Select the correct answer.
Simplify.
V96

Answer:

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Step-by-step explanation:

Given that:

y = 6x - x² , y = 8  about  x = 2

To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8

6x - x² - 8

6x - x² - 8 = 0

-x² + 6x - 8 = 0

x² - 6x + 8 = 0

(x -4) (x - 2  ) = 0

So;

x = 2 , x = 4

Thus, the region bound of the integral  are from a = 2 and b = 4

Therefore , the volume of the solid can be computed as :

[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]

[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]

[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]

[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Answer:

10

Step-by-step explanation

Answer:

10

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1

Answer:

see explanation

Step-by-step explanation:

f(g(2)) = f(0) = -2

g(f(1)) = g(0) = 0

Answer:

The correct answers for both of them is -2 and 0.

Step-by-step explanation:

I)

[tex](f\circ g)(2)=f(g(2))[/tex]

From the red graph, we can see that g(2) is 0.

Therefore, f(g(2)) is equal to f(0).

And from the blue graph, we can see that f(0) is -2.

Therefore:

[tex](f\circ g)(2)=-2[/tex]

II)

[tex](g\circ f)(1)=g(f(1))[/tex]

From the blue graph, we can see that f(1) is 0.

Therefore, g(f(1)) is equal to g(0).

And from the red graph, g(0) is 0.

Therefore:

[tex](g\circ f)(1)=0[/tex]

So, you got one correct. Nicely done!

Answer:

Bottom right option

Step-by-step explanation:

To find this, we can calculate:

1/2 * 4.32 * 10⁻⁴

= (1/2 * 4.32) * 10⁻⁴

= 2.16 * 10⁻⁴

The diameter of a new cell is 2.16×10−⁴millimeters

First step is to calculate 4.32×10−⁴ to the original numbers

4.32×10−⁴ =0.000432

Second step is to determine the diameter of a new cell

New cell diameter=0.000432×1/2

New cell diameter=0.000216

New cell diameter=2.16×10−⁴millimeters

Inconclusion The diameter of a new cell is 2.16×10−⁴millimeters

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Answer:

using the equilateral formula of solution

Answer:

[tex]x^2-3\geq 12[/tex]

Step-by-step explanation:

[tex]x^{2} -3[/tex] is the difference of a number squared and three

is at least 12, means that is greater but not less

[tex]x^2-3\geq 12[/tex]

Answer:

8.48

Step-by-step explanation:

After removing the perfect square inside √72 we get,

6√2

The given square root is,

√72

Since we know that,

A perfect square is a number that is stated as the product of an integer multiplied by itself. The perfect square is also represented as the second exponent of an integer since the same number is multiplied twice. The squares of all integers are hence referred to as perfect squares.

Simplify the square root of 72.

Factor 72 into 36 and 2,

Giving us the square root of 36 times the square root of 2.

Therefore,

√72 = √36 x √2

We know that the square root of 36 is 6,

So we can substitute that in:

√72 = 6 x √2

Hence after removing the perfect square inside √72 we get,

6√2.

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Answer:

21r +3

Step-by-step explanation:

3(7r + 1) =​

Distribute

3*7r +3*1

21r +3

Answer:

21r+3

Step-by-step explanation:

3(7r + 1)

Use the distributive property.

This property is normally used when the 2 numbers inside of the parentheses can not be added easily.

3*7r+3*1

21r+3

Step-by-step explanation:

Hello, there!!!

The answer is option D.

I have given solution on the picture.

Hope it helps.....

Hence, the m∠DCA is 59.2

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs, and sometimes the arms of the angle.

m∠DCB = (4x) + (6x-58) = 90

10x = 148

x = 14.8

m∠DCA = 4x

             = 4(14.8)

             = 59.2

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Hey there! I'm happy to help!

Sine is a trigonometric ratio. It is the ratio of the opposite side of the angle to the hypotenuse. Since it is a ratio, it does matter how big or small the triangle is as long as the sides remain in proportion. If the opposite side is 4 and the hypotenuse is 5, the sine of x will be the same as it would be if the opposite were 16 and the hypotenuse were 20 because they simplify to the same ratio (4/5).

The sine (or any trigonometric ratio) of any number stays the same even if the triangle is dilated because the proportion between the sides stays the same no matter how big or small. So, they told us the answer at the beginning. The sine of angle x is 4/5.

Have a wonderful day! :D

Answer: 4/5

Step-by-step explanation: Took the test and got it right. I assumed it was the same because angles do not change after being dilated.

Answer:

going from new to original would be times 2.5

from original to new would be time 0.4

Step-by-step explanation:

new to original is the 250/100

original to new is 100/250

Answer:

-60%

Step-by-step explanation:

First, find the difference

250 - 100 = 150

Then divide the decrease by the original number

150/250 = 0.6

And to convert this to a percentage all you have to do is multiply it by 100

0.6(100) = 60

The percent of change is -60% which is a decrease since it's negative

Answer:

The length of one side of the octagon is 7.65 cm

Step-by-step explanation:

The parameters given are;

A regular octagon inscribed in a circle of radius, r, of 10 cm.

The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon

The sum of interior angles in a polygon, ∑θ[tex]_i[/tex] = 180 × (n - 2)

Where;

n = The number of sides of the polygon

θ[tex]_i[/tex] = The interior angle of the polygon

For the octagon, we have;

n = 8, therefore;

∑θ[tex]_i[/tex] = 180 × (8 - 2) = 1080

Given that there are eight equal angles in a regular octagon, we have;

∑θ[tex]_i[/tex] = 8 × θ[tex]_i[/tex] = 1080

θ[tex]_i[/tex] = 1080/8 = 135°

The sum of angles at the center of the circle = 360

Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°

The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ[tex]_i[/tex]/2

The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon

From trigonometric ratios, the length of the base of the isosceles triangle is therefore;

2 × r × cos(θ[tex]_i[/tex]/2) = 2×10 × cos(67.5°) = 7.65 cm

The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.

Answer:

The inequality shown is p>-3

Explanation:

An open hole on the number line means that the inequality will be greater or less than a number. So far we have p <or> some number.

Since the line goes to the left then we know that p is greater than some number. Now we have, p> some number.

The inequality starts at -3 so we know that the equation must be p>-3.

The inequality shown is in the given number line will be p>-3.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An open hole on the number line refers to that the inequality will be greater or less than a number.

So far we have p <or> some number.

Since the line goes to the left then we know that p is greater than few number on the line.

Now we have, p> some number.

Thus, The inequality starts at -3, so we know that the equation must be p>-3.

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Answer:

The conjugate is 2+5i and the product is 29.

Step-by-step explanation:

The conjugate of a complex number [tex]a+bi[/tex] is [tex]a-bi[/tex]

Our complex number is 2-5i.

Here, a = 2 and b = -5

Thus, the conjugate of 2-5i is

[tex]2-(-5i)=2+5i[/tex]

Using this rule:

[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

And the fact that [tex]i^{2} = -1[/tex]

We can find the product of any complex number and its conjugate:

[tex](a+bi)(a-bi)=a^{2} - (bi)^{2}=a^{2} - b^{2} i^{2} = a^{2} + b^{2}[/tex]

As our complex number is [tex]2-5i[/tex], the product with its conjugate will be

[tex]2^{2} + (-5)^{2} =4+25=29[/tex]

Answer:

25

Step-by-step explanation:

The overall range of all scores in all three sections is 25.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

The range of 3 sections is 28, 25 and 22.

So, the overall range of all scores in all three sections

= (28+ 25+ 22)/ 3

= 75/3

= 25

Hence, the overall range of all scores in all three sections is 25.

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Answer: interval from -8 to 5

In interval notation, we would write [-8, 5]

The domain is the set of allowed x inputs to a function. The left-most point is (-8,0) so x = -8 is the smallest x value allowed. The largest x value allowed is x = 5 due to the point (5,0) being the right-most point.

The use of square brackets in interval notation says "include this endpoint as part of the interval".

Answer:

A. 1010 FT^3

Step-by-step explanation:

19 x 14.5 x 5 = 1377.5

you need to subtract now, so the only option would be A

Answer:

[tex]1,010 ft^{3}[/tex]

Step-by-step explanation:

You can break the figure into 2 sections; one with the dimensions of 4, 5 and 7; the other with dimensions of 14.5, 5, and 12.

Multiply the first three dimensions (4, 5 and 7) to get 140 ft cubed.

Multiply the last three dimensions (14.5, 5, and 12) to get 870 ft cubed.

Now, just add both volumes together to get 1,010 ft cubed!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

$4661.77

Step-by-step explanation:

100 + 4.7 = 104.7%

104.7% = 1.047

$2340.73 x 1.047^15 = $4661.77

Answer:

D) (–5,0), (0,2), (5,0), (0,–2)

Step-by-step explanation:

The vertices are basically the x and y intercepts.

The type of model best fits the given situation is a quadratic equation

Quadratic equations are equation that has a leading degree of 2.

From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation

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Answer:

200in²

Step-by-step explanation:

I separated the shaded face into two squares. Both squares would be 10 by 10.

Area of a square: [tex]a=s^2[/tex]

For each square, they have a side of 10 in.

[tex]a=10^2\\\\a=100[/tex]

The area for one square is 100in². This means that for the whole face, which is made out of 2 squares, the area would be 200in².

The second option should be the correct answer.

Answer:

x = 148

Step-by-step explanation:

CPD is a straight line so it equals 180

CPB + BCD = CPD

x + 32 = 180

Subtract 32 from each side

x+32-32 = 180-32

x =148

Answer:

D

Step-by-step explanation:

Answer:

a is the answer 28.50 + b = 45.50

Step-by-step explanation:

so if i move 28.50 to the right side then it becomes b=45.50-28.50 and that equals to 17 . hope i helped have a great day

=================================================

Explanation:

28.50 = cost of shirt

b = cost of belt, some unknown value

45.50 = total cost (given)

28.50+b = total cost (add the first two items shown above)

equate the two total cost expressions to end up with 28.50+b = 45.50

Answer:

  13.4 meters

Step-by-step explanation:

About the diagram

Attached is a diagram of the problem. The directions North and East are shown so that the usual clockwise from +x measurement of angles will correspond to the bearing angles given in the problem. That is, the bearing of 120° is an angle of 120° measured from North toward East. (The mirroring across the line y=x can be a little mind-bending, but it is isomorphic, so all angles and lengths remain unchanged.)

The other feature of this diagram is the projection of the 3-D problem into two dimensions. Effectively, the center angle rabbit-O-coyote represents a plan view (in the plane of the ground), and the triangles coyote-O-C1 and rabbit-O-R1 represent side views (views in the vertical plane).

The side views let us work out the ground distances O-rabbit and O-coyote, so that we can find the ground distance rabbit-coyote as the problem requests.

__

Problem solution

The distance from the tree (O) to the rabbit is the "adjacent" leg of the 30° angle of elevation from the rabbit to the tree top. The 10 m tree height is the "opposite" leg of that rabbit-O-R1 right triangle. We know the ratio of opposite to adjacent sides gives the tangent of the angle, so we have ...

  tan(30°) = 10/(rabbit distance from tree)

Solving for the rabbit distance, we get

  rabbit distance = 10/tan(30°) ≈ 17.3205 m

Similarly, the coyote distance from the tree will be ...

  coyote distance = 10/tan(20°) ≈ 27.4748 m

__

These are two legs of the rabbit-O-coyote triangle. The angle at O between the rabbit and coyote is 120° -97° = 23°. These values are sufficient to let us use the Law of Cosines to find the distance d from rabbit to coyote:

  d² = r² +c² -2rc·cos(23°)

  d² = 17.3205² +27.4748² -2·17.3205·27.4748·cos(23°) ≈ 178.769

  d ≈ √178.769 ≈ 13.37 . . . . meters

The distance from the rabbit to the coyote is about 13.4 meters.

_____

Additional comment

Note that the angle of depression to the rabbit from the horizontal is the same as the angle of elevation from the rabbit. This lets us draw the diagram without a bunch of extra lines.

On a graph, points are grouped closely together to form a line and decrease.

====================================

Explanation:

Negative association is where the points decrease as you move from left to right. In other words, you move downhill as you move from left to right. There could be random upward bumps here and there, but overall the general trend is down.

Linear association is when the points are close to the same straight line, known as the regression line.

When points have strong negative linear association, we combine the two ideas mentioned above. The points are close to the same straight line and this line has a negative slope. The correlation coefficient r is close to r = -1.

Choice C is a close answer, but choice D is the better answer due to the "to form a line". If all points are on the same straight line, then r = -1 exactly and we have the strongest possible negative correlation.

The strongest negative linear association is depicted by the graph where points are grouped closely together to form a line and decrease.

Therefore, a graph with closely grouped points which forms a line and decreases infers a strong negative linear association.

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