Use disks and washers to find the volume of the solid the results when the area of the region y=x^3 y = 0, and x = 2 is revolved about the line x= 2
Answers
Solution
The functions that define the region in consideration are given below:
[tex]\begin{gathered} y=x^3 \\ y=0 \\ x=2 \end{gathered}[/tex]The Washer Method:
- Plotting these functions would help us visualize the question better. This is done below:
- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:
[tex]\begin{gathered} V=\int ^b_a{f(y)\mathrm{dy}} \\ \text{where,} \\ a\text{ and }b\text{ are the bounds of the integration along the y-axis} \end{gathered}[/tex]-
We can represent the region bounded by the function by rearranging the functions as follows:
[tex]undefined[/tex]
Related Questions
A store charges $140 for every 10 bags of fertilizer a farmer buys. a. Complete the table. Graph the values. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840 b. How much would a farmer pay for 50 bags of fertilizer? Explain. a. Complete the table. 30 40 Fertilizer (bags) 10 Cost ($) 140 280 840
Answers
Question:
Solution
a) If for every 10 bags the store charges $140 then
1. for 10x2 = 20 bags the store charges 2x$140 = 280.
2. for 10x3 = 30 bags the store charges 3x$140 = 420.
3. for 10x4 = 40 bags the store charges 4x$140 = 560
4. for 10x6 = 60 bags the store charges 6x$140 = 840
b) According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
c)
According to the previous item, we can conclude that for 10x5 = 50 bags the store charges 5x$140 = 700 then, the farmer must pay $700 for 50 bags.
Finding Slope
Help mee
Answers
Answer:
-5 over 30
Step-by-step explanation:
John owes $25.20 to his mom. He borrowed $27.60 from his dad. Howmuch does he owe in all? Write your answer as a rational number *
Answers
John owes to his Mom and Dad.
From Mom = 25.20
From Dad = 27.60
The total amount he owes is the sum of both. We just add both the amounts.
Total: 25.20 + 27.60 = $52.80
What is 35% of 125?
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The 35% of 125 is computed as follows:
[tex]125\cdot\frac{35}{100}=43.75\text{ \%}[/tex]Find the percent markdown. Cost of a pants $36.95, selling price $24.02
Answers
Answer:
35%
Explanation:
Given cost of a pant = $36.95 and selling price = $24.02.
Let the markdown percent be y.
To determine the markdown percent, we'll use the below formula;
Sale Price = Original Price x (1 - Markdown% in decimal)
So let's go ahead and substitute the given values into the equation;
[tex]\begin{gathered} 24.02=36.95\ast(1-y) \\ 24.02=36.95-36.95y \\ -12.93=-36.95y \\ y=\frac{-12.93}{-36.95} \\ y=0.35 \\ \therefore y=35percent \end{gathered}[/tex]So the markdown percent is 35%
18. What is the probability of drawing a BLACK card with an odd number OR a card with a LETTER?A.21261B..ع1726p D. 13
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Let:
A = Draw a black card
B = Draw and odd number
C = Draw a card with a letter
so:
[tex]\begin{gathered} P(A\cap B)=\frac{8}{52}=\frac{2}{13} \\ P(C)=\frac{16}{52}=\frac{4}{13} \end{gathered}[/tex]Therefore:
[tex]P((A\cap B)\cup C)=\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}[/tex]a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?
Answers
In this case
[tex]\begin{gathered} 48=45+3 \\ 51=45+2(3) \end{gathered}[/tex]Therefore, the percentage that lies between 45 and 48 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]And, the percentage that lies between 45 and 51 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]7. f(x) = x² + 4 (a) f(-2) (b) f(3) f) f (c) f(2) (d) f(x + bx)
Answers
212385758487✖️827648299199375
Answers
Answer:
1.7578071e+26
Step-by-step explanation:
What is your answer? estion 3 Why is this your answer? 60 40 20 Which is the correct answer? 4 5 6 Time (seconds) Why is this the correct answer? statement is TRUE about the motion of this object as shown in the graph? The object was accelerating from t = 1 tot = 3 The object was slowing down from t = 4.5 to t= 6. © The object returned to its original location by t = 6 seconds. The object was traveling at a constant speed from t = 3 to t = 45 seconds
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As we can see in the graph the object returned to its original position in t=6.
It's not accelarating because acceleration is the second derivate of the position, and the position is determined by a linear equation.
The answer is C.
12*pi=pi*12Name the property that the following statement illustratesA. Identify property of multiplicationB. Associative property of multiplication C. Commutative property of additionD. Commutative property of multiplication E. Identity property of additionF. Associative property of addition
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The commutative law says that we can swap the position of numbers when we add or multiply and still get the same result
The commutative property of multiplication can be expressed as
ab = ba
The commutative property of addition can be expressed as
a + b = b + a
Looking at the given expression,
12 and pi were swapped and the sign involved is multiplication. Thus, the correct option is
D. Commutative property of multiplication
I need help with my math assignment thank you :)
Answers
Okay, here we have this:
Considering the provided information, we are going to match the situations to their corresponding functions, so we obtain the following:
1: The total pages a person reads in x days, if the person reads 6 pages a day: f(x)=6x.
2: The cost of x boxes of mangoes, if 1 box cost $6 and the shipping charge is $6 per order: f(x)=6x+6 -> f(x)=6(x+1)
3: The total cost of x notebooks, if one notebook cost $6 and students receive a discount of $1 off their bill: f(x)=6x-1
4: The total cost of x novels and a pocket dictionary if you buy a novels each at $6 and get a pocket dictionary at $1: f(x)=6x+1
The bike you have been saving for is discounted 25%. You have $400 saved to purchase it. The original, non-discounted price of the bike is $450. There is a 5.44% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
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1) Let's begin considering that our budget is $400.
Since the bike is discounted by 25%, we can get to know the price with this formula:
[tex]400\times(1-0.25)=\$300[/tex]2) Note that there is an increase in the price since there are taxes to pay. The original price is taken into consideration to charge the tax. So, let's find how much we have to pay:
[tex]450\times0.0544=\$24.48[/tex]So, let's add that to the discounted price:
[tex]\$300+\$24.48=\$324.48[/tex]3) Since I've got $400 let's find how much is left after that purchase:
[tex]\$400-\$324.48=\$75.52\approx\$76[/tex]Note that as requested we rounded off to the nearest dollar.
Thus, that's what's left after the purchase
Just the number 2 please a ball is tossed in the air in such a way that …..
Answers
Note that a quadratic function is increasing and decreasing at exactly half between the roots.
The roots are the point on the ground when tossing the ball into the air.
So we need to get the roots of the given equation.
Roots are the values of x when y = 0
[tex]\begin{gathered} y=-x^2+6x \\ 0=-x^2+6x \\ 0=-x(x-6) \\ -x=0\Rightarrow x=0 \\ (x-6)=0\Rightarrow x=6 \end{gathered}[/tex]So the roots are 0 and 6, this will be the x coordinate or the point on the ground.
Since the equation is increasing halfway and decreasing up to the ground, the halfway point is the midpoint between the roots.
Midpoint = (0 + 6)/2 = 3
Therefore, the ball's height is always decreasing at 3 < x < 6
The answer is 3 < x < 6
A rectangle has a length of 9 inches and a widt of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec. What is the rate of change of the perimeter?
Answers
Given:
A rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec.
To find:
The rate of change of the perimeter.
Solution:
It is known that the perimeter of the rectangle is twice the sum of length and width.
[tex]P=2(l+w)[/tex]DIfferentiate the perimeter with respect to t:
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})[/tex]From the given information:
[tex]\begin{gathered} \frac{dP}{dt}=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}[/tex]Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. 2 -14 - 5
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In order to find the determinant we just multiply the diagonals
Then we substract the second result to the first:
[tex]\begin{gathered} \begin{bmatrix}{2} & {-1} & {} \\ {4} & {-5} & {} \\ & {} & {}\end{bmatrix}=2\cdot(-5)-4\cdot(-1) \\ =-10-\mleft(-4\mright)=-10+4 \\ =-6 \end{gathered}[/tex]Answer: the determinant of this 2x2 matrix is -6Write the product using exponents. I need help I’m not sure how to do this
Answers
Given:
The given expression is,
[tex]\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}[/tex]Required:
Write the product using exponent.
Answer:
Let us compute the product using exponents.
[tex]\begin{gathered} \frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5} \\ =(\frac{1}{5})^5 \\ =\frac{\left(1\right)^5}{\left(5\right)^5} \\ =\frac{1}{3125} \end{gathered}[/tex]Final Answer:
The product using exponents is given by,
[tex]\frac{1}{3125}[/tex]
ok so I understand the first 2 steps of solving this but I dont entirely get it........
Answers
You have the following equation:
2x² - 12x + 16 = 0
in order to solve the previous equation, first divide by 2 both sides:
x² - 6x + 8 = 0
next, consider that the factors of the previous expression has the form:
(x - )(x - ) = 0
consider the first number inside the first factor is the result of the sum of two numbers, and the number of the second factor is the product of the same numbers. Such numbers are:
(2)·(4) = 8
2 + 4 = 6
hence, the factorized expression is:
(x - 8)(x - 2) = 0
the solutions of the equations are:
x = 8
x = 2
Translate the sentence into an equationThe difference of Mai’s height and 13 is 53Use a variable M to represent Mai’s height
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The difference in math means the result of subtracting one number from another.
m = Mai’s height
Therefore, the equation is:
[tex]m-13\text{ = 53}[/tex]Find the volume of a cube with a side length of 2.8 in, to the nearest tenth of a cubic inch (if necessary).
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Given:
Length of side = 2.8 in
Let's find the volume of the cube.
To find the volume of a cube, apply the formula:
[tex]V=a^3[/tex]Where:
a is the side length = 2.8 in
Hence, to find the volume, we have:
[tex]\begin{gathered} V=2.8^3 \\ \\ V=2.8*2.8*2.8 \\ \\ V=21.952\approx22.0\text{ in}^3 \end{gathered}[/tex]Therefore, the volume of the cube is 22.0 cubic inch.
ANSWER:
22.0 in³
Complete the following proof
Given: = 3(5x + 1) = 13x + 5
Prove: x = 1
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Solving the Question
[tex]3(5x + 1) = 13x + 5[/tex]
Plug in x=1:
[tex]3(5(1) + 1) = 13(1) + 5\\3(5 + 1) = 13 + 5\\3(6) = 18\\18=18[/tex]
This statement is true.
Find the cosine of angle R. Reduce the answer to the lowest terms.
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Cosine formula
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hypotenuse}}[/tex]Considering angle R, the adjacent side has a length of 9 units, and the hypotenuse of the triangle has a length of 15 units. Substituting this information into the above formula:
[tex]\cos (m\angle R)=\frac{9}{15}=\frac{\frac{9}{3}}{\frac{15}{3}}=\frac{3}{5}[/tex]a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in still water and what is the rate of current?
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jeslie ann has a 48 month installment loan of 82.91. the amount she borrowed was 3600
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Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.
Step 1
Loan Amount(p)= 3600
Number of Payments per year(n)= 12
Time in Years (t)=4
Installment Payment (m)=83.81
Total amount paid in 48 installments= 4022.88
Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.
To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.
Finance Charge/ Amount financed × 100= 522.88/ 3600× 100= 14.5
To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.
:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]
Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17
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Where may estimation of decimals be useful in every-day life? Give an example
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You can use decimal numbers (those numbers that have a comma after an interger part and before the decimal part)
You can use decimal numbers in real life in measures as:
Examples:
weight (you can weight 132,27 lb)
volumen of soda (you can drink a glass of soda of 8,45 oz = 0,25 L)
The temperature ( the temperature can be 89,9 F)
All the examples above have decimal number that can be useful in every-day life.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
The range of f(x) = 3x + 9
{y | y > 9}, Option B
This is further explained below.
What is the range?Generally, Based on the possibilities that have been presented to us, we may speculate that x is inside the exponent of 3.
Therefore, the formula for the function f(x) is really f(x) = 3x +9
Now that we have a function, we need to determine its range of values.
It is clear that the first component is an exponential term denoted by 3x, and that the second term is the number 9.
It is common knowledge that the product 3x will always be higher than 0.
As a result, the result of adding 3x to 9 will always be more than 9.
As a result, the range would be y more than 9.
In conclusion, option B "y | y > 9" is the range
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Answer: B
Step-by-step explanation: Trust
A number decreased
by the sum of the number and three
Answers
Answer:
-3
Step-by-step explanation:
x - (x+3)
x - x -3
-3
What is the value of 7C4?A). 35B). 840C). 2,520D). 5,040
Answers
Answer:
A) 35
Explanation:
The combination nCx can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Where n! = n(n-1)(n-2)...(2)(1)
So, to find 7C4, we need to replace n by 7 and x by 4 to get:
[tex]7C4=\frac{7!}{4!(7-4)!}=\frac{7!}{4!(3)!}[/tex]Therefore, 7C4 is equal to:
[tex]7C4=\frac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\frac{5040}{24(6)}=\frac{5040}{144}=35[/tex]So, the answer is:
A) 35
How do you evaluate the following polynomials for a domain value?P(x) = -3x² + 9x find P(-5)
Answers
The given polynomial is expressed as
P(x) = - 3x^2 + 9x
The domain values are the x values. To find P(-5), it means that we would substitute x = - 5 into the polynomial. It becomes
P(- 5) = - 3(- 5)^2 + 9(- 5)
P(- 5) = - 3 * 25 - 45
P(- 5) = - 75 - 45
P(- 5) = - 120
Question 1
Is the sequence arithmetic: 78, 785, 7855, 78555, ...
O No
5 pts
Yes
Next >
Answers
The sequence is not arithmetic
What is a sequence?
A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which might be infinite). Unlike a set, the same components can occur numerous times in a sequence at various points, and the order does important. Formally, a sequence may be defined as a function from natural numbers (the sequence's places) to the items at each point. The concept of a sequence may be extended to include an indexed family, which is defined as a function from an arbitrary index set.
The given sequence 78, 785, 7855, 78555, ... is not arithmetic.
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