What is the gfc of 24 and 36

We need to find the indefinite integral using any method for the given function csc(√3x) dx.  

Let's begin solving it:It is known that we can use the substitution u= √3x to solve this problem. Therefore, we can replace csc(√3x) with csc(u) and dx with 1/√3 du. Let's substitute it below:

∫csc(√3x) dx = 1/√3 ∫csc(u) du

Now we use the identity of csc(u) which is equal to -(1/2) cot(u/2) csc(u).∫csc(u) du = ∫ - (1/2) cot(u/2) csc(u) du

Now, we substitute u with √3x.∫ - (1/2) cot(u/2) csc(u) du = ∫ - (1/2) cot(√3x/2) csc(√3x) (1/√3)dx

Hence the final solution for ∫csc(√3x) dx = -1/2 ln│csc(√3x) + cot(√3x)│ + C, where C is the constant of integration

The trigonometric substitution is the substitution that replaces a fraction of the form with a trigonometric expression. The csc(√3x) can be substituted using u = √3x, and this gives us an integral of the form ∫ csc(u) du.

We use the identity of csc(u) which is equal to -(1/2) cot(u/2) csc(u).

Finally, we substitute u back with √3x to get the final solution.

Therefore, the indefinite integral of csc(√3x) dx is -1/2 ln│csc(√3x) + cot(√3x)│ + C, where C is the constant of integration.

The indefinite integral of csc(√3x) dx is -1/2 ln│csc(√3x) + cot(√3x)│ + C, where C is the constant of integration.

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Answer: 54 feet

Step-by-step explanation:

3(18) = 54 feet

The trigonometric identity of `sin²x + cos²x = 1` is a fundamental trigonometric identity. Here, the value of sin A is given as 0.03, and we are supposed to find cos A. Angles with 0 degrees are zero, and angles with 90 degrees are equivalent to one, as sin (0) = 0 and cos (90) = 0.

The value of A is between 0 and 90 degrees. Therefore, sin (A) and cos (A) are both positive.Here is the work: Squaring both sides of `sin(A) = 0.03`, we get:$$\sin^2A=0.03^2$$$$\sin^2A=0.0009$$ Using the identity `sin²x+cos²x=1`, we get:$$\sin^2A+\cos^2A=1$$$$0.0009+\cos^2A=1$$$$\cos^2A=1-0.0009$$$$\cos^2A=0.9991$$Taking the square root of both sides of the above equation, we get:$$\sqrt{\cos^2A}=\sqrt{0.9991}$$$$\cosA=0.9995$$ Therefore, the value of cos A is `0.9995`.

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Answer:

The answer is 10.89. I dont know how to solve it but my dad told me this is the answer!

Step-by-step explanation:

Please give me brainliest! UnU

Answer:

Option B will be your answer

Step-by-step explanation:

V=2 1/2×1/2×2

=2.5 cube

volume of 1/2 cubic units =)(1/2×1/2×1/2=0.125cube^3

2.5/0.125=20

Hope it helps...

v = 2½

number of half unit cubes = 20

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Step-by-step explanation:

sum of interior angles of a polygon with n sides =

(n−2) × 180°

for a pentagon that is 3×180 = 540°

therefore,

540 = x + 121 + 108 + 102 + 100 = x + 431

x = 109°

In order to identify these mentioned terms, it is important that each of them is defined.

Diameter: It is a line that passes through the center of the circle from one endpoint to another. It is two times the radius of the circle

Radius: It is a line drawn from the center of the circle to one endpoint of the circle.

It is half of the diameter.

Chord: It is a line drawn from one endpoint of the circle to another but does not necessarily pass through the center. Diameter is an example of a chord, but a chord does not have to be a diameter

Arc: It is a segment of the circumference of a circle

Circumference: is the total distance around the circle

From the diagram above:

|AB| is a diameter

|OA| or |OB| is the radius

|CD| is the chord

Arc CD is indicated on the diagram

If a circle has a radius of 2 cm:

Diameter = 2 x radius

Diameter = 2 x 2

Diameter = 4 cm

Therefore, if a circle has a radius of 2 cm, the diameter is 4 cm

Answer:

C

Step-by-step explanation:

Angle Bisector means the line is being split in half evenly. So, when angle 3 is 60, so is angle 4. Angles 1 and 2 are both 30 degrees because 30 + 60 equals to 90 degrees.

I hope this helps!

Answer:

60⁰..................

To minimize the cost of the fence, we need to find the dimensions of the rectangular field that will result in the smallest perimeter. Let's assume the length of the rectangle is x feet.

Since we want to divide the field in half with a fence parallel to one of the sides, the width of the rectangle will also be x feet.

The area of the rectangular field is given as 37.5 million square feet, so we have the equation x * x = 37.5 million.

Simplifying, we find x² = 37.5 million.

To minimize the cost, we need to minimize the perimeter of the rectangular field. The perimeter is given by P = 2x + 2x = 4x.

Using the equation x² = 37.5 million, we can solve for x by taking the square root of both sides. This gives us x = √(37.5 million).

Substituting this value of x into the perimeter equation, we get P = 4 * √(37.5 million).

Therefore, the lengths of the sides of the rectangular field that will minimize the cost of the fence are √(37.5 million) feet and √(37.5 million) feet.

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Using Green's Theorem to evaluate ∫ C → F ⋅ d → r , where → F = 〈 √ x + 6 y , 2 x + √ y 〉 and C consists of the arc of the curve y = 3 x − x 2 from (0,0) to (3,0) and the line segment from (3,0) to (0,0).The orientation of C is counterclockwise, so the integral evaluates to:

              ∫ C → F ⋅ d → r = ∫ 0 3 ∫ 0 3 x − 2 y dx dy = −2/3.

Let's understand this in detail:

1. Parametrize the curve C

Let x = t and y = 3t - t2

2. Calculate the area enclosed by the curve

A = ∫ 0 3 (3t - t2) dt

       = 9 x 3/2 - x2/3 + 10

3. Check the orientation of the curve

Since the curve and the line segment are traced in the counterclockwise direction, the orientation of the curve will be counterclockwise.

4. Use Green's Theorem

∫ C → F ⋅ d → r  = ∇ x F(x,y) dA

            = 9 x 3/2 - x2/3 + 10

5. Simplify the Integral

∫ C → F ⋅ d → r = [ √ (3t - t2) + 6 (3t - t2) ] [6t - 2t2] dt

                 = [ 3 (3t - t2) + 6 (3t - t2) ] (36t2 - 12t3 + 2t4)

                 = −2/3.

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The magnitude of the vector QP is √73.

To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.

Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:

x-component of QP = x-coordinate of Q - x-coordinate of P

                 = (-4) - 4

                 = -8

y-component of QP = y-coordinate of Q - y-coordinate of P

                 = 4 - 1

                 = 3

Therefore, the component form of the vector QP is (-8, 3).

To find the magnitude of the vector QP, we can use the formula:

Magnitude of a vector = √(\(x^2 + y^2\))

Substituting the x-component and y-component of QP into the formula, we get:

Magnitude of QP = √((\(-8)^2 + 3^2\))

              = √(64 + 9)

              = √73

Therefore, the magnitude of the vector QP is √73.

In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.

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Answer:

6 is greater than -6

Explanation:

Hope it helps you..

Your welcome in advance..

(ㆁωㆁ)

Answer:

D : reflection over the y-axis followed by a translation to the right one unit

Answer: 6 bags 5 fire balls and 7 jolly ranchers in one bad

Step-by-step explanation:Ok so you got 30 fire balls 42 ranchers what you can do is see like wow more ranchers in a bag we know that hmm 42/6 is ya know 7 and that 6 does it go into 30 yeah it does 30/6=5 so you got 5 fire balls and 7 jolly ranchers is each bag with 6 bags

Answer:

6 bags

Step-by-step explanation:

The GCF of 30 and 42 is 6.

30/6 = 5

42/6 = 7

To use all candy, put 5 fireballs and 7 jolly ranchers in each bag. You will make 6 bags.

For a normal distribution of SAT critical reading scores with a mean of 513 and a standard deviation of 124:

(a) Approximately 86.69% of the SAT verbal scores are less than 650.

(b) If 1000 SAT verbal scores are randomly selected, we would expect approximately 618 scores to be greater than 550.

(a) To find the percentage of SAT verbal scores that are less than 650, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the z-score:

z = (x - μ) / σ = (650 - 513) / 124 = 1.107.

Using the standard normal distribution table or a calculator, we find that the cumulative probability associated with a z-score of 1.107 is approximately 0.8669.

To convert this to a percentage, we multiply by 100:

0.8669 * 100 = 86.69%.

Approximately 86.69% of the SAT verbal scores are less than 650.

(b) To estimate the number of SAT verbal scores greater than 550 out of a randomly selected 1000 scores, we can use the mean and standard deviation provided.

First, we calculate the z-score:

z = (x - μ) / σ = (550 - 513) / 124 = 0.298.

Next, we find the cumulative probability associated with a z-score of 0.298, which is approximately 0.6179.

To estimate the number of scores greater than 550 out of 1000, we multiply the probability by the sample size:

0.6179 * 1000 = 617.9.

We would expect approximately 618 SAT verbal scores to be greater than 550 out of the randomly selected 1000 scores.

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The slope of the function showing by table is,

⇒ m = - 6

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table represents a linear function.

Let Two points on the line are (- 2, 8) and (- 1, 2).

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 8) / (-1 - (-2))

m = - 6 / 1

m = - 6

Thus, The slope of the function showing by table is,

⇒ m = - 6

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Answer:

17

Step-by-step explanation:

Answer:

y = -2.5

Step-by-step explanation:

_________________

Answer:

.770

Step-by-step explanation:

Answer:

2a +ab-9

Step-by-step explanation:

First, write out what you have:

3a-2b-ab-(a-b+ab)+3ab+b-9

Then, distribute the "-" to the "a-b+ab" inside the parenthesis:

3a-2b-ab-a+b-ab+3ab+b-9

Finally, combine like terms and simplify:

3a-a-2b+b+b-ab+3ab-ab-9

2a-2b+2b+3ab-2ab-9

2a+0+ab-9

2a+ab-9 is you equation fully simplified

The annual maintenance collected in 2014 will be $1,750,000.

To calculate the annual maintenance collected in 2014, we need to find the number of customers who will renew their maintenance contract and the number of customers who will pay for maintenance as a percentage of product sales in 2013.

Number of customers renewing maintenance in 2014 = 80% of $2,000,000 = $1,600,000

Number of customers paying for maintenance in 2014 = 75% of $2,000,000 = $1,500,000

So, the total annual maintenance collected in 2014 will be:

$1,600,000 + $1,500,000*10% = $1,750,000

Therefore, the annual maintenance collected in 2014 will be $1,750,000.

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False. A self-selected sample is the group of individuals who volunteered to participate in the study, not those who were randomly selected to be in the sample then agreed to participate in the study.

Self-selection sampling or voluntary response sampling is a form of non-probability sampling in which participants voluntarily choose to participate in a study or survey. This kind of sampling method is not random since the individuals decide whether or not to participate in the research.

For instance, if a company is conducting research on its products, it may ask its customers to participate. Those who agree to participate in the research will be part of the self-selected sample.

A self-selected sample, also known as a voluntary response sample, can have issues with sample bias because those who volunteer may not represent the entire population.

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The container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

The dimensions of the container are given as 40 ft by 8 ft by 8 ft 6 in. We need to convert the height of 8 ft 6 in to feet by dividing it by 12 since there are 12 inches in a foot:

8 ft 6 in = 8 ft + (6 in / 12) ft

         = 8 ft + 0.5 ft

         = 8.5 ft

Now we can calculate the volume of the container:

Volume = Length × Width × Height

      = 40 ft × 8 ft × 8.5 ft

      = 2720 ft³

To find the volume when the container is three-quarters full, we multiply the total volume by 0.75:

Volume when three-quarters full = 2720 ft³ × 0.75

                              = 2040 ft³

Therefore, the container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

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Answer:

95.67

Step-by-step explanation:

The quadrature formula for the natural cubic spline with evenly spaced knots becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + k1 + k2 + ⋯ + kn-1 + kn), where h is the distance between the knots and ki = yi''.

To show that if y = f(x) is approximated by a natural cubic spline with evenly spaced knots, the quadrature formula becomes I = 2h(y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3(k0 + 2k1 + k2 + ⋯ + 2kn-1 + kn), where h is the distance between the knots and ki = yi''.

The natural cubic spline interpolates the function f(x) using piecewise cubic polynomials between each pair of adjacent knots. Let's denote the spline functions as Si(x) for i = 0 to n-1, where Si(x) is defined on the interval [xi, xi+1].

The composite trapezoidal rule is used to approximate the integral of f(x) over each interval [xi, xi+1]. It is given by the formula:

Ti = h/2 * (yi + yi+1)

where Ti represents the approximation of the integral over the interval [xi, xi+1].

Summing up the trapezoidal approximations over all intervals, we get:

I = T0 + T1 + T2 + ⋯ + Tn-1

 = (h/2) * (y0 + y1) + (h/2) * (y1 + y2) + ⋯ + (h/2) * (yn-1 + yn)

 = h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn)

Now, let's consider the correction term for curvature. The curvature term measures the second derivative of the spline functions at each knot. Using the notation ki = yi'', we have:

C = (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)

Adding the curvature correction term to the trapezoidal approximation, we obtain the final quadrature formula:

I = h/2 * (y0 + 2y1 + 2y2 + ⋯ + 2yn-1 + yn) - (2/4)h^3 * (k0 + k1 + k2 + ⋯ + kn-1 + kn)

This formula represents the integration approximation using the natural cubic spline with evenly spaced knots. The first part corresponds to the composite trapezoidal rule, and the second part provides a correction for the curvature of the spline.

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Answer:

x= -13 (a)

Step-by-step explanation:

-2x=35-9

-2x=26

x=-13

hope this helps x.

Answer:

-13

Step-by-step explanation:

9-2/x=35

9-2/x=35

-2/x=35-9

-2/x=26

-2=26x

26x=-2

x=-1/13

tha range of the function is all real number greater than 0

Answer:

Step-by-step explanation:

since you moved -1 in the x-axis

+1 to reverse it

(-1,5)

and since you moved +6 in the y-axis

-6 to do the reverse

(-1,-1)

Answer:

-3,-1 maybe

Step-by-step explanation: