find the area of the surface the part of the sphere x^2+y^2+z^2 = b^2 that lies inside the cylinder x^2+y^2 = a^2 where 0

Answer:

To find the length of the intercepted arc, we need to use the formula:

length of intercepted arc = (central angle / 360°) x 2πr

where r is the radius of the circle.

Given that the central angle is 110° and the radius is 15 feet, we can plug in these values into the formula and get:

length of intercepted arc = (110° / 360°) x 2π x 15 feet

length of intercepted arc = (0.3056) x (30π) feet

length of intercepted arc ≈ 9.17 feet

Therefore, the length of the intercepted arc is approximately 9.17 feet.

Factorise simplified expressions are:

(a⁶ - b⁶)/(a³ × b³)

(x⁶ + 1)/(x⁴)

(p⁶ - q³)/(p² ×  q)

Let's simplify each of the given expressions:

a³/b³ - b³/a³

To simplify this expression, we can find a common denominator and then subtract the fractions:

(a³ × a³)/(b³ × a³) - (b³ × b³)/(a³ × b³)

(a⁶)/(a³ × b³) - (b⁶)/(a³ × b³)

Now, we have a common denominator, so we can subtract the fractions:

[(a⁶ - b⁶)/(a³ ×  b³)]

x⁴ + 1/x²

To simplify this expression, we can combine the terms by finding a common denominator:

(x⁴ ×  x²)/(x² ×  x²) + 1/x²

(x⁶)/(x⁴) + 1/x²

Now, we have a common denominator, so we can combine the terms:

(x⁶ + 1)/(x⁴)

p⁴/q - q²/p²

To simplify this expression, we can find a common denominator and then subtract the fractions:

(p⁴ ×  p²)/(q ×  p²) - (q²× q)/(p² ×  q)

(p⁶)/(p² × q) - (q³)/(p² × q)

Now, we have a common denominator, so we can subtract the fractions:

[(p⁶ - q³)/(p² × q)]

For similar questions on Factorise

https://brainly.com/question/25829061

#SPJ11

Based on the given information, the test statistic (t0) is -3.56, which indicates that the sample mean is 3.56 standard errors below the hypothesized population mean of 9 mobile apps.

The significance level (α) is 0.10, which means that the researcher has allowed for a 10% chance of rejecting the null hypothesis (H0) when it is actually true. The p-value is less than 0.01, which indicates that the probability of observing a sample mean at least as extreme as the one obtained, assuming the null hypothesis is true, is less than 1%. Therefore, we need to compare the p-value with the significance level. Since the p-value is less than the significance level, we reject the null hypothesis. This means that we have strong evidence to conclude that the average number of mobile apps on a person's cell phone is different than 9 mobile apps. Therefore, the correct answer is option d: Reject H0. There is strong evidence to conclude that the average number of mobile apps on a person's cell phone is different than 9 mobile apps.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

The scale for Paco's new drawing include the following: D. 1 inches : 2.5 yards.

In Mathematics and Geometry, a scale factor can be determined through the division of the side length of the image (new figure) by the side length of the original or actual geometric figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

Substituting the given side lengths into the scale factor formula, we have the following;

Scale factor = 10/5

Scale factor = 2.

New scale = (2/2 inches) : (5/2 inches)

New scale = 1 inches : 2.5 yards.

Read more on scale factor here: brainly.com/question/29967135

#SPJ9

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The model can then be used to determine the relationship between the two variables and make predictions about future values of the dependent variable based on the independent variable.

I can suggest a general process for selecting a topic and relevant data for a simple linear regression model. First, choose a topic or question of interest, for example, "Does the amount of exercise affect the quality of sleep?" or "Is there a relationship between the number of hours spent studying and exam scores?" Next, identify relevant datasets that contain at least two numerical variables, one for the dependent variable (e.g., quality of sleep or exam score) and one for the independent variable (e.g., amount of exercise or number of hours spent studying). Datasets can be found on websites such as Kaggle or through academic research databases.

Once the dataset is selected, the data must be cleaned and prepared for analysis. This includes checking for missing values, outliers, and ensuring that the variables are in the correct format for analysis.

Finally, a simple linear regression model can be constructed using statistical software such as R or Python.

Learn more about dependent variable here

https://brainly.com/question/30386143

#SPJ11

The sin() function can calculate the exact value of sin(pi/2) without introducing any significant rounding errors.

This is because of how the sin() function in MATLAB (and in most programming languages) is implemented. The trigonometric functions in MATLAB are computed using a numerical approximation algorithm that uses a series expansion. This algorithm has a finite precision and can introduce some small errors in the calculation of the trigonometric functions.

In particular, the value of pi used in MATLAB is a floating-point approximation of the mathematical constant π, which is irrational and has an infinite number of decimal places. The approximation used in MATLAB has a finite number of decimal places, so it is not exactly equal to π. Therefore, when you pass pi as an argument to the sin() function, the result is not exactly zero, but a very small number close to zero.

On the other hand, the value pi/2 is a known value that has a simple and exact representation as a fraction. Therefore, the sin() function can calculate the exact value of sin(pi/2) without introducing any significant rounding errors.

Learn more about sin() function here

https://brainly.com/question/20376882

#SPJ11

The correlation is unlikely to have come from a zero association population that is option B.

The p-value being less than .05 indicates that there is less than a 5% chance that the correlation coefficient of .32 could have been obtained by random chance alone, assuming a null hypothesis of zero correlation. Therefore, it is unlikely that the correlation came from a population with zero association. This does not tell us whether the correlation is statistically significant or not, as this is dependent on factors such as sample size and the desired level of significance. The p-value also does not indicate the effect size or direction of the correlation.

To know more about correlation,

https://brainly.com/question/31963083

#SPJ11

The interest on $5.255 at 12% for 30 days using ordinary interest is approximately $0.0511.

To calculate the interest using ordinary interest, we can use the formula:

Interest = Principal * Rate * Time

Here, the principal (P) is $5.255, the rate (R) is 12% (or 0.12), and the time (T) is 30 days.

Plugging in the values:

Interest = $5.255 * 0.12 * (30/365) = $0.0511 (rounded to four decimal places)

Know more about interest here:

https://brainly.com/question/30393144

#SPJ11

a) Basis is {[1 0 0;0 0 0;0 0 0], [0 0 0;0 1 0;0 0 0], [0 0 0;0 0 0;0 0 1]} and dimension is 3.  b) Basis is the union of the basis for diagonal matrices and skew-symmetric matrices, which is {[1 0 0;0 0 0;0 0 0], [0 0 0;0 1 0;0 0 0], [0 0 0;0 0 0;0 0 1], [0 1 0;1 0 0;0 0 0], [0 0 1;0 0 0;1 0 0], [0 0 0;0 0 1;0 1 0]} and dimension is 6. c) Basis is {[0 1 0;-1 0 0;0 0 0], [0 0 1;0 0 0;-1 0 0], [0 0 0;0 0 1;0 -1 0], [0 -1 0;1 0 0;0 0 0], [0 0 -1;0 0 1;0 0 0], [0 0 0;0 -1 0;1 0 0]} and dimension is 3.

a) To find a basis for the subspace of all diagonal matrices, we can use the standard basis for 3x3 matrices and select the matrices that have non-zero entries only on the diagonal. Therefore, a basis for this subspace is:

B = {

[1 0 0;

0 0 0;

0 0 0],

[0 0 0;

0 1 0;

0 0 0],

[0 0 0;

0 0 0;

0 0 1]

}

The dimension of this subspace is 3.

b) To find a basis for the subspace of all symmetric matrices, we can use the fact that any symmetric matrix can be written as the sum of a diagonal matrix and a skew-symmetric matrix. Therefore, we can take the basis for the subspace of all diagonal matrices found in part (a) and add to it a basis for the subspace of all skew-symmetric matrices, which we will find in part (c).

c) To find a basis for the subspace of all skew-symmetric matrices, we can use the standard basis for 3x3 matrices and select the matrices that satisfy AT = -A. Therefore, a basis for this subspace is:

B = {

[0 1 0;

-1 0 0;

0 0 0],

[0 0 1;

0 0 0;

-1 0 0],

[0 0 0;

0 0 1;

0 -1 0],

[0 -1 0;

1 0 0;

0 0 0],

[0 0 -1;

0 0 1;

0 0 0],

[0 0 0;

0 -1 0;

1 0 0]

}

The dimension of this subspace is 3.

Therefore, a basis for the subspace of all symmetric matrices can be obtained by taking the union of the basis for the subspace of all diagonal matrices with the basis for the subspace of all skew-symmetric matrices:

B = {

[1 0 0;

0 0 0;

0 0 0],

[0 0 0;

0 1 0;

0 0 0],

[0 0 0;

0 0 0;

0 0 1],

[0 1 0;

1 0 0;

0 0 0],

[0 0 1;

0 0 0;

1 0 0],

[0 0 0;

0 0 1;

0 1 0]

}

The dimension of this subspace is 6.

To know more about skew-symmetric matrices,

https://brainly.com/question/20630589

#SPJ11

Answer:

your question is not technically detailed enough

Step-by-step explanation:

provide more information Sir

The perimeter of the regular hexagon is 42 inches.

Since a regular hexagon can be divided into six equilateral triangles, each triangle shares a side with the hexagon. Let's denote the perimeter of the hexagon as P.

Since the perimeter of one equilateral triangle is 21 inches, each side of the triangle has a length of 21/3 = 7 inches.

Since the hexagon consists of six equilateral triangles, it will have six sides, each of length 7 inches. Therefore, the perimeter of the hexagon is given by:

P = 6 * 7 = 42 inches.

Know more about regular hexagon here:

https://brainly.com/question/1694257

#SPJ11

It is not meaningful to interpret the y-intercept for "biking" and "heart disease" because these two variables are not linearly related.

The y-intercept is the value of the dependent variable (heart disease) when the independent variable (biking) is equal to zero. However, in this case, it does not make sense for biking to equal zero since it is a continuous variable that can take on any positive value.

Furthermore, even if we were to restrict the range of biking to a meaningful subset (such as the minimum and maximum values in the dataset), the relationship between biking and heart disease is not expected to be linear. Instead, it is likely to be nonlinear, with potential thresholds or inflection points where the relationship changes in direction or magnitude.

Therefore, it is not appropriate to interpret the y-intercept for "biking" and "heart disease" as it does not provide meaningful information about the relationship between these two variables. Instead, we should focus on interpreting the coefficients of a nonlinear regression model or other appropriate measures of association for nonlinear relationships.

Know more about y-intercept click here:

https://brainly.com/question/14180189

#SPJ11

The factor that affects the computation of depreciation and is not listed among the options is Book value.

Depreciation is a method used to allocate the cost of an asset over its useful life. The factors that affect the computation of depreciation include the cost of the asset, its useful life, and the salvage value.

Book value, on the other hand, is the value of an asset as recorded in the company's accounting books and represents the asset's cost minus accumulated depreciation. While book value may change over time due to depreciation, it is not a factor that directly affects the computation of depreciation.

LEARN MORE ABOUT depreciation here: brainly.com/question/31793570

#SPJ11

a. The class width for all intervals in this frequency distribution is 3.

b. Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

c. Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

The number of full oscillations that any wave element performs in one unit of time is how we determine the frequency of a sinusoidal wave.

To find the class width, class midpoints, and class boundaries for the given frequency distribution, let's analyze the temperature intervals and frequencies:

Temperature (°F)    Frequency

32-35                      1

36-39                      3

40-43                      5

44-47                      11

48-51                      7

52-55                      7

56-59                      1

(a) Class width:

The class width is the difference between the upper and lower boundaries of each temperature interval. In this case, all the intervals have the same width.

Class width = Upper boundary - Lower boundary

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class width = 35 - 32 = 3

The class width for all intervals in this frequency distribution is 3.

(b) Class midpoints:

The class midpoint is the average value of the upper and lower boundaries of each interval. It represents the central value of the interval.

Class midpoint = (Upper boundary + Lower boundary) / 2

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class midpoint = (35 + 32) / 2 = 33.5

Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

(c) Class boundaries:

The class boundaries are the values that separate each interval. They are calculated by adding or subtracting half of the class width from the upper and lower boundaries.

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35, and the class width is 3.

Lower class boundary = Lower boundary - (0.5 * class width) = 32 - (0.5 * 3) = 32 - 1.5 = 30.5

Upper class boundary = Upper boundary + (0.5 * class width) = 35 + (0.5 * 3) = 35 + 1.5 = 36.5

Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

Note: The class boundaries are inclusive of the lower boundary and exclusive of the upper boundary.

These are the calculations for the class width, class midpoints, and class boundaries for the given frequency distribution.

Learn more about frequency on:

https://brainly.com/question/254161

#SPJ4

To find the class width, subtract the lower class limit from the upper class limit. To find the class midpoints, add the lower and upper class limits and divide by 2. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.

(a) Class width:

To find the class width, we subtract the lower class limit from the upper class limit. For example, the class width for the first class interval (32-35) is 35 - 32 = 3.

(b) Class midpoints:

To find the class midpoints, we add the lower class limit and the upper class limit and divide the sum by 2. For example, the class midpoint for the first class interval (32-35) is (32 + 35) / 2 = 33.5.

(c) Class boundaries:

To find the class boundaries, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. For example, the class boundaries for the first class interval (32-35) are (32 - 0.5) and (35 + 0.5).

https://brainly.com/question/35559032

#SPJ12

A confidence interval is a range of values that is likely to contain the true population parameter. In this case, we are given a 95% confidence interval for a population proportion. The correct option is D.

The point estimate for the population proportion is the sample proportion, which is denoted by p-hat. In this case, we are asked to find the best estimate of p-hat based on the given confidence interval.

To find the best estimate of p-hat, we need to take the midpoint of the confidence interval. The midpoint is calculated by taking the average of the lower and upper bounds of the interval. In this case, the midpoint is: Midpoint = (0.640 + 0.675)/2 = 0.6575

To know more about parameter visit:-

https://brainly.com/question/28249912

#SPJ11

The height of the right rectangular prism is 6 feet.

To find the height of the right rectangular prism, we divide the volume of the prism by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Rearranging the formula to solve for the height, we have h = V / (lw). Given that the base area is 25 1/2 square feet and the volume is 153 cubic feet, we can substitute these values into the formula. Therefore, the height of the right rectangular prism is 153 / 25.5 = 6 feet.

Learn more about Height

brainly.com/question/29131380

#SPJ11

Step-by-step explanation:

answer

12a^3+2a^2_a+2

The value of xxx in terms of aaa is 0.

To find the value of xxx in terms of aaa, we can set up the equation based on the given conditions.

The sum of xxx and a−xa−xa, minus, xx is aaa:

x + (a - x) - x = a

Simplifying the equation:

a - x = a

Subtracting a from both sides:

-x = 0

Dividing both sides by -1:

x = 0

Know more about equation here:

https://brainly.com/question/29538993

#SPJ11

Answer:

Step-by-step explanation:

㏒₃[tex]27^{x}[/tex]
= ㏒₃[tex]3^{3^{x} }[/tex]

= [tex]3x[/tex]㏒₃[tex]3[/tex]

= [tex]3x[/tex]

The radius of convergence, r, is infinity, meaning the series converges for all values of x.

To determine the radius of convergence, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is L, then the series converges if L is less than 1, and diverges if L is greater than 1.

Let's apply the ratio test to the series:

∑(n=1 to infinity) 9n/(n^4)

To apply the ratio test, we need to calculate the limit of the absolute value of the ratio of consecutive terms:

L = lim(n→∞) |(9(n+1)/(n+1)^4) / (9n/n^4)|L

= lim(n→∞) |9(n+1)n^4 / (n+1)^4 * n|L

= lim(n→∞) |9n(n+1)n^4 / n^4(n+1)^4|L

= lim(n→∞) |9(n+1) / (n+1)^4|L

= lim(n→∞) 9/(n+1)^3

As n approaches infinity, the term (n+1)^3 dominates the denominator, so we can simplify the expression to:

L = 9/∞^3

Since the denominator approaches infinity, the ratio L becomes 0.L = 0 < 1

Since the limit of the ratio is less than 1, the series converges.

Therefore, the radius of convergence, r, is infinity, meaning the series converges for all values of x.

Learn more about radius of convergence here, https://brainly.com/question/17019250

#SPJ11

English statements in symbolic language using the variables P, Q, and R and the logical connectives are  a) ¬R and b) R ∧ ¬P respectively.

a) The statement "Ann's family did not go to the park on Saturday" is the negation of the proposition R, which can be represented symbolically as ¬R.

b) The statement "Ann's family went to the park on Saturday and Ann did not go to the park" can be expressed using the logical connective "and" between the propositions R and ¬P, which can be represented symbolically as R ∧ ¬P. This means that both R and ¬P must be true for the statement to be true.

To know more about Logical connectives, visit,

https://brainly.com/question/14562011

#SPJ1

After considering the given data we conclude that English statements in symbolic language apply the variables P, Q, and R and the generated logical connectives are  a) ¬R and b) R ∧ ¬P respectively.

a) The statement "Ann's family did not go to the park on Saturday" is considered the negation of the proposition R, which can be projected symbolically as ¬R.

b) The statement "Ann's family went to the park on Saturday and Ann did not go to the park" could be elaborated applying the logical connective "and" between the propositions R and ¬P, which could be represented symbolically as R ∧ ¬P. This potrays that both R and ¬P must be true for the statement to be true.
To learn more about symbolic language,
https://brainly.com/question/29547191
#SPJ1

With an interest rate of 3% compounded continuously and an initial deposit of $15,000, the amount of money in the account after 20 years would be approximately $27,322.80.

Using the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = the amount of money in the account after the given time period

P = the initial deposit amount

e = the mathematical constant approximately equal to 2.71828

r = the interest rate (expressed as a decimal)

t = the time period (in years)

Let's assume an interest rate of 3% (0.03) compounded continuously and an initial deposit of $15,000. We can calculate the amount of money in the account after 20 years:

A = $15,000 * e^(0.03 * 20)

Using a calculator, we can evaluate the expression:

A ≈ $15,000 * e^(0.6)

A ≈ $15,000 * 1.82212

A ≈ $27,322.80

Therefore, with an interest rate of 3% compounded continuously and an initial deposit of $15,000, the amount of money in the account after 20 years would be approximately $27,322.80.

Learn more about compound interest at https://brainly.com/question/24274034

#SPJ1

The volume of a cube with a 9 m side is 729 cubic meters

The volume of a cube with an 8 in side is 512 cubic inches

The volume of a rectangular prism with the given length 5 ft., width 5 ft., height 7 ft is  175 cubic feet

The volume of a rectangular prism with the given length 10 ft., width 4 ft., height 5 ft is 200 cubic feet

The volume of a cube with a 9 m side:

V = s³

= 9³

= 729 cubic meters

The volume of a cube with an 8 in side:

V = s³

= 8³

= 512 cubic inches

The side of a cube with a volume of 343 cu.ft.:

s = cube root of V = cube root of 343 = 7 feet

The volume of a rectangular prism with the given length 5 ft., width 5 ft., height 7 ft.:

V = lwh

= 5 x 5 x 7

= 175 cubic feet

The volume of a rectangular prism with the given length 10 ft., width 4 ft., height 5 ft

V = lwh = 10 x 4 x 5 = 200 cubic feet

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

The relation r = {(0, 0), (1, 1), (3, 3), (5, 5), (0, 1), (1, 3), (0, 3), (3, 1)} on {0, 1, 3, 5} is not a partial ordering because it violates the antisymmetry property. There exist pairs of distinct elements that are related in both directions.

To be a partial ordering on a set, the relation must be reflexive, antisymmetric, and transitive.

In this case, the relation r = {(0, 0), (1, 1), (3, 3), (5, 5), (0, 1), (1, 3), (0, 3), (3, 1)} is reflexive since every element in {0, 1, 3, 5} is related to itself.

However, the relation is not antisymmetric since there exist pairs of distinct elements that are related in both directions. For example, (0, 1) and (1, 3) are in the relation, but (0, 1) and (1, 3) are also in the relation, which means that 0 is related to 3 and 3 is related to 0, violating the antisymmetry property.

Therefore, the relation r is not a partial ordering on {0, 1, 3, 5}.

Learn more about antisymmetry :

https://brainly.com/question/31729915

#SPJ11

Answer:
A's Salary is 3,000

B's Salary is 750.

Step-by-step explanation:

Divide 3,750 by 5 = B's salary.
Multiply that by 4. that is A's salary.

Hope you get an A+ <3

Based on the conclusions drawn from the given probabilities and suggest that children have a much greater chance of having side effects than adults. a and d.

To compare the probability of side effects between adults and children, we need to compare the given probabilities:

p(side effects child) = 0.40

p(side effects adult) = 0.12

p(side effects child) = 0.20

p(side effects adult) = 0.60

p(side effects child) = 0.20

p(side effects adult) = 0.60

p(side effects child) = 0.40

p(side effects adult) = 0.12

From these probabilities, we can draw the following conclusions:

The probability of side effects in children (0.40) is higher than the probability of side effects in adults (0.12).

The conclusion is that children have a much greater chance of having side effects than adults.

The probability of side effects in children (0.20) is lower than the probability of side effects in adults (0.60).

The conclusion is that children have a much lower chance of having side effects than adults.

The probability of side effects in children (0.20) is lower than the probability of side effects in adults (0.60).

The conclusion is that children have a much lower chance of having side effects than adults.

The probability of side effects in children (0.40) is higher than the probability of side effects in adults (0.12).

The conclusion is that children have a much greater chance of having side effects than adults.

For similar questions on probabilities

https://brainly.com/question/251701

#SPJ8

This statement is true that an optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.

In linear programming, an optimal solution to a problem can be found at any of the extreme points (also known as vertices) of the feasible region. This is known as the vertex principle.

The feasible region is the set of all possible solutions that satisfy the constraints of the problem. The extreme points of the feasible region are the corners or endpoints of the boundary that encloses the region.

Since the objective function in a linear programming problem is a linear function, it can be represented by a straight line in the two-dimensional case or a plane in the three-dimensional case. Therefore, the optimal solution can be found at the point where this line or plane intersects one of the extreme points of the feasible region.

To know more about optimal solution,

https://brainly.com/question/31994094

#SPJ11

Given,the art teacher will supply each student with fourteen pounds of clay to create a sculpture.The art teacher needs a total of 784 pounds of clay to supply 56 students, with each student receiving fourteen pounds of clay.

To determine the total amount of clay needed, we multiply the amount of clay per student (14 pounds) by the number of students (56). By doing this calculation, we obtain:

14 pounds/clay per student x 56 students = 784 pounds of clay.

Therefore, the art teacher will require 784 pounds of clay to supply each of the 56 students with fourteen pounds of clay for their sculptures.

To learn more about supply click here, brainly.com/question/13296654

#SPJ11

The antiderivative of the function -2sin(2x) with c = 0 is cos(2x).

To find the antiderivative of the function f(x) = -2sin(2x) with c = 0, we can apply the basic integration rules for trigonometric functions.

The antiderivative, also known as the indefinite integral, of a function represents the set of all functions whose derivative is equal to the original function. In this case, we want to find the function F(x) such that F'(x) = f(x) = -2sin(2x).

We can start by applying the power rule of integration, which states that the integral of sin(x) is equal to -cos(x). However, since we have sin(2x) in the given function, we need to adjust for the coefficient of 2.

Applying the chain rule, we divide the argument of sin(2x) by the derivative of the inner function, which is 2. This gives us:

∫sin(2x) dx = -1/2 cos(2x) + C

Now we need to account for the coefficient of -2 in the original function. The antiderivative of -2sin(2x) becomes:

∫-2sin(2x) dx = -2 * ∫sin(2x) dx

Substituting the antiderivative of sin(2x) that we found earlier, we have:

-2 * (-1/2 cos(2x)) + C

Simplifying, we get:

∫-2sin(2x) dx = cos(2x) + C

Finally, since c is given as 0, we can replace C with 0 in the equation. Therefore, the antiderivative of f(x) = -2sin(2x) with c = 0 is:

F(x) = cos(2x) + 0

F(x) = cos(2x)

Hence, the antiderivative of the function -2sin(2x) with c = 0 is cos(2x).

To know more about power rule of integration refer here:

https://brainly.com/question/30995188

#SPJ11

Answer:

-------------------

3% is half the 6%, hence half of the number is: