Find the distance between the pair of points: (-14, 9) and (3, 9)

Using the shell method, the volume is

[tex]\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx[/tex]

Each cylindrical shell has radius [tex]2-x[/tex] (the horizontal distance from the axis of revolution to the curve [tex]y=8x^3[/tex]); has height [tex]8x^3[/tex] (the vertical distance between a point on the [tex]x[/tex]-axis in [tex]0\le x\le1[/tex] and the curve [tex]y=8x^3[/tex]).

Compute the integral.

[tex]\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}[/tex]

Answer:

Let

x--------> the number

we know that

solve for x

Adds  both sides

Multiply by  both sides

therefore

the answer is

the number is 12

Step-by-step explanation:

Answer:  The answer is -1

Step-by-step explanation:

-28/-4+-48/6

7-8

-1

Answer: -1

Step-by-step explanation:

-28 divided by -4 is 7

-48 divided by 6 is -8

7 - 8 would be a total of -1

Answer:

5y + 12x

Step-by-step explanation:

Let's simplify step-by-step.

5y+3x+9x

Combine Like Terms:

=5y+3x+9x

=(3x+9x)+(5y)

=12x+5y

Answer:

5y + 12x

Step-by-step explanation

Simplify step-by-step.

5y+3x+9x

Combine like terms:

=5y+3x+9x

=(3x+9x)+(5y)

=12x+5y

Answer:

h(10) = -25

Step-by-step explanation:

h(x) = -3x + 5

h(10) = -3(10) + 5

        = -30 + 5

        = -25

I hope this helps!

Answer:

36.3 seconds per lap

Step-by-step explanation:

200m in 2.42  if each lap = 50m

50m = 36.3 seconds

In linear equation , $8  the amount of money (cost) to play laser tag.

What are a definition and an example of a linear equation?

let x = number of games, let y = cost of  tag

then        Total cost = x•$3 + y

In this case, TC = 3•$2 + $2

TC = $8

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The number of black-and-white is 60 and the number of color copies is 8.

Let b = the number of black-and-white.

Let c = the number of color copies.

The equation will be:

b + c = 68

0.08b + 0.15c = 6

Multiply equation I by 0.08

Multiply equation ii by 1.

0.08c + 0.08c = 5.44

0.08b + 0.15c = 6

Subtract

0.07c = 0.56

c = 0.56/0.07

c = 8

Since b + c =68

b= 68 - 8 = 60

Therefore, the number of black-and-white is 60 and the number of color copies is 8.

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Since the pairs of y values have singular and unique x values, the following set of points are a function.

Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.

[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]

Option: C

Trent writes 10×6=60, then in multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

Given,

Trent writes 10×6=60,

Here,

10 represents the number of muffin boxes

6 represents the numbers of muffins in each box

60 represents the total numbers of muffins

Hence, Trent writes 10×6=60, then in the multiplication equation 10 represents the number of muffin boxes, 6 represents the numbers of muffins in each box and 60 represents the total numbers of muffins.

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Solution:

A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]

Hope this helps!

2/5 get dumps out of the box from 4 and 7/10 pounds of candy then weight of the candy left in the box  is 2 and [tex]\frac{41}{50}[/tex] pounds.

As given,

Total weight of the candy =  4 and 7/10 pounds =  [tex]\frac{47}{10\\}[/tex] pounds

pound is the  imperial unit of weight generally written as lb.

one pound = 0.4535 kilograms = 453.5 gm.

[tex]\frac{2}{5}[/tex] th of candy is dumps out of the box.

1- [tex]\frac{2}{5}[/tex] = [tex]\frac{3}{5}[/tex] th of the total candy is left in the box.

weight of the candy left in the box = [tex]\frac{3}{5}[/tex] * [tex]\frac{47}{10}[/tex] = [tex]\frac{141}{50}[/tex] pounds.

now 141= 50*2 + 41

[tex]\frac{141}{50}[/tex] pound = 2 and [tex]\frac{41}{50}[/tex] pounds

Hence, weight of the candy left in the box= 2 and [tex]\frac{41}{50}[/tex] pounds.

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Answer:

Area = 192.5 ft.²

Step-by-step explanation:

By splitting the shape in 2, we can find the area much simpler.

Starting with the parallelogram (on the left), the area formula is A = b × h.

b (base) = 11 ft.

h (height) = 7 ft.

A (area) = (11 ft.)(7 ft.)

A = 77 ft.² (save this for later)

Then, the trapezoid's (on the right) area formula is A = [(a + b) ÷ 2] × h.

a (first base) = 8 ft.

b (second base) = (20 - 7) = 13 ft.

h (height) = 11 ft.

A = [(8 ft. + 13 ft.) ÷ 2] × 11 ft.

A = [(21 ft.) ÷ 2] × 11 ft.

A = (10.5 ft.) × 11 ft.

A = 115.5 ft.²

Now, bringing back the first area, we can add them together to find the total:

A = 77 ft.² + 115.5 ft.²

A = 192.5 ft.²

Hope this helps! I'd appreciate Brainliest but if not it's totally fine!

Answer:

Step-by-step explanation:

Colin paid the loan at a ten percent annual interest rate.

Simple interest is the form of interest calculation in which the principal amount remains the same for the entire duration for which the loan is taken.

It is also assumed that Colin will repay $35 per month for the next two years.

We must calculate a simple interest rate on Colin's borrowings.

As a result, Colin's total payment to his parents for two years is $35.

We are required to find simple interest rate on Colin's borrowings

Therefore, total amount paid by Colin to his parents= 35$ for 2 years

        =35*24=840

The amount paid by Colin is principal + interest

Thus, the simple interest amount= 840-700=140$

We know that the simple interest formula is principal*rate*time/100.

We know that the simple interest is 140, the principal is 700, the time is two years, and we need to find the rate of interest.

SI= P*R*T/100

140= 700*R*2/100

140/7*2=R

R=140/14=10

Therefore, The Rate of interest on which Colin paid the loan is 10 per cent per annum

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The scale drawing which is equal to 9 yards in real time is 12 cm.

Given that 4cm on the scale, drawing is equal to 3 yards in real-time

we have to find the scale drawing which is equal to 9 yards in real-time.

Let the scale drawing be 'x'

Now it can be written as

4 cm ------ 3 yards

x cm ------- 9 yards

Now we can divide this as

4/x = 3/9

By cross multiplication, we get

4 * 9 = 3 * x

x = 4 * 9 / 3

x = 12

Therefore, the scale drawing which is equal to 9 yards in real time is 12 cm.

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Answer:

see attached

Step-by-step explanation:

The vector difference u -v can be represented on a vector diagram by the sum u +(-v), where -v is a vector the same length as v, but in the opposite direction.

__

The Perimeter of rectangle 3cm 5cm is 16 cm.

In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.

Some important formulas for rectangle :

Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .

Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)

                                                 = 2 ( length + breadth )

In the given question,

length of rectangle =  3cm

breadth of rectangle = 5cm

therefore, perimeter of rectangle = 2(3+5) = 16cm

Hence, The Perimeter of rectangle is 16 cm.

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Answer:

a

Step-bye-step explanation:

that's the correct answer

Based on the fact that the widow got an exemption on homestead tax, the amount that the owner would pay in property taxes is $3,471.20.

The widow received a homestead tax exemption of $25,000 on the property.

The amount to be paid in property tax is:

= (8.8 + 9.3 + 6.5) / 1,000 x (185,000 - 25,000)

= 21.7/1,000 x 160,000

= $3,471.20

In conclusion, the property tax to be paid is $3,471.20.

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Answer:

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]7\frac{3}{4} *4\frac{2}{5}[/tex]

→ Convert both fractions into improper

[tex]\frac{31}{4} *\frac{22}{5}[/tex]

→ Simplify

[tex]\frac{31}{2} *\frac{11}{5}[/tex]

→ Calculate

[tex]\frac{341}{10} =34\frac{1}{10}[/tex]

The value of x and y by using the given expressions is x = -5/2 and y = -15/2.

What is an expression?

An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.

Simplifying the expressions for x and y

The given expressions are:

x - y = 5           —--- 1

x + y = -10             —---- 2

Adding the expression 1 and 2, we get,

2x = -5

x = -5/2

Subtracting the expression 1 and 2, we get,

-2y = 15

y = -15/2

Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.

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The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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Answer:

translation

all the points are in the same orientation, and all the lengths are the same.

all that has changed are the coordinates.

Answer:

1.5 pounds

Step-by-step explanation:

3/2 = 1.5

Answer:

Step-by-step explanation:

Answer:

4 + -1 = 3, 3 - 5 = -2.

Step-by-step explanation:

Hope this helps!!