The answer is 1) V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex]; 2) V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]; 3) V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] ; 4) V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] .
1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:
V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex] = [tex]2\pi [(/3) + 2x][/tex] evaluated from 0 to 1 = (4/3)π.
2) The height of the region is equal to - (2x) = -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:
V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]=[tex]2\pi [/5 - 2/3 + /2][/tex] evaluated from 0 to 1 = (8π/15).
3) The height of the region is equal to (2-x) - = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:
V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] = [tex]2\pi [(x^4/4)][/tex] evaluated from 0 to √2 = (π/2).
4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:
V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] = [tex]4\pi [(2/3)\± (2\sqrt{2} /3)][/tex]
The complete Question is:
Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the
1. y = x, y = -x/2, and x = 2
2. y = 2x, y = x/2, and x = 1
3. y = x/2, y = 2-x, and x = 0
4. y = 2-x/2, y = x/2, and x = 0
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Never mind i got it!
Answer:
OOk
Step-by-step explanation:
Which expression is equivalent to 3^2 ⋅ 3−5
While you are on vacation you start keeping track of how far your family is from home and how long it has taken after 3 hours you are 90 miles from home after 6 hours you are 250 miles from home
-write an equation that relates distance from home (d) and the amount of time (t) it has been
A possible equation that relates distance from home (d) and the amount of time (t) is d = tx, which can be expressed as 90= 3x.
How to write an equation?An equation relates variables using the equality symbol (=) as well as other symbols such as addition or subtraction. Due to this follow these steps:
Identify the variables: In this case, the variables are distance and time.Identify the unknown variables: We know distance increases with time but there is an unknown variable that will be identified as x.Relate the variables.Based on this a possible equation is: d = tx
The missing value can be found by solving the equation 90= 3x.
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The least common multiple
of 10,14, and 3
Answer:
the lcm of 14 10 and 3 is 210
Please help me. The function g(x) is a transformation of f(x). If g(x) has a y-intercept at 3, which of the following functions could represent g(x)?
The function that represent the function g(x) is g(x) = f(x) + 4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
The graph of the function f(x) is given.
We know that, a linear function in slope intercept form can be represented as, y = mx + d, where m is slope and d is the y intercept.
y intercept is the y coordinate of the point where the line touches with the Y axis. At this point x coordinate is 0.
From the graph, we have f(x) = y = -1 when x = 0.
So y intercept, d = -1
Take two points from the graph (1, 0) and (0, -1).
Slope, m = (-1 - 0) / (0 - 1) = -1 / -1 = 1
f(x) can be represented in slope intercept form as f(x) = x - 1
We have a second function g(x) from the transformation of f(x).
y intercept of g(x) = 3
f(x) + 4 = x - 1 + 4 = x + 3 which can be g(X), since y intercept is 3.
Hence g(x) = f(x) + 4 is the function that represents the transformation of f(x) with y intercept 3.
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Match each quadratic equation with its solution set.
2x²8x+5=0
2x²9x-1=0
2x²10x - 3=0
2x²9x+6=0
2x²8x3=0
Based on the completed Form 1040 and 2018 Taxable Income Tiers, what is the total tax
that the employee is responsible for paying?
Answer in complete sentences.
The total tax that the employee is liable for paying will be $17,836 if the taxpayer declares $100,000 as income on the finished Form 1040.
What are income tiers or tax brackets?An income range that is subject to a particular income tax rate is referred to as a tax bracket. A progressive tax system includes tax brackets, which indicates that when an individual's income increases, the amount of the tax rates increases gradually. Tax rates for low-income taxpayers are generally low, whereas those for high-income taxpayers are often higher.
For instance, a single filer in 2022 with $100,000 in taxable income will pay $17,836 in taxes, or an average tax rate of 18%. Your effective marginal tax rate, however, is 24%. As a result, the employee is accountable for paying a total of $17,836 in taxes.
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A dance team has two competitions on the same day. The coaches decide to split the 96-member team, sending some to each competition. Competition A requires four-member dance teams per event and Competition B requires six-member dance teams per event. The equation 4x + 6y = 96 models this situation, where x is the number of four-member teams and y is the number of six-member teams. Graph the equation. Interpret the intercepts
Answer:
see attached
Step-by-step explanation:
intercept on Y is when x=0, y = 16 so if no one goes to competition A, they'll have 16 six-member teams
intercept on x is when y=0, x=24 so if no one goes to competition B, they'll have 24 four-member teams
Dont know how to answer, can i get an explanation and an answer
Answer:
Below
Step-by-step explanation:
It goes UP from -20 but does not include -20 ( due to the hollow dot) and it is less than or equal to 30 :
-20< x <= 30
for questions that require a numerical answer, you may be told to round your answer to a specified number of decimal places or you may be asked to provide an exact answer. when asked to provide an exact answer, you should enter repeating decimals in their fraction form and irrational numbers such as e^5, ln(4), or V2 in their symbolic form. consider the function f(x)= e^x +1/3x a. Find f(5), Give an exact answer b. Find f(11), Give your answer rounded to 3 decimal places
The value of f(5) is e^5 + 5/3, which is exactly 150.0798257693, and the value of f(11) is e^11 + 11/3, which is approximately 59877.808.
The function is f(x)= e^x + 1/3x
To find the value of f(5), put the value of x = 5 in the function f(x)= e^x + 1/3x. Which is equal to f(5) = e^5 + 5/3.
Similarly, to find the value of f(11), put the value of x = 11 in the function f(x)= e^x + 1/3x.
Which is equal to f(11) = e^11 + 11/3
f(11) = 59874.141715198 + 3.6666666667
f(11) = 59877.808381865
f(11) ≈ 59877.808
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There are four classes in a school. Now if we want to draw two classes out of four classes to compete, what is the probability of drawing one class and two classes?
Answers: 3/8, one eighth, one sixth, a half.
Answer:
3/8
Step-by-step explanation:
0.375 im hoping thats correct good luck
Need help ASAP Will REWARD
The value of exponential function f (4) is 1,296.
What is the exponential function?
The value of the exponential function is obtained from the common ratio of the resultant value of the number.
f ( 2 ) = 36
f ( 3 ) = 216
common ratio = ( f (3) ) / ( f (2) )
common ratio = ( 216 ) / ( 36 )
common ratio = 6
so, f (2) = 6² = 36
f (3) = 6³ = 216
The value of exponential function f (4) is calculated as follows
Now, f (4) = 6⁴ = 1,296
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necessary.
Tyler borrowed $42,000 from the bank to open
up a skateboard shop. If he had a simple
interest rate of 5%, how much will he have
paid to the bank in total once he paid the
loan back in full after 15 years?
Answer:
To calculate the total amount Tyler will have paid to the bank, you can use the formula for simple interest:
I = Prt
Where:
I = Interest (the amount Tyler will pay to the bank)
P = Principal (the original amount borrowed)
r = Interest rate (expressed as a decimal)
t = Time (in years)
Plugging in the given values, we have:
I = 42,000 * 0.05 * 15
I = 42,000 * 0.75
I = 31,500
So, Tyler will have paid a total of $31,500 in interest to the bank once he paid the loan back in full after 15 years.
Answer:
Step-by-step explanation:
we’ll I don’t know if this is right but I will try my best first I divide what ever I have then divide or multiply it by the next number
Please help me with this question.
The increased number of tickets will be 220.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number of tickets is increased by a factor of 1.1. The increased amount will be calculated as:-
Amount = 200 x 1.1
Amount = 220
Hence, the increased number of tickets will be 220.
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find the set values of k for which the curve y=(k+1)x^2 - 3x + (k+1) lies below the x-axis
The set of values of k for which the curve y = (k + 1) x² - 3x + (k + 1) lies below the X axis is k > 1/2 and k < -5/2.
What is Quadratic Functions?Quadratic functions are polynomial functions of second degree.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given function is y = (k + 1) x² - 3x + (k + 1).
If the curve lies below the X axis, then the curve will not touch the X axis.
This means that, there will be no zeroes for the quadratic function.
So the discriminant will be negative.
Discriminant = [tex]\sqrt{b^{2}-4ac }[/tex] , for f(x) = ax² + b x + c.
So, for the function given,
Discriminant = [tex](-3)^{2} -[4*(k+1)*(k+1)][/tex]
= [tex]9-4(k+1)^{2}[/tex]
= 9 - 4(k² + 2k + 1)
= 9 - 4k² - 8k - 4
= -4k² - 8k + 5
-4k² - 8k + 5 < 0
4k² + 8k -5 > 0
Find the zeroes of 4k² + 8k - 5.
Zeroes are, k = [ -8 ± [tex]\sqrt{8^2-(4*4*-5)}[/tex] ] / (2 × 4)
= [ -8 ± [tex]\sqrt{144}[/tex] ] / 8
= [-8 ± 12] / 8
Zeroes are k = 4/8 = 1/2 and k = -20/8 = -5/2
4k² + 8k -5 = 0 when k = 1/2 and k = -5/2
4k² + 8k -5 > 0, when k > 1/2 and k < -5/2
Hence the values of k are k > 1/2 and k < -5/2 for which the function lies below the X axis.
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A model car at Target cost $130 after a discount and the original price of the car was $160. What was the percent discount that the store offered?
Answer: the store offered an 18.75% discount on the car
Step-by-step explanation:
i cant get this question figured out
Therefore , the solution of the given problem of expression comes out to be [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex] is the left expression.
Explain expression.Mathematical operations including addition, subtraction, multiplication, and division are required. They result in the following when combined: An equation, some information, and an arithmetic operator Values, parameters, and operations like adds, omissions, multiplications, and divisions make up a statement of fact. Different phrases and words can be contrasted and compared.
Here,
Given :
=>[tex](5x - 3)^\frac{1}{4} - 1/2(5x-3)^\frac{1}{4}[/tex]
=> [tex](5x-3)^{1/4} {1-\frac{1}{2 }[/tex]
=>[tex](5x -3)^\frac{1}{4} \times \frac{1}{2}[/tex]
=> [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex]
Thus , answer is [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex]
Therefore , the solution of the given problem of expression comes out to be [tex]\frac{1}{2} \times(5x-3)^{\frac{1}{4}}[/tex] is the left expression.
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Choose the correct graph to fit the equation
The equation of the line passing through (2, 3) and (-1, -1). is 3y = 4x + 1
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear function is:
y = mx + c
m is the rate of change and b is the y intercept
The graph passes through (2, 3) and (-1, -1). Hence:
y - 3 = [(-1-3)/(-1-2)] (x - 2)
y - 3 = (4/3)(x - 2)
multiply through by 3:
3y - 9 = 4(x - 2)
3y - 9 = 4x - 8
3y = 4x + 1
The equation of the line is 3y = 4x + 1
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please help me with math i’ll give you brainlist
On solving the provided question we can say that equation of new line is y + 2 = -1/3(4x + 2)
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
lines,
y - 1 = -3(x-2)
3y = x- 9
here slope, m is -3
equation of new line is
y + 2 = -1/3(4x + 2)
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The green family is selecting a furniture set there are 3 beds 1 desk and 4 dressers
The number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are 12.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that green family is selecting a furniture set there are 3 beds 1 desk and 4 dressers.
The total number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are -
{x} = 3 x 4 x 1
{x} = 12
Therefore, the number of possible ways in which 3 beds, 1 desk and 4 dressers can be arranged are 12.
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Kens target heart rate range is 122-139 bpm. His resting heart rate is 73 bpm. What is his age?
Ken's age can be calculated as follows: x x x = maximum target heart range − - − resting heart rate x = 139 − 73 = 66 x = 139 - 73 = 66 x=139−73=66.
What is the heart rate of the resting heart ?Based on your age, you may calculate your maximum heart rate. Subtract your age from 220 to get a ballpark idea of your maximal age-related heart rate.
For instance, the predicted maximum age-related heart rate for a 50-year-old person would be computed as 220 - 50 years = 170 beats per minute (bpm).
15 seconds are needed to take your pulse. For beats per minute calculation, multiply this number by 4.
The highest rate is determined by deducting your age from 220. Therefore, the maximum heart rate for a 50-year-old is 220 minus 50, or 170 beats per minute.
Therefore, at a 50% level of effort, your goal would be 50% of that maximum, or 85 beats per minute.
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Free ez 20 points
Using this equation, match the correct part of the equation to the correct term.
5x - 8 = 12
Question 3 options:
-8 and 12 1. Contant(s)
5 2. Variable(s)
x 3. Coefficient(s)
The variable is x, the coefficient is 5, and the constant is -8 and 12.
Linear terms in an algebraic equation.A linear algebraic equation is an equation whose degree of the highest variable is 1. In an algebraic equation, we have variables, coefficients, and the constant.
An algebraic equation may be expressed as ax + b = 0 or ax + by + c = 0, where a, b, and c are real integers and x and y are variables with a maximum degree of one.
In 5x - 8 = 12
The variable is x, the coefficient is 5 i.e. the number prior(before) the variable, and the constant is -8 and 12.
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Ali opens his shop at 8:00a.m and closes at 9.00 pm. How long does the shop remains open?
Correct Answer:
Ali keeps his shop open for 13 hours straight.
Correct Step-by-step explanation:
Well that is that! Can't say anything about it....
It is simple babyish counting that you should learn too!
Hope this helped you count!
P.S: BRAINLIEST IS REQUIRED
red and blue ceramic tiles are laid according to a pattern such that every 18 red tiles used, 7 blue tiles are used. if a total of 350 tiles are used, how many of them are blue? setup a proportion for this scenario( use x for your unknown number of blue tiles).
Answer:
There are 98 blue tiles.
Step-by-step explanation:
-this question is solved by proportions, using a rule of three
-For every 18 red tiles used, 7 blue tiles are used, hence, adding 18 and 7 gives you the total tiles, 7 are blue. How many blue tiles are there out of 425?
The rule of three is:
7 blue- 25 total
x blue- 350 total
Applying cross multiplication:
[tex]25x= 7(350)[/tex]
[tex]x=\frac{7(350)}{25}[/tex]
[tex]x= 98[/tex]
Which of the values shown are potential roots of f(x) = 3x3 - 13x2 - 3x + 45? Select all that apply.
A. +1/3
B. +5
C. +5/3
D. +9
E. +1
F. +15
G. +3
H. +45
The potential roots of f(x) = 3x³ - 13x² - 3x + 45 are given as follows:
A. +1/3
B. +5
C. +5/3
D. +9
E. +1
F. +15
G. +3
How to obtain the potential zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 45.The factors are given as follows:
Factors of 3: {1,3}.Factors of 45: {1,3, 5, 9, 15, 45}.Hence the possible roots are given as follows:
±1/3, ±1, ±3, ±5, ±5/3, ±9, ±5, ±15.
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Consider the equation 2(5x-4)= ax + b.
Find a value for a and a value for b so the equation has no solution.
Show your work.
There is no solution to the problem because both a and b have values.[tex]a = 10 , b\neq -8[/tex] .
An equation example is what?The definition of an equilibrium in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A.[tex]a = 10 , b\neq -8[/tex]
B.[tex]a= 10 , b= -8[/tex]
Consider the equation
[tex]2(5x-4)= ax + b.[/tex]
A. When the coefficient at x are the same but the unbound coefficients are different, the equation has no solutions.
First, use distributive property:
[tex]2(5x-4)= 10x - 8[/tex] (by solving )
So, the equation is
[tex]10x - 8 = ax + b.[/tex]
This equation has no solutions when
[tex]a = 10 , b\neq -8[/tex]
B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.
So, the equation
[tex]10x - 8 = ax + b[/tex]
has infinitely many solutions when
[tex]a= 10 , b= -8[/tex]
In some situations, the formula has a singular solution.
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The mean of a set of statistics test scores is 63 with a standard deviation of 7.0. For a set of Biology test scores the mean was 38 and the standard 3.9. Jeremy scored 60 on the Statistics test and 28 on the Biology. What is the standardized score of each outcome and on which did Jeremy do better?
The standardized score of each outcome is 3.85.
What is Z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by;
z = (x - μ)/σ
Where x is raw score, μ is mean and σ is standard deviation.
Given that;
μ = 23, σ = 3.9, hence for a score x = 38:
Now, substituting the values;
z = (38 - 23) / 3.9 = 3.85
z= 15/3.9
z=3.85
Therefore, the answer will be z score of 3.85;
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Calculate the standard deviation of the following data set:
0000000000
0000000000
all fourth grade children on long island are given an examination on mathematical achievement. a random sample of 60 fourth graders are selected. their examination results are summarized in the following stem-and-leaf plot. find the sample upper quartile. 6 4
6 6
88 88
1 1
33 33
445 445
6667777 6667777
8888889 8888889
11111 11111
2233333 2233333
4455 4455
66777 66777
899 899
1 1
223 223
45 45
The small upper quartile is 81.
A random sample of 60 fourth graders are selected.
Since, there are 60 values.
The median of a set of data is the middlemost number or center value in the set. The median is also the number that is halfway into the set.
Sample median will be Average of [tex](\frac{60}{2} )^{th}[/tex] value and [tex](\frac{60}{2}+1)^{th}[/tex] value
The formula to calculate the median of the finite number of data set is given here. The median formula is different for even and odd numbers of observations. Therefore, it is necessary to identify first if we have odd number of values or even number of values in a given data set.
If the total number of observations given is odd, then the formula to calculate the median is:
Median[tex]=(\frac{n+1}{2} )^{th}[/tex]termIf the total number of observation is even, then the median formula is:
Median=[tex]= (\frac{n}{2}) ^{th}+(\frac{n}{2}+1)^{th} /2[/tex]Sample median = Average of 30th value and 31st value
From the stem and leaf plot :
30th value = 81
31st value = 81
Sample median = (81+81)/2 = 81
Therefore, the sample upper quartile is 81.
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15 POINTS
O Function
O Not a function
Relation 1
Domain Range
O Function
E
V
d
r
f
Not a function
с
с
с
r
Relation 3
{(-3, -3),(-5, 9), (-8, 9), (9, -3))
с
O Function
Domain Range
2
pencil
8
Relation 2
Not a function
-7
2
-4
30
Function
Not a function
moon
pencil
door
moon
Relation 4
{(x, -3), (v, -3), (c, -3), (y, -3)}
Relation 1: Function
No input in the domain is used more than once.
Relation 2: NOT a function
Input of 2 is used more than once, so it has two outputs for that one input.
Relation 3: Function
No x-value is repeated.
Relation 4: Function
No x-value is repeated.
