The base of a solid is bounded by the curve y = sqrt (x+1) the x-axis and the line x = 1. the cross sections, taken perpendicular to the x-axis, are squares. find the volume of the solid.
a. 1
b. 2
c. 2.333
d. none of these
(will vote brainlest, like and rate)
Answers
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
[tex]\displaystyle \int_{-1}^1 (x+1) \, dx = \left(\frac{x^2}2 + x\right) \bigg|_{-1}^1 = \boxed{2} ~~~~ (B)[/tex]
Related Questions
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each description with the correct inequality.
(5x)2 ≤ 46,
(5x)2 ≥ 46,
x2 + 5x ≥ 46,
5x2 > 46,
x2 + 5x ≤ 46,
5x2 < 46,
The square of the product
of 5 and a number is
no less than 46.
arrowBoth
The product of 5 and the
square of a number is
greater than 46.
arrowBoth
The sum of the square of a
number and five times that
number is no more than 46.
Answers
Answer:
(5x)² ≥ 46
x² + 5x ≤ 46
5x² > 46
Step-by-step explanation:
Suppose number is x
1)The square of the product of 5 and a number is not less than 46.
Step 1
Product of 5
5x
Step 2
Square of the product of 5
(5x)²
Step 3
A number is not less than 46
(5x)² ≥ 46
2)The sum of square of a number and five times that number is no more than 46
Step 1
Square of a number
x²
Step 2
Five times that number
5x
Step 3
The sum
x² + 5x
Step 4
Is no more than 46
x² + 5x ≤ 46
3)The product of 5 and the square of a number is greater than 46
Step 1
The square of a number
x²
Step 2
The product of 5
5x²
Step 3
Is greater than 46
5x² > 46
Solve the system using linear combination. Show all work.
{9x + 4y = 28
{2x + 4y = 0
Answers
Answer:
(4,-2)
Step-by-step explanation:
What is linear combination?
Linear combination is the process of adding two equations to eliminate a variable so that we are able to solve for the other variable.
Here we are given the two equations 9x + 4y = 28 and 2x + 4y = 0. We can use linear combination to cancel out the two 4y terms leaving us with only x variables in which we can solve for.
Adding the two equations. (subtracting the second equation from the first) we really are subtracting the second equation from the first because if we were to add we would get 4y + 4y which wouldn't cancel out the terms therefore we would have to subtract the two equations to get 4y - 4y which cancels out the terms.
9x + 4y = 28
- (2x + 4y = 0)
==> remove parenthesis and apply negative sign
9x + 4y = 28
-2x - 4y = -0
----------------------
7x = 28
==> divide both sides by 7
x = 4
Finding the y value:
The solution is written as (x,y) meaning we also need the value of y. To find it we can plug in the value of x into one of the equations and then we can solve for y.
2x + 4y = 0
==> plug in x = 4
2(4) + 4y =0
==> multiply 2 and 4
8 + 4y = 0
==> subtract 8 from both sides
4y = -8
==> divide both sides by 4
y = -2
so we have x = 4 and y = -2
the solution of the equation would be (4,-2)
Checking our work
If our answer is correct we can plug in the values of x and y into both equations and the outcome will be valid ( or correct )
Equation 1 : 9x + 4y = 28
==> plug in x = 4 and y = -2
9(4) + 4(-2) = 28
==> multiply 9 and 4
36 + 4(-2) = 28
==> multiply 4 and -2
36 - 8 = 28
==> subtract 8 from 36
28 = 28
Equation 2 : 2x + 4y = 0
==> plug in x = 4 and y = -2
2(4) + 4(-2) = 0
==> multiply 2 and 4
8 + 4(-2) = 0
==> multiply 4 and -2
8 - 8 = 0
==. Subtract 8 from 8
0 = 0
Both are correct so our solution is correct!
Learn more about solving systems using linear combination here! : https://brainly.com/question/12691830
Step-by-Step Explanation:
Lets solve using Elimination Method.
9x + 4y = 28 (Eq. 1)
2x + 4y = 0 (Eq. 2)
Subtracting Eq. 2 from Eq. 1, we get :-
7x = 28
x = 28/7
=> x = 4
Therefore, x = 4
Substituting value of ‘x’ in Eq. 2 :-
2x + 4y = 0
2(4) + 4y = 0
8 + 4y = 0
4y = 0 - 8
4y = -8
y = -8/4
=> y = -2
Therefore, y = -2
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r? (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14) (startfraction 3 over 3 5 endfraction) (negative 14 minus 2) 2 (startfraction 3 over 3 5 endfraction) (2 minus 14) 14 startfraction 3 over 3 5 endfraction (negative 14 minus 2) minus 2
Answers
The mathematical expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r is:
" (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14)" (Option A)
What is a mathematical expression?A mathematical expression is a statement that contains numbers, variables, functions, etc that are related to one another in a very logical way.
It can also be defined as a mathematical phrase that comprises:
NumbersVariables or both.Learn more about mathematical expression at:
https://brainly.com/question/4344214
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Answer:
A
Step-by-step explanation:
can someone explain how to do this
im not very smart
Answers
Answer:
50.24sq units
Step-by-step explanation:
4^2=4x4
4x4=16
16x3.14=50.24
Question 3 :
Find the value of 3x3 - 4x2 + x - 5 when x = -3
(A) -54 (B) -71 (C) -32
Answers
Lacey had $603 in her checking account. Then, she spent $252 from the account. How much money is left in Lacey's checking account?
Answers
Answer:
In this problem we are given the initial amount of money that Lacey has in her account and we are also given the amount of money that she has spent using that account. We are told to check how much money is left in her account and we can do this with a simple subtraction.
[tex]Initial\ Amount - Money\ Spent[/tex]
[tex]\$603-\$252[/tex]
[tex]\$351[/tex]
Therefore, our final answer is that Lacey has $351 left in her account.
Hope this helps! Let me know if you have any questions
Given 184% what is the equivalent fraction and decimal in simplest form?
Answers
Step-by-step explanation:
184% = 46/25 = 1 21/25 as a fraction
If f(x) = x2 – 2x and g(x) = 6x 4, for which value of x does (f g)(x) = 0? –4 –2 2 4
Answers
The sum of function is a way of adding two or more functions together
The values of x for which f(g(x)) = 0 are -2/3 and -1/3
Sum of functionsThe sum of function is a way of adding two or more functions together
Given the following functions
f(x) = x² - 2x
g(x) = 6x + 4
f(g(x) = f(6x +4))
f(6x+4) = (6x+4)² - 2(6x+4)
(6x+4)² - 2(6x+4) = 0
(6x+4) = 0 and 6x+4-2 = 0
x = -2/3 and -1/3
Hence the values of x for which f(g(x)) = 0 are -2/3 and -1/3
Learn more on functions here: https://brainly.com/question/2833285
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What type of number is -5.41?
Choose all answers that apply:
A. Whole Number
B. Integer
C. Rational
D. Irrational
Answers
The type of number -5.41 is is an rational number.
What type of number is -5.41?A rational number is a number that can be expressed as a fraction of two integers. 5.41 can be expressed as -5.41 / 1000.
An integer and whole number is a number that does not have any fraction or decimal. -5.41 is a decimal number, thus it is not an integer and a whole number.
To learn more about irrational numbers, please check: https://brainly.com/question/20435423
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This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.
Answers
Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
Peter has 96 stamps and Sam has 63. How many stamps should Sam give Peter so that Peter will have twice as many stamps as Sam? equation please
Answers
Answer:15
Step-by-step explanation:
96÷2=48
63-48=15
So Sam should give Peter 15 of his stamps so that Peter will have twice as many stamps as him.
Answer:
10 stamps
Step-by-step explanation:
Let n = the number of stamps Sam gives Peter.
63 - n is the number stamps Sam has after giving some of them to Peter.
Peter starts with 96 stamps.
After Sam gives Peter n stamps, Sam will have 96 + n stamps.
2(63 - n) = 96 + n
126 - 2n = 96 + n
-3n = -30
n = 10
Answer: 10 stamps
Please answer the following for 50 points, if you get it right you can get brainly, Please hurry!
Answers
Answer:
3.2 and 3.92
Step-by-step explanation:
Nick's science class is learning about animal classification, and they listed as many animals as they could in a minute. They came up with 32 mammals, 16 birds, 8 amphibians, 8 reptiles, 12 fish, and 4 invertebrates.
Select all of the statements that describe the data.
They listened to an equal of amphibians and reptiles.
There are more mammals on the list than birds and fish combined.
The modes of the data are amphibians and reptiles.
A quarter of the animals they listened are either amphibians or fish.
Answers
Answer:
The second one is the correct answer
Step-by-step explanation:
There are more mammals on the list than birds and fish combined.
Find y.
Do not round your answer.
9 in
у
5 in
Х
19 in
y = [ ? ] in
=
Answers
Answer: 11.2
I found the answer in the comments and figured I should make it an answer, so it's easy to find:)
<3
Answer this question to get 10 pts!
Answers
A = 70x30 = 2100
B = 4x30 = 120
C = 9x70 = 630
D = 9x4 = 36
Total Area = 2100+120+630+36 = 2886
So 74x39=2886
B = 30 x 4 = 120
C = 9 x 70 = 630
D = 9 x 4 = 36
to find area use length x breadth
Use the distributive property to write an equivalent expression.
10(y-7z+1)
Answers
Answer:
10y - 70z + 10.
Step-by-step explanation:
10(y-7z+1) Multiply each term in the brackets by 10:
= 10y - 70z + 10
Combine the polynomials
(z2 - 5z + 3) - (z2 – 13z + 12)
-
Please help the twos are squared
Answers
Answer:
i think its 8z-9 if im not wrong :)
Step-by-step explanation:
i have a slight feeling the answer ain’t 21
Answers
Answer:
I think it is
Step-by-step explanation:
4,8,5,15,6,12,7,6
8,5,15,6,12,7
5,15,6,12
15,6
15+6=21
Mick recently had new carpet installed. the cost of the carpet including installation was $8.14 per square foot before any discounts. the rectangular room he had carpeted measured 24 feet long and 18 feet wide. if mick actually paid $3,235.16, what discount percentage did he receive? assume there are no taxes.
Answers
Answer:
8%
Step-by-step explanation:
Let’s first determine the cost before any discount.
To do so, we first need to determine the area to be carpeted:
Area of Rectangle = Length × Width = 24 ft × 18 ft = 432 square feet.
To find the cost before discount we need to multiply the area by the cost per square foot:
Cost Before Discount = Area × Cost per square foot
Cost Before Discount = 432 square feet × $8.14 per square foot
Cost Before Discount = $3,516.48
We can now determine the discount percentage he received:
Cost After Discount = Cost Before Discount − (Discount % × Cost Before Disc.)
$3,235.16 = $3,516.48 – (Discount % × $3,516.48)
To solve, it is easiest to plug in each answer to see which discount percentage is the correct solution (i.e. “work backwards” from the given answers) or use the equation solver on our calculator.
We find that a discount of 8% is the correct solution.
If you instead prefer to use algebra to solve for the discount percentage, here are the steps.
We will rewrite the equation, using x to represent “Discount %”.
$3,235.16 = $3,516.48 − (x × $3,516.48)
$3,235.16 = $3,516.48 − $3,516.48x
Factoring out $3,516.48 we have:
$3,235.16 = $3,516.48(1 − x)
Note: Once you get comfortable with this type of problem you should skip straight to the step above.
Dividing both sides by $3,516.48 we have:
$3,235.16$3,516.48=1−x
0.92 = 1 − x
x = 0.08 = 8%
Simpifly : -5/6-7/-8+11/12–1/6+0- -7/16
Answers
Answer:
the chosen topic is not meant for use with this typ of problem try the examples below
Step-by-step explanation:
3x∧2±6x±x±20 sole by factorization
Answers
Answer:
just look at the algebra formula and simplify to get your answer. Remember to use your powers well
A right rectangular prism has a base area of 20 cm? and a height of 9. 2 cm.
Answers
Answer:
the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.
Step-by-step explanation: hopefully that is the correct and have a great day.
HELP PLEASE!!!
The two-way table shows the number of students in a school who like painting and/or dance.
Like Painting
Do Not Like Painting
Like Dance
28
?
Do Not Like Dance
17
18
45
What is the missing number in the table?
016
023
033
079
Answers
Answer:
The total for liking and not liking painting is 51.
28 like painting, so to find the missing number subtract 28 from 51.
The missing number is 23
Tim, Ryan, and Joe are brothers. Their mom, Lisa gives them each a weekly allowance. Since Tim is older, she gives him 4 more dollars than Joe. Ryan is the youngest and receives 2 less dollars than Joe. Lisa gives a total of 20 dollars a week in allowance. With Joe receiving m dollars, which equation demonstrates the situation?
Answers
Answer:
m + (m+4) + (m-2) = 20 or 3m + 2 = 20
Step-by-step explanation:
are all natural numbers also a rational number? (yes/no)
Answers
Answer:
Yes
Step-by-step explanation:
But not all rational numbers are natural numbers, so be careful of that.
MARKING BRAINLIEST!
This is Poe’s most well-known poem, published in 1845, which quickly became famous. What words, lines, or features of the poem stand out to you? List three.
This is about “The raven”
Answers
Step-by-step explanation:
where is the figure and question
GIVING BRAINLIEST!!!!!
Answers
Find three consecutive even integers such that the sum of 5 and the second is multiplied by -7, the result is 11 greater than 5 times the opposite of the third
Answers
Answer:
-20, -18, -16
Step-by-step explanation:
For consecutive integer problems, it often works well to let a variable represent the middle one (or their average value).
__
Here, we can let x represent the second integer. Then the first is (x-2), and the third is (x+2). The given relation can be written as ...
(5 +x)(-7) = 11 +5(-(x+2))
-35 -7x = 11 -5x -10 . . . . . . eliminate parentheses
-36 = 2x . . . . . . . . . add 7x -1
-18 = x . . . . . . . . divide by 2
The three integers are -20, -18, -16.
A cylindrical tank has diameter 3.2 m and length
12.7 m.
What is the surface area of the tank, to 1 decimal
place?
Answers
Answer:
143.8 m²
Explanation:
Surface Area of cylinder = 2πr(r + h)
Here given,
diameter: 3.2 mradius: d/2 = 3.2/2 = 1.6 mlength: 12.7mSurface Area of cylinder:
⇒ 2π(1.6)(1.6+ 12.7)
⇒ 174.2955 m²
⇒ 143.8 m² (rounded to nearest 1 decimal place)
what’s the circumference, to this problem ?
Answers
Answer:
= 20.7345115137
or
≈ 21
Step-by-step explanation:
Circumference = 2 x π x radius
Circumference = 2 x π x 3.3
hope this helps
have a good day
Answer:
The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex]. We can then input the value and we get that [tex]C=2*\pi*3.3[/tex] and as we solve it more the final answer that we get is [tex]C=20.735[/tex].
Hope this helps! Let me know if you have any questions