Determine the sum of the interior angles of a polygon with 30 sides.

The volume of the solid obtained by rotating the region bounded by x = y² and x = 1 − y² about x = 4 is 16.

The volume of a solid obtained by rotating a region about a line is calculated by using the method of cylindrical shells.

In this problem, we are given the region bounded by the curves x = y² and x = 1 − y², and we are asked to find the volume of the solid obtained by rotating this region about the line x = 4

Next, we set up a coordinate system with the y-axis being the axis of rotation and the x-axis being the height of the cylindrical shell.

We will be rotating the region about the line x = 4, so the width of the cylindrical shell is 4 - y².

The height of the cylindrical shell is the change in x from one shell to the next, which is given by the bounds of the region. The circumference of the shell is

=> 2πy,

and the width of the shell is 4 - y².

We integrate the product of these three quantities over the bounds of the region to find the total volume of the solid.

This integration can be done using a definite integral, with the bounds being the y-coordinates of the two points where the curves intersect.

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The result of applying the power rule to \((A^{x} )^{y}\) is \(A^{xy}\).

The power rule of exponentiation states that when a base is raised to a power, and that power is then raised to another power, we can simply multiply the exponents. In other words, \((A^{m} )^{n}\) = \(A^{mn}\).

Therefore, when we apply the power rule to \((A^{x} )^{y}\), we can simply multiply the exponents. This gives us the result of \((A^{x} )^{y}\) = \(A^{xy}\).

To understand this, let's take an example. Suppose A=2, x=3, and y=4. So we have \((2^{3} )^{4}\). By applying the power rule, we can simplify this as \((2^{3} )^{4}\)=\(2^{12}\).

In essence, what the power rule does is it allows us to simplify complex expressions involving exponents into simpler forms. This is particularly useful when dealing with algebraic expressions or mathematical formulas that involve multiple exponentiations.

In summary, the result of applying the power rule to \((A^{x} )^{y}\) is\(A^{xy}\), which represents the simplified form of the expression.

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The distance of the mid point of the chord to the center is 8 cm.

Given a circle.

Length of the chord of a circle = 12 cm

Radius of the circle = 10 cm

We have to calculate the distance of the mid point of the chord to the center.

When a line is drawn from the mid point of the chord to the center, there forms a right triangle where hypotenuse is the radius and the legs are the half of the chord and the distance from the mid point to the center.

Using the Pythagoras theorem,

Distance from mid point to the chord = √10² - 6² = √64 = 8 cm

Hence the distance from the center of the chord to the mid point is 8 cm.

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Considering that the first angle of a triangle has a 105° angle. As is common knowledge, a triangle's total angle measurement is 180°.

1- If one angle is 105 degrees, the total remaining angles must be 75 degrees. This indicates that both angles will be sharp. Hence, this claim is accurate.

2 If one angle is 105 degrees, it is obviously obvious that the total of the other angles must be 75 degrees. So, this claim is also accurate.

3- The total of the angles of the triangle cannot be greater than 180°, hence it is impossible for the sum to equal 155°. Thus, this claim is untrue.

4- If one angle is 105°, it is not feasible for another angle to be 90° since the result would be 105+90=195°, which is not conceivable.

5 This claim is accurate since 180-105=75°. Hence, no angle is more than 75°.

6- This is impossible since, in that scenario, the total would be 210°, which negates the triangle's inherent features.

7. That is impossible since the total of all other angles must be 75°. This is not conceivable if one angle is 75 degrees and the third angle is 0 degrees.

8- It is feasible for one angle to be 45 degrees and the other to be 30 degrees.

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                                      "Complete question"

Two angles form a linear pair with each other . If one angle measures 105 degree , Find the measure of the other angles ?​

Nick's z -score is -1.833.

According to the given question.

Total points scored by Nick, x = 24

Mean score for the test was, μ = 35

Standard deviation, σ = 6

As, we know that z-score can be caluated by using the formula

z = (x - μ)/σ

Where, x is a score

μ is mean score

σ is standard deviation

z is z-score

Therefore, Nick's z-score is given by

z = (24 - 35)/6

z = -1.833

ence, Nick's z -score is -1.833.

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Answer:

8

Step-by-step explanation:

First, let's find the derivative of the equation.

According to one of the rules of derivatives, d/dx tan(x) = sec²(x)

We also don't mess with the 2 since it's a constant

f'(x) = 2sec²(x)

Now just plug in 2π/3

2sec²(2π/3) = 8

Instantaneous rate of change is 8 at x = 2π/3

Therefore, the truth value of Proposition 2A is False.

To determine the truth value of Proposition 2A, let's substitute the given truth values for the variables:

A = True

B = True

X = False

Y = False

Now let's evaluate the truth value of each component of the proposition:

(X ⊃ A) • (B ⊃ ∼ Y):

(False ⊃ True) • (True ⊃ ∼ False)

(True ⊃ True) • (True ⊃ True)

True • True

True

(B ∨ Y) • (A ⊃ X):

(True ∨ False) • (True ⊃ False)

True • False

False

[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]:

True ⊃ False

False

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-13 and 6

-13x6 = -78

-13 + 6 = 13

Step-by-step explanation:

cos 28=\(\frac{AB}{8}\)

AB= cos28 * 8

   =7.06

hope this helps

Answer:

AB ≈ 7.1 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos28° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{AB}{8}\) ( multiply both sides by 8 )

8 × cos28° = AB , thus

AB ≈ 7.1 cm ( to the nearest tenth )

The initial length of the scarf is 50 centimeters.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.

Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:

L + 25h = length of scarf after h hours

Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:

L + 25(3) = 125

L + 75 = 125

L = 50

Therefore, the initial length of the scarf is 50 centimeters.

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Cassandra is knitting a scarf. She increases the length of

the scarf by 25 centimeters each hour she knits. After 3

hours, the scarf is 125 centimeters long what is initial length of scarf.

Answer:

Ans of A is A

Ans if B is C = 14

Answer:

< C

Step-by-step explanation:

because 23 is the largest number on the triangle so the angle opposite of that side would be C

Answer:

They must have lost 19 games.

Step-by-step explanation:

If you plug in 53 into the equation, you get 53 = 3w + 11. You subtract 11 from both sides, resulting in 42 = 3w. You divide 3 from both sides this time, resulting in 14 = w. Since W is the number of wins, and you're trying to figure out games lost, you subtract 14 from the number of games played, so 33-14 is equal to 19.

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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The only transformation that would carry rectangle ABCD onto itself is a single rotation of 180 degrees in a parallelogram.

Rectangle ABCD's characteristics and how each transformation affects its orientation and location must be examined in order to identify the collection of reflections and rotations that would carry the rectangle onto itself of a parallelogram.

First, using the provided coordinates, let's determine the sides of the rectangle: AB is parallel to DC, and AD is parallel to BC. Also, we can observe that the lengths of AB and AD are equal to DC and BC, respectively, indicating that the opposite sides are congruent.

The rectangle is first suggested to be rotated 180 degrees. This transformation simply maps each point to its corresponding point on the rectangle; the rectangle's orientation is left unchanged. Hence, rectangle ABCD would be carried onto itself by this transformation alone.

The rectangle is first reflected over the x-axis, rotated 180 degrees, and then reflected once more over the x-axis is the second transformation suggested. This series of transformations flips the rectangle's orientation while mapping each point to its equivalent point on the other side of the rectangle. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.

The third suggested transformation involves reflecting the rectangle first over the y-axis, then over the line y = x, and then back over the y-axis. The rectangle's orientation is maintained but its position is altered by this series of modifications. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.

The rectangle is to be rotated 180 degrees, reflected over the line y = x, and then reflected over the x-axis as the fourth transformation suggested. Each point is moved and mapped to a point on the other side of the rectangle via this series of transformations. The rectangle's orientation is also altered, though. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.

Hence, a single 180° rotation is the only transformation that could turn rectangle ABCD upon itself.

In conclusion, we studied the features of the rectangle and the consequences of each transformation on its orientation and location to find the set of reflections and rotations that would transport rectangle ABCD onto itself. In contrast to the other suggested transformations, we discovered that only a single rotation of 180 degrees would keep the rectangle's orientation and location intact.

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The growth rate in a village of 25,000 people has 5000 births and 500 deaths is 18%

The growth rate is the parameter that shows the increase in the population in the village. It is described as the ratio of change in population to the original population.

Change in population = Number of births - Number of death

Number of birth = 5000

Number of death = 500

Change in population = 4500

Original population = 25,000

Growth rate = \(\frac{4500}{25000}\) * 100%

= 0.18 * 100%

= 18%

With an increase of 4,500 to the population of 25,000 of the village the growth rate is 18%.

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Answer:

She put in $7.50

Step-by-step explanation:

\(\frac{4-6\sqrt{2}+6\sqrt{2}\sqrt{3}}{3\sqrt3}\) is the simplified form of the given expression.

The given expression is 4/3√3-2√2× 3/3√3+2√2

Simplifying the expression,

\(\frac{4}{3\sqrt3}-2\sqrt2\frac{ 3}{3\sqrt3}+2\sqrt2\\\\\frac{4-6\sqrt{2}+6\sqrt{2}\sqrt{3}}{3\sqrt3}\)

Therefore, the simplified form of the given expression is \(\frac{4-6\sqrt{2}+6\sqrt{2}\sqrt{3}}{3\sqrt3}\).

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Answer:

No, the vertices of the image and pre-image do not correspond.

Step-by-step explanation:

Answer: No, the vertices of the image and pre-image do not correspond.

Step-by-step explanation:

The geometric sequence is option(D) i.e, 1, 3, 9, 27, 81,..

What is Geometric sequence ?

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In this, the last option have the geometric sequence. since, there is a common ration between each term. If you multiplying the previous term in the sequence by 3 gives the next term.

Hence, The geometric sequence is 1, 3, 9, 27, 81,

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Let's check each student's response for different values of x:Student 1: 7x - 5 > 3x - 2

For x = 1:

7(1) - 5 =

2,

3(1) - 2 = 1

=> 2 > 1 (True)

For x = 2: 7(2) - 5

= 9, 3(2) - 2

= 4

=> 9 > 4 (True)

Student 2: 6x - 3 > 5x + 4

For x = 1:

6(1) - 3

= 3,

5(1) + 4

= 9

=> 3 is not greater than 9 (False) Student 3:

5x + 1 > 3x + 2

For x = 1:

5(1) + 1 = 6,

3(1) + 2 = 5

=> 6 is greater than 5 (True)

For x = 2: 5(2) + 1 = 11,

3(2) + 2 = 8

=> 11 is greater than 8 (True)

Student 4: 4x + 8 > 5x + 2

For x = 1: 4(1) + 8

= 12,

5(1) + 2 = 7

=> 12 is greater than 7 (True)

For x = 2: 4(2) + 8

= 16,

5(2) + 2 = 12

=> 16 is greater than 12 (True)

Therefore, Student 1 has the correct response to Mrs. Mueller's inequality because their inequality is true for all values of x.

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The number 90 is 25 % of the number 360

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Let the number be x

90 is 25% of x

or, 25 % of x is 90

(25/100) x = 90

x = 90(100/25)

x = 360

Therefore, the number 90 is 25 % of the number 360

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Step-by-step explanation:

I have attached the working

Answer: 829393

Bn

Step-by-step explanation:

Answer:

−5x + 4y = 8

−x + 5y = 10

Step-by-step explanation:

Answer:

I'm a genius

Step-by-step explanation:

-15/8 or -1.875

The matrix A to the power of one can be found by simply taking the inverse of A to the power of five minus A to the power of two. In order to solve this, we need to use the basic properties of matrix algebra. The first step to solving this is to recognize that A⁵-A² is the same as A^5(I-A³).

This means that we can use matrix inverses to solve this problem. To do this, we simply take the inverse of A⁵ and multiply it with I-A³. This gives us A⁻⁵(I-A³). Next, since we are attempting to find A¹, we must take the inverse of both sides of the equation. This leaves us with A¹ as A(A⁻⁵(I-A³))⁻¹.

This means that, in order to find A¹, we just need to take the inverse of the product of the inverse of A to the power of five, I, and A to the power of three. This can be done by first taking the inverse of A to the power of five and then multiplying it with I-A³. Finally, we can take the inverse of this product and we will have A¹.

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Answer:

-4

Step-by-step explanation:

-8x + 6y = -4 is the same as

6y - 8x =