Figure A ~ Figure B
Find the volume of figure A

I think it is 49123.52

Step-by-step explanation:

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

Our Sun is a bright, hot ball of hydrogen and helium at the center of our solar system. It is 864,000 miles (1,392,000 km) in diameter, which makes it 109 times wider than Earth. It's 10,000 degrees Fahrenheit (5,500 degrees Celsius) at the surface, and 27 million degrees Fahrenheit (15,000,000 degrees Celsius) in the core.

Step-by-step explanation:

did this help

The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy mainly as visible light and infrared radiation. It is by far the most important source of energy for life on Earth.                        maybe this will help a little

Answer:

Step-by-step explanation:

distribute the 3

you get 3x+24=15

subtract 24 from both sides

you get 3x=-9

divide 3 from both sides

you get x=-3

If u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

Vectors are used in science to describe anything that has both a direction and a magnitude.

Since u and v are unit vectors, their magnitudes are both 1.

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v

= 1 + 2u⋅v + 1

= 2 + 2u⋅v.

On the other hand, we also have:

|u + v|² = (u + v)⋅(u + v) = u⋅u + 2u⋅v + v⋅v = 2,

since u and v are linearly independent and hence orthogonal.

Equating the two expressions for |u + v|² we get:

2 + 2u⋅v = 2,

u⋅v = 0.

Therefore, the only possible value for u⋅v is 0.

Hence,  u and v be linearly independent unit vectors then  the set of all possible values of u⋅v is zero.

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Answer:

56 ...

Step-by-step explanation:

70-14 = 56

Since it’s the sum of their age it’s just jiri’s age plus Pamela’s so you just subtract Pamela’s age from the total sum. And that would make jiri 56. (Sum means the total from adding) So if you do the problem over again. “The sum of 56 and 14” it would take you back to the question you have now. This is inverse addition.

Answer:42

Step-by-step explanation: you split 70 in half, 35 and 35. Then you add 7 to one (Jiri) and subtract 7 from one(Pamela). You get 42 and 28. To check you do 42-28=14 and 42+28=70.

Answer:

2 OUTFITS

Step-by-step explanation:

The Circle Sector Area correct answer is: O n(30in)2

To calculate the area of the sector in the circle, you would typically use the formula:

Area = (θ/360) * π *\(r^2\)

where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

From the options you provided, the correct choice would be:

O n(30in)2

This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)

Therefore, the Circle Sector Area correct answer is: O n(30in)2

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The amount you have after 18 months is $ 1143.96 .

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

\(A=P {(1 +\frac{r}{n})^{nt} }\)

Given:

P = 1000 , r in decimal  = 0.09 ,

n = 12 ,  t = 1.5 ( 18 months = one and a half years).

Substituting the values into the formula:

A = 1000 ( 1 + 0.09/ 12 ) ^[12 ( 1.5 )]          

  ≈ 1000 ( 1.143960 )          

  = 1143.960

Rounding to the nearest cent, we get $ 1143.96 .

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Answer:

3) x = -4 and y = 6

4) x = -1 and y = 0

5) x = 1 and y = -3

6) x = -4 and y = -3

Step-by-step explanation:

3) Add the equations:

(3x + 4y = 12) + (-3x - y = 6) (eliminate the x)

= 3y = 18

y = 18/3

y = 6

3x + 4(6) = 12

3x = 12 - 24

x = -12/3 = 4

4) Add the equations:

(-5x - 6y = 5) + (-6x + 6y = 6)

-11x = 11

x = -1

-5(-1) -6y = 5

-6y = 5 - 5

y = 0

5) 7x -4y = 19

10x - 2y = 16

Multiply the second equation by -2 to eliminate the y and add both equations.

-2(10x -2y = 16) =

(-20x + 4y = -32) + (7x - 4y = 19)

-13x = -13

x = 1

7(1) - 4y = 19

-4y = 19-7

y = 12/-4

y = 3

6) multiply the second equation by -2 to eliminate the x and then add the equations.

-2(5x - 3y = - 11) =

(-10x + 6y = 22) + (10x - 9y = - 13)

= -3y = 9

y = - 3

10x - 9(-3) = - 13

10x = -13 - 27

x = -40/10

x = -4

Answer: Jane incorrectly evaluated (-2)² in step 2.

Step-by-step explanation:

\((-2)^{2}=4\), not -4.

1-Line- A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

2- Circle- A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”

3- Cardioid- a limacon with a pointed indent occurs when a=b.

4- Limacon with a loop- a limacon with an inner loop occurs when a is less than b.

5- Limacon without a loop- A Limacon graph could be said to resemble a lima bean. It takes the form of a circle with a dented side.

6- Lemniscate - A lemniscate is a polar graph taking the shape of a propeller or figure upright, at an angle, or on its side.

7-Rose Curves- One type of curve defined by a polar equation is a rose curve. The rose curve graph is often described as flower petals arranged around the pole. The petals are all congruent to each other and can have symmetry across the polar axis or the line θ=π/2

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Answer: (h-g)(-2)=18

Step-by-step explanation:

(h – g) (-2) means the same as subtracting h(-2) and g(-2). Since we are given h(x) and g(x), we can use them to solve. There are two ways to solve. One is to find h(-2) and g(-2), and then subtract them. Another way is to do (h-g)(x), then plug in x=-2. I will show both methods.

Method 1

h(-2)=2(-2)²-5(-2)+2                   [exponent]

h(-2)=2(4)-5(-2)+2                      [multiply]

h(-2)=8+10+2                               [add]

h(-2)=20

g(-2)=(-2)²-2(-2)-6                       [exponent]

g(-2)=4-2(-2)-6                            [multiply]

g(-2)=4+4-6                                 [add then subtract]

g(-2)=2

(h-g)(-2)=20-2                            [subtract h(-2) and g(-2)]

(h-g)(-2)=18

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Method 2

(h-g)(x)=2x²-5x+2-(x²-2x-6)      [distribute -1]

(h-g)(x)=2x²-5x+2-x²+2x+6        [combine like terms]

(h-g)(x)=x²-3x+8

(h-g)(-2)=(-2)²-3(-2)+8                [plug in x=-2, exponent]

(h-g)(-2)=4-3(-2)+8                    [multiply]

(h-g)(-2)=4+6+8                          [add]

(h-g)(-2)=18

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Now, we know that (h-g)(-2)=18. We confirmed this with both methods.

Answer:

144

Step-by-step explanation:

\(x^2+24x +144\\\\=x^2 + 2\cdot 12x +12^2\\\\=(x+12)^2\)

Answer:

Answer: H x 8 = P

Explanation: Every hour Lucy gets paid $8 so if she works for 1 hour she gets $8 and for 2 hours of work she gets paid $16. It's just multiplying by 8.

Answer:

Center ( -8, 1 )

Radius ( 13 )

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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Answer:

$1,105.08.

Step-by-step explanation:

Given that Alice invests $ 1000 at 2% interest compounded monthly over a 5 year period, assuming no other money is deposited or withdrawn, to determine what is the total amount of money in her account after 5 years, the following calculation must be performed:

X = 1,000 (1 + 0.02 / 12) ^ 5x12

X = 1,105.08

Thus, the amount of money in her account after 5 years would be $ 1,105.08.

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

right isosceles triangle.

Right Scalene Triangle

Angles

Acute angle:  An angle whose measure is less than 90 degrees.

Right angle:  An angle whose measure IS 90 degrees.  As a consequence, the two rays that form the angle are perpendicular.

Obtuse angle:  An angle whose measure is greater than 90 degrees.

Triangles (defined by side lengths)

Equilateral Triangle:  A triangle with all three sides congruent (all three sides have the same length)

Isosceles Triangle:  A triangle that contains two congruent sides (two sides with the same length).

Scalene Triangle: A triangle with three different length sides.

Triangles (defined by angle measures)

Acute Triangle:  A triangle whose angles are all acute angles

Right Triangle:  A triangle that contains one right angle.

Obtuse Triangle:  A triangle that contains one obtuse angle.

By angle

Our triangle has an angle that appears to be a right angle (the two sides look perpendicular).  This would be a Right Triangle (when classified by angles).

By side length

All three sides of this triangle are different in length.  This would be a Scalene Triangle (when classified by side length).

Combining the attributes:

This is both a Right Triangle and a Scalene Triangle.  Together, it is a Right Scalene Triangle.

Right Isosceles

To be a Right Isosceles Triangle, the triangle needs to be both a Right Triangle, and an Isosceles Triangle.

A Right triangle contains one right angle, and an Isosceles Triangle contains a pair of sides that are the same length.

While this triangle does contain a right angle, all three sides appear to be different length (scalene).

This is not a Right Isosceles Triangle.

Acute Isosceles

To be an Acute Isosceles Triangle, the triangle needs to be both an Acute Triangle, and an Isosceles Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and an Isosceles Triangle contains a pair of sides that are the same length.

However, this triangle contains a right angle (equal to 90 degrees, not less than), so it cannot be an Acute Triangle, and this triangle does not contain a pair of sides that are the same length, so it cannot be an Isosceles Triangle.

This is not an Acute Isosceles Triangle.

Acute Scalene

To be an Acute Scalene Triangle, the triangle needs to be both an Acute Triangle, and a Scalene Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and a Scalene Triangle has sides that are all different length.

While this triangle does have sides that are all different length, it contains a right angle, whose measure IS 90 degrees (not less than 90 degrees).  So it cannot be an Acute Triangle

This is not an Acute Scalene Triangle.

A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

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Answer:

2/5

Step-by-step explanation:

To express a common fraction such as 2/5 as a decimal fraction you divide the denominator into the numerator. /5 = ?/100 Using your knowledge of fractions you can see that ? = 40. Thus 2/5 = 40/100 or 2/5 is 40 per one-hundred, that is 40 percent.

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Answer:

40/100 = 2/5

Divide by the common factor, 20.

Answer:

I hope I am right or close

Step-by-step explanation:

I believe He would get an 32,000 commission!