consider the family of functions f(x) , where p is a real number. for what values of p does the integral exist? what is its value?

Answer:

Dimensions: 22m x 22m

Step-by-step explanation:

Let x be the width of the rectangle and y be its length (in meters).

Since the perimeter of the rectangle is 88m, so it follows:

\(2x+2y=88\\x+y=44\\y=44-x\)

Then, recall that the area A of the rectangle is:

\(A=xy\\A=x(44-x)\\A=44x-x^2\\\)

Find the first derivative of the area function as follows:

\(\frac{dA}{dx}=44-2x\)

Then, solve the following for x:

\(\frac{dA}{dx}=0\\44-2x=0\\2x=44\\x=22\)

Then, observe that:

\(y=44-22=22\)

So, the rectangle with the largest area is a square of side length 22 meters; the optimum dimensions are 22m x 22m.

the dimensions of the rectangle with a perimeter of 88 m and the largest possible area are:

Length (L) = 22 m

Width (W) = 22 m

To find the dimensions of a rectangle with the largest possible area given a fixed perimeter, we can use the concept of optimization. In this case, we want to maximize the area of the rectangle while keeping the perimeter constant at 88 m.

Let's assume the length of the rectangle is L and the width is W. The perimeter of a rectangle is given by the formula:

Perimeter = 2L + 2W

Given that the perimeter is fixed at 88 m, we have:

2L + 2W = 88

Dividing both sides of the equation by 2, we get:

L + W = 44

Now, we need to express the area of the rectangle in terms of L and W. The area of a rectangle is given by the formula:

Area = L * W

To maximize the area, we can express it as a function of a single variable. Using the equation L + W = 44, we can express W in terms of L:

W = 44 - L

Substituting this value of W into the area formula, we get:

Area = L * (44 - L)

Expanding the equation, we have:

Area = 44L - L^2

Now, we have the area of the rectangle as a function of L. To find the maximum area, we can take the derivative of the area function with respect to L and set it equal to zero:

d(Area)/dL = 44 - 2L = 0

Solving this equation, we find L = 22.

Substituting this value of L back into the equation L + W = 44, we find W = 22.

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The  required solution to the system of equations using elimination, as follows:

18. The solution is (x, y) = (40/11, -17/11).

19. The solution is (x, y) = (6, 1).

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

To solve the system of equations using elimination, we can multiply one equation by a scalar so that one of the variables has the same coefficient in both equations.

18.

-6x + 4y = -28

6x + 7y = 11

Add the two equations to eliminate x:

11y = -28+11

11y = -17

y = -17/11

Now that y is known, we can substitute back into either equation to find x:

-6x + 4(-17/11) = -28

-6x - 68/11 = -28

x = 40/11

So the solution is (x, y) = (40/11, -17/11).

19.

2x + 3y = 15

x - 3y = 3

Add the two equations to eliminate y:

3x = 18

x = 18/3

x = 6

Now that x is known, we can substitute back into either equation to find x:

2(6) + 3y = 15

12 + 3y = 15

3y = 3

x = 1

So the solution is (x, y) = (6, 1).

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Answer: A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

8^2   m/hr   *   8^18 hr = 8^(2+18) = 8^20 miles

Answer:

boi just use a claculator

Step-by-step explanation:

bye luve

Answer: A 21,369

Explanation I got it right on the test :)

The two numbers that add up to 158 are 99 and 59.

The equation of variables that have a maximum power of 1 is known as a linear equation.

Let the lesser number be x.

So, the greater number will be x+40.

And the sum of both the numbers is 158.

So, the resulting linear equation based on given conditions is,

x + x + 40 = 158

2x = 158 - 40

2x = 118

x = 118/2

x = 59

So, the lesser number is 59.

And the greater number is 59 + 40 = 99.

Hence, the two numbers that add up to 158 are 99 and 59.

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We round up to 97 and the divide to the point it can to be divided anymore

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector. Therefore, option C is the correct answer

Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.

A) Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

B) An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.

C) Perpendicular bisector: A line that bisects a line segment in two equal parts.

D) Median: The middle number; found by ordering all data points and picking out the one in the middle.

A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector. Therefore, option C is the correct answer

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The lengths JL and PM are the lengths that make up the triangle JMP

The side length JL is twice the side length PN.

So, we have:

JL = 2 * PN

This gives

JL = 2 * 39

JL = 78

Hence, the length of JL is 78 units

The side length PM is half the side length KL.

So, we have:

PM = 0.5 * KL

This gives

PM = 0.5 * 95

PM = 47.5

Hence, the length of PM is 47.5 units

The angle MLK is congruent to the angle JMP.

So, we have:

MLK = JMP

This gives

MLK = 105 degrees

Hence, the measure of angle MLK is 105 degrees

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Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

five because 5×3 is 15 and 5×1 is 5

Answer:

x = 1

Step-by-step explanation:

Since both equations are equal to k(x), both equations are also equal to each other.

Begin by setting up the equation like this: -6 = -7x + 1

Simply solve for x by subtracting each side by 1 (-7 = -7x)

Finally, divide both sides by -7 to get 1.

Step-by-step explanation:

I am biased against people, who put an English question into Mathematics.

it is a fundamental, basic, personality defining mindset or believe that drives preferences.

we have the expression

therefore

The answer is

Answer:

\(y=5/6\approx0.83\)

Step-by-step explanation:

So we have the equation:

\(5(2y+1)=4y+10\)

First, let's distribute the left side of our equation:

\(5(2y)+5(1)=4y+10\)

Multiply:

\(10y+5=4y+10\)

Now, let's isolate the y-variable. Subtract 4y from both sides:

\((10y+5)-4y=(4y+10)-4y\)

The right side cancels. Subtract on the left. So:

\(6y+5=10\)

Now, subtract 5 from both sides:

\((6y+5)-5=(10)-5\)

The left side cancels. Subtract on the right:

\(6y=5\)

Now, divide both sides by 6. So:

\(\frac{6y}{6}=\frac{5}{6}\)

The left will cancel. Therefore:

\(y=5/6\approx0.83\)

And we're done!

Answer:

29 :)

it is 29 because 29 falls under all the prime number characteristics

To find the probability that the mean of the sample would be greater than 48.83 months, we will use the central limit theorem.

We will first find the z-score for the given values using the formula: `z = (x - μ) / (σ / √n)` where `x` is the sample mean, `μ` is the population mean, `σ` is the population standard deviation and `n` is the sample size.

Then we will find the probability using a standard normal distribution table.

Given,The mean lifetime of a tire, μ = 48 monthsStandard deviation of the lifetime of a tire, σ = 7Sample size, n = 147Sample mean, x = 48.83 months

We need to find the probability that the mean of the sample would be greater than 48.83 months.

Using the formula for z-score,z = (x - μ) / (σ / √n)z = (48.83 - 48) / (7 / √147)z = 0.83 / 0.577 = 1.44

Using a standard normal distribution table, the probability corresponding to a z-score of 1.44 is 0.9251.Approximately, the probability that the mean of the sample would be greater than 48.83 months is 0.9251.

Summary: The probability that the mean of the sample would be greater than 48.83 months is 0.9251.

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Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Answer:

The relation \(y^{2} - 4x = 3\) does not represent y as a function of x.

Step-by-step explanation:

Consider the relation

\(y^{2} - 4x = 3\)

\(y=\pm \sqrt{4x+3}\)

Thus, the equation \(y=\pm \sqrt{4x+3}\) does not represent function because there is at least one x-value with two or more values.

For example, if you look at the attached graph,

at x = 0, y = 1.73

at x = 0 , y = -1.73

It means the same input is generating two outputs; also if we draw a vertical line on the graph, the vertical line would intersect the graph more than once.

Please check the red vertical line on the graph would intersect the graph more than once.

Therefore, the relation \(y^{2} - 4x = 3\) does not represent y as a function of x.

Explanation:

The normal curve, aka bell curve, has mirror symmetry with the mean at the very center. Half of the data is below the mean, while the other half is above the mean.

About 68% of the data will lie below the mean in a normally distributed data set. This is known as the Empirical Rule, which states that if a data set is approximately normally distributed, then approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Given:

a.) Amplitude = 9 cm

b.) Period = 0.5 seconds

c.) At time = 0, displacement from rest is -9 cm

The general equation for displacement as a function of time is:

The amplitude is given by A. Here, since amplitude is 9 cm, so we have:

A = 9

The period of the object is 0.5 seconds, so we have:

Since the minimum displacement is at t = 0, so there is no phase shift.

Therefore, C = 0

Also since there is no vertical shift, so D = 0.

In Summary, we get: A = 9, B = 4π, C = 0 and D = 0

Thus the equation modeling the displacement d as a function of time t is given by:

Therefore, the equation is:

The two triangles have a common base EF, with vertex G at the top and H at the bottom. Angle GFE measures 60°.

To calculate the measure of angle GFE, start by labeling the two vertices of the angle. In this case, vertex G is at the top of the triangle and vertex H is at the bottom. Next, draw a perpendicular line from the common base EF to the vertex G. This will create two right triangles. Now use the Pythagorean theorem to calculate the lengths of the two sides of the triangle adjacent to the angle GFE. This is done by taking the square root of the sum of the squares of the other two sides. Once the lengths of the two sides are known, use the arctangent function to calculate the measure of angle GFE. Finally, compare the result to the known angle measure of 60° to confirm that the calculation is correct.

The complete question: Select the correct answer. a pair of triangles with a common base ef and a vertex g (top) and h (bottom). angle gfe is 60 & deg. angle and EFH is ( 2× 2). Angles GEF and HEF are equal & nbsp

In the diagram, ΔGEF and ΔHEF are congruent. what is the value of X?

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Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).

Answer:

Claim 1

Step-by-step explanation:

Step-by-step explanation:

4x+3+8x-9+y=180