^2-80=0
Please help me understand?
Answers
Answer:
x = ± √20
or if you want an approximate solution correct to the nearest hundredth:
x = -4.47, 4.47.
Step-by-step explanation:
4x^2-80=0
This a quadratic equation and will have 2 solutions.
Add 80 to both sides of the equation:
4x^2 = 80
Divide both sides by 4:
x^2 = 20
Take the square root of both sides:
x = ± √20.
A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is 0.12. The p-value is 0.03? a) If H0 were true, for what probability of a Type I error was the test designed?
b) What conclusion (reject or fail to reject) would you make for this test?
c) If this test resulted in a decision error, what type of error was it?
Answers
Answer: 28282
Step-by-step explanation:
I think
Using the interior angel measure 150 degrees find the exterior angel measure
Please help
Answers
Answer:
30 degrees.
Angles must add up to 180 so,
180 - 150 = 30.
Step-by-step explanation:
+add me a brainliest and drop some thanks i did picture too
Step by step
Assuming the interior angles are opposite the exterior angle, we can use the Exterior Angle Theorem that says the exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. If 150 is the measurement of the two opposite interior angles, that is the measurement of the exterior angle.
If this is a straight angle and you are looking for the adjacent angle measurement, a straight angle is equal to 180 degrees. 180 - 150 given = 30 for the adjacent.
Your answer will depend on what the question is looking for.
The net of a right rectangular pyramid is shown.
What is the surface area of the right rectangular pyramid?
Answers
The surface area of the right rectangular pyramid is 96 sq. ft.
What is the net's surface area?A net pattern is produced when the surface of a three-dimensional figure or solid is spread out flat and each aspect of the shape is visible. The net may then be used to calculate the solid's surface area.
The surface area of the net is calculated by adding the areas of all of its faces. The net's surface area is calculated by summing the surface areas of all its forms.
The surface area of the given net is calculated by adding the area of all the individual shapes in the net.
For the given net the area of the triangle with h= 5 ft and b = 8 ft is:
A1 = 1/2(8)(5)
A1 = 20 sq. ft.
There are two such triangles thus:
A1 = 2(20) = 40 sq. ft
For the triangle with h = 6 ft and b = 4 ft:
A2 = 1/2)(4)(6)
A2 = 12
There are two such triangles thus:
A2 = 2(12) = 24 sq. ft
The area of the rectangle in the center is:
A3 = (8)(4)
A3 = 32 sq. ft
The total surface area of the net is:
A = A1 + A2 + A3
A = 40 + 24 + 32
A = 96 sq. ft.
Hence, the surface area of the right rectangular pyramid is 96 sq. ft.
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how to multiply fractions with the same denominator
Answers
when multiplying fractions , multiply across the numerator and denominator
you dont need common denominators
example
[tex]\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}[/tex]
Hope this helps : -)
- Jeron
teh dance committee at jefferson high school decides to change students different prices for dance tickets depending on whether they are a student at jefferson or at another school. A student attending jefferson pays $5, whereas a student attending a different school pays $10. the dance committee didn't make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and brought in $3135. How many jefferson and non-jefferson student came to the dance ?
Answers
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' and 'y' be the number of students at Jefferson School and non-Jefferson school, respectively. Then the equations are given as,
x + y = 500 ...1
5x + 10y = 3135 ...2
From equations 1 and 2, then we have
5(500 - y) + 10y = 3135
2500 - 5y + 10y = 3135
5y = 635
y = 127
Then the value of 'x' is given as,
x + 127 = 500
x = 373
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
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write 72 as a fraction in simplest form and as a decinal
Answers
The simplest form of the fraction 7/2 is 7/2.
3.5 is the decimal number form of 7/2.
What is decimal?Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.
Given:
A fraction number is 7/2.
And 2 and 7 are the prime numbers.
The factors of 7 are 7 and 1.
The factors of 2 are 2 and 1.
There is no other than 1 common factor between 7 and 2.
So, the simplest form of the fraction 7/2 is 7/2.
Now, fraction as a decimal,
= 7/2
= 3.5
Therefore, 3.5 is the required decimal number.
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The complete question;
Write 7/2 as a fraction in simplest form and as a decimal.
Given y = x/x-1 and x > 1, which of the following is a possible value of y?
Answers
Answer: E
Step-by-step explanation: This is from my mathematical knowledge however there is an asymptote at y=1. All values for y must be higher than one for it to be viable. So E is the only one that works.
If equation y = x/x-1 and x > 1, then 1.9 is the possible value of y.Option E is correct.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation is y=x/x-1
Where value of x should be greater than one.
x>1
We have to find the possible value of y from the given options.
We have to check the options by considering the value is greater than one or not.
-1.9 is less than one so it is not possible value of y.
-0.9 is less than one so it is not possible value of y.
0.0 is less than one so it is not possible value of y.
0.9 is less than one so it is not possible value of y.
1.9 is greater than one so it is possible value of y.
Hence, if equation y = x/x-1 and x > 1, then 1.9 is the possible value of y.
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Find the 18th term in the following
arithmetic sequence:
-2, -6, -10, -14, . . .
Answers
Answer:
-70
Step-by-step explanation:
-2, -6, -10, -14, ...
-6 - (-2) = -4
The common difference in -4.
The nth term of an arithmetic sequence with common difference d is
a_n = a_1 + d(n - 1)
For n = 18,
a_18 = -2 + (-4)(18 - 1)
a_18 = -2 + (-4)(17)
a_18 = -2 - 68
a_18 = -70
Answer: -70
Step-by-step explanation:
{[tex]a_{n}[/tex]=[tex]a_{1}[/tex]+(n-1)d}
a_{1}= -2
d= -4
[tex]a_{18} =-2+(18-1)*(-4)=-2-68 = -70[/tex]
Fill in the missing number to write an equivalent ratio. Show your work.
3/8 = blank/24
Answers
Answer:9
Step-by-step explanation:
3/8=x/24
3/8=x/3*8
[tex]\frac{3}{8} =\frac{\frac{x}{3} }{8}[/tex]
3=x/3
x=9
Answer:
First, we evaluate the amount that the portion has been multiplied by. We want to determine how many number 8's fit in to the number 24 because the bottom of the portion is 24.
The solution would be 3, because eight multiplied by 3 equals 24. Also because the bottom of the fraction has been multiplied by three, the top, known as the numerator, also needs to be multiplied by three. As a result, the top becomes 3 multiplied by 3, which equals 9. As a result, the portion is 9/24.
Step-by-step explanation:
3/8=?/24
3/8*3/3=9/24
9/24
____ =/8
3/3
Adrian has 75 baseball cards. He wants the same number of cards in each pile. How many cards can he have in each pile. List all possibilities.
Answers
If Adrian has 75 baseball cards. He wants the same number of cards in each pile. He can have 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.
What is the number of cards?Adrian wants to divide his 75 baseball cards into piles such that each pile has the same number of cards. This means the number of cards in each pile must be a factor of 75. To find all the possible numbers of cards in each pile, we can find all the factors of 75.
The factors of 75 are:
1, 3, 5, 15, 25, and 75.
So, Adrian can have the same number of cards in each pile as:
1, 3, 5, 15, 25, or 75.
Therefore, Adrian can have his 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.
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Is the product of (x − 3)^2 a perfect square trinomial? Explain your reasoning...
Answers
The product of (x - 3)² is a perfect square trinomial.
What is a perfect square?
An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax² + bx + c. Real numbers a, b, and c are present here, and a ≠ 0.
By multiplying a binomial by another binomial, perfect square trinomials—algebraic expressions with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of just two terms, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions. When a binomial made up of a constant and a variable is multiplied by itself, a perfect square trinomial with three terms is produced. A positive or a negative sign separates each term in a perfect square trinomial.
Given expression is
(x - 3)²
Apply the formula (a - b)² = a² - 2ab - b²:
= x² - 2×x×3 + 3²
= x² - 6x + 9
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Use the triangle shown on the right to answer the
question.
Which equation can you use to solve for a?
a
30
sin (35°) sin(35°)
a
30
sin (35°) sin(60°)
a
30
sin (85⁰) sin(35°)
DONE ✔
C
35°
Answer is B and second one is 19.9
Answers
Answer:
Second option:
[tex]\mbox{\large \dfrac{a}{\sin(35^\circ)} = \dfrac{30}{\sin(60^\circ)}}[/tex]
Step-by-step explanation:
The law of sines states that the ratio of the sides of a triangle to the sine of the angle opposite the sides is the same for both sides
So we get
[tex]\dfrac{AB}{\sin 85} = \dfrac{BC}{\sin 35} = \dfrac{AC}{\sin B}}[/tex]
We are not given ∠B but we know the three angles of a triangle must add up to 180°
Therefore m∠B + 35 + 85 = 180
m∠B + 120 = 180
m∠B = 180 - 120 = 60°
and we also have AB = c. BC = a and AC = 30
Hence
[tex]\dfrac{c}{\sin 85} = \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\\\\textrm{from which}\\\\ \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\[/tex]
The equation which will yield the value of a will be : a/sin35 = 30/sin60
Given,
Triangle.
Here,
According to sine law,
30/sinB = c / sin85 = a/ sin35
Firstly calculate angle B .
Therefore m∠B + 35 + 85 = 180
m∠B + 120 = 180
m∠B = 180 - 120 = 60°
Here,
AB = c.
BC = a
AC = 30
Hence to calculate a ,
Use the proportion,
a/sin35 = 30/sin60
Thus equation 2 is correct .
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Can someone help me with this? There could be more than 1 answer
Answers
The correct statement regarding the quadratic function is given as follows:
C. The ball hit the ground after 3.5s.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.For this problem, the intervals are given as follows:
Increasing: (0, 1.75) -> moving upwards.Decreasing: (1.75, 3.5) -> hits the ground after 3.5 seconds.More can be learned about quadratic functions at https://brainly.com/question/1214333
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Help please…………………………………..
Answers
Answer:
4/3
Step-by-step explanation:
This is the worse piecewise function I have ever seen in my life.
4/3. Just plug in an infinitely close number to -1 in a calculator and you get 1.3
A process that repeats a series of steps over and over until the desired outcome is obtained.
Answers
Answer:Iterative
Step-by-step explanation: