Subtract 8−2x from 3−6x . Enter your answer by filling in the boxes. $$

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])

[tex]f(x) = g(x)[/tex] (1)

[tex]4\cdot x - 2 = x^{2}+1[/tex]

[tex]x^{2}-4\cdot x +3 = 0[/tex]

[tex](x-1)\cdot (x-3) = 0[/tex]

The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:

[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)

If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:

[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]

[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]

[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]

[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]

[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]

[tex]V = \frac{16\pi}{3}[/tex]

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

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Answer:

Step-by-step explanation:

Let x or y be the variable in each case.

1. Twice the product of the numbers ... x and y (just a guess, its incomplete):

2. Seven less than a number:

3. The sum of three consecutive numbers:

4. The sum of two consecutive even numbers is 42:

5. The sum of a number and 5 times its reciprocal:

6. Four more than twice a number:

7. The square of a number increase by five:

8. The sum of two numbers is equal to four more than their difference:

9. Rian's age four years from now:

10. Clara's age 10 year from now​:

Step-by-step explanation:

1. Let, Number = x

2x

2. Let, Number = x

x - 7

3. Let,

Consecutive numbers = x, x + 1 and x + 2

x + x + 1 + x + 2

3x + 3

4. Let,

Consecutive numbers = a and a + 2

a + a + 2 = 42

2a + 2 = 42

5. Let, Number = x

Reciprocal = 1/x

x + 5/x

6. Let, Number = y

2y + 4

7. Let, Number = y

(x + 8)²

x² + 16x + 64

8. Let,

First number = x

Second number = y

x + y = 4 + (x - y)

9. Let,

Rian's age = y

y + 4

10. Let,

Clara's age = y

y + 10

Answer:

If f(x) =3x^3+10x^2-13x-20 and f(-4)=0, then find all of the zeros of f(x) algebraically

Answer:

Option B,option D and option F are the correct statements.

Answer:

4606

Step-by-step explanation:

5234 · 0.12 = 628

5234 - 628 = 4606

Answer:

The answer to this question should be C: 4605.

Step-by-step explanation:

For this problem we need to know what 12% of 5,234 is. 12% of 5,234 is 628.08. Since their was a decrease in visitors we need to subtract 5,234-625.08=4,605.92. The probelm states that we need to find the "Approximate number", so have the .92 doesnt matter. So therefore the answer to this probelm is C: 4605.

yw :)

Answer:

x=17.333

Step-by-step explanation:

3x+8=60

3x=60-8

3x=52

x=52\3

x=17.333

Answer:

542.04 × 1.88 = 1020

Facts about 1,020

Sig Figs

3

1020

Decimals

0

Scientific Notation

1.02 × 103

E-Notation

1.02e+3

Words

one thousand twenty

Answer:

1 , 2 , 4 , 8

Step-by-step explanation:

Factors of 16:

1, 2, 4, 8, 16

Factors of 24:

1, 2, 3, 4, 8, 6, 12, 24

Common factors are factors that are shared by both numbers, in this case, it i: 1 , 2 , 4, 8

Answer:

corresponding segments

Step-by-step explanation:

BK = KB'

AJ - JA'

CL = LC'

Answer:

4th option

Step-by-step explanation:

7x(8x² - 4y² + 3y - 5) ← multiply each term in the parenthesis by 7x

= 56x³ - 28xy² + 21xy - 35x

The expression in the expended version will be equal to 56x³ - 28xy² + 21xy - 35x. Hence, option D is correct.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given expression,

7x (8x² - 4y² + 3y - 5)

Solve the equation by multiplying 7x with the bracket,

56x³ - 28xy² + 21xy - 35x

To know more about the expression:

https://brainly.com/question/14083225

#SPJ2

Answer:

52.4

Step-by-step explanation:

% change = 100 x final initial/initial

I have no idea math should have been working hade books bye sorry

Answer:

Cardiovascular system

Step-by-step explanation:

Answer:

y = -2x + 3

Step-by-step explanation:

the original formula is

y = mx + b

m is the slope

b is the inteception on the y axis

Answer:

.

Step-by-step explanation:

Answer:

64 degrees

Step-by-step explanation:

X equals 64 degrees because it shares a vertical angle pair with another angle which is 64 degrees. Since they are across from each other, x is 64 degrees.

Vertical angles are a pair of opposite angles formed by intersecting lines.

Answer:

d. 7, -14, 28, -56, 112

Step-by-step explanation:

f(2) = -2(7) = -14

f(3) = -2(-14) = 28

f(4) = -2(28) = -56

f(5) = -2(-56) = 112

Answer:

12

Step-by-step explanation:

We can solve this by setting up an equation with the variable x representing the number of boards. Since x number of 1.75 inches thick boards sum up to the height of 21 inches, the equation is 1.75x = 21, so x = 12. There are 12 boards.

Step-by-step explanation:

Since [tex]x[/tex] varies directly as [tex]\sqrt{y}[/tex] we can write the relation as

[tex]x = k\sqrt{y}[/tex]

where k is the constant of proportionality.

a) To solve for the k, we substitute the given values:

[tex]5 = k\sqrt{13} = k(13)[/tex]

[tex]\Rightarrow k = \dfrac{5}{13}[/tex]

b) The equation relation x and y can be written as

[tex]x = \dfrac{5}{13}\sqrt{y}[/tex]

c) When y = 9,

[tex]x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}[/tex]

Answer:

m ≥ 1229

Step-by-step explanation:

Use m for the number of minutes

30 + 0.05×m ≥ 91.45

0.05*m ≥ 91.45-30

0.05*m ≥ 61.45

m ≥ 1229

Answer:

The answer is 33.6.

Hope that helps?

Step-by-step explanation:

Answer:

2/8

Step-by-step explanation:

22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.

Since Amina recently moved and got a new job, and the quickest way to get to work is to take a freeway that charges a toll, and there are two options for paying the tolls:

Option A: No monthly fee, each trip on the tollway is $ 2.80.

Option B: $ 30 monthly fee, each trip on the tollway is half-priced at $ 1.40.

To determine how many trips on the tollway are needed for Option B to be cheaper; y, if Amina plans to travel to and from work 5 times a week, which option should she purchase; the following calculation must be performed:

Therefore, 22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.

Learn more about maths in https://brainly.com/question/25806839

Answer:

1867

Step-by-step explanation:

What do you need it for?

Answer:

.....

Step-by-step explanation:

merry Christmas to you too