Calc II Question
Find the average value of the function on the given interval
F(x) = sin4x, [-pi, pi]


Correct answer is 45/28 but I'm not sure how to get to that answer

Answer:

Step-by-step explanation:

We must simplify and rearrange the variables to divide x in order to determine the comparable inequality to the supplied inequality, -4(x + 7) 3(x - 2).

Below are the steps to solve the problem:

-4(x + 7) < 3(x - 2)

Expanding the equation:

-4x-28<3x-6

Gather the variable term on one side and constants on the other:

Adding -4x and 28 on both sides:

-4x + 4x - 28 + 28 < 3x + 4x - 6 + 28

=>0 < 7x + 22

To make the coefficient of x positive, we divide the entire inequality by 7:

0/7 < (7x + 22)/7

=> 0 < x + 22/7

The height, h, of the cylinder is approximately 1.27 centimeters when the volume is 100 cm^3 and the radius is 5 cm, rounded to the nearest tenth.

To find the height, h, of the cylinder, we can rearrange the formula for the volume of a cylinder:

V = πr^2h

Given that the volume, V, is 100 cm^3 and the radius, r, is 5 cm, we can substitute these values into the formula:

100 = π(5^2)h

Simplifying further:

100 = 25πh

To solve for h, divide both sides of the equation by 25π:

100 / (25π) = h

To calculate the value, we'll use an approximation for π as 3.14:

100 / (25 * 3.14) ≈ h

Simplifying:

100 / 78.5 ≈ h

h ≈ 1.27 cm

Therefore, when the volume is 100 cm3 and the radius is 5 cm, the cylinder's height, h, is about 1.27 centimetres, rounded to the closest tenth.

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The diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm (option e).

Given that the diameter of the engine cylinder needs to be 5 cm wide with a tolerance of ± 0.005 cm.

To determine the permissible range of the diameter, we need to consider both the upper and lower limits.

Upper limit: Add the tolerance to the desired diameter.

  Upper limit = 5 cm + 0.005 cm = 5.005 cm.

Lower limit: Subtract the tolerance from the desired diameter.

  Lower limit = 5 cm - 0.005 cm = 4.995 cm.

Therefore, the permissible range for the diameter of the engine cylinder is between 4.995 cm and 5.005 cm.

Hence, the final answer is that the diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm.

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Answer:

To evaluate the expression when a = 5 and b = 1, we substitute the values into the expression:

12 + 2(4(5)²) ÷ 7 + 8

= 12 + 2(4 * 25) ÷ 7 + 8 (Note: 5² means 5 raised to the power of 2)

= 12 + 2(100) ÷ 7 + 8 (Note: 4 * 25 = 100)

= 12 + 200 ÷ 7 + 8

= 12 + 28.57 + 8 (Note: ÷ means divide)

= 48.57

To plot the resulting value on the provided number line , we would need to know the scale and range of the number line. Without this information, we cannot accurately plot the value.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, we multiply 2×2 then the answer we obtain we add to it 6 which in total gives us 10

Answer:

Step-by-step explanation:

all circles have same round shape with no edges and corners so they all are similar in terms of their shape and appearance but not all the circles are congruent.

two circles are congruent if they have the same measurements of radius, circumference, diameter as well as the surface area. So, to determine whether the two circles are congruent or not we have to perform the calculations.

The strength of the correlation as shown in the scatter plot can be concluded to be: b) no correlation.

To estimate the strength of the correlation in a scatter plot, visually assess the clustering and linearity of the data points. If the points cluster tightly around a linear trend, it indicates a strong correlation, whereas dispersed and non-linear points suggest a weak correlation.

However, if the points on a scatter plot do not exhibit a discernible pattern (as shown in the image given above), it can be concluded that there is no correlation between the variables being plotted.

Therefore, the answer is: b. no correlation.

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Answer:

The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(8 ÷ 4)³ + √64

(8 ÷ 4)³ + √64

2³ + √64

8 + 8

16

Answer:

16

Step-by-step explanation:

To solve, use PEMDAS as it applies to the expression.

First, you must carry out what is in the parenthesis.

Multiply (3*5 = 15), then subtract (7 - 15 = -8). The two little vertical lines surrounding (7 - 3 x 5) mean absolute value. This means that you will write -8 as +8.

Continuing on in the parenthesis, carry out (8 ÷ 4 = 2).

Next, we must do exponents.

We see that everything in the parenthesis is being raised to the power of three (cubed). Since we've solved what was in the parenthesis, we simply need to carry out ([tex]2^{3}[/tex] = 8).

Now, we need to quickly carry out [tex]\sqrt{64}[/tex]. Square roots are just whatever number can be multiplied by itself to get, in this case, 64.

[tex]\sqrt{64} = 8[/tex].

Finally, we must add what remains.

8 + 8 = 16.

So, (|7 - 3 x 5) | ÷ [tex]4)^{3}[/tex] + [tex]\sqrt{64}[/tex] = 16.

The length of the arc in terms of π and the actual length is as follows;

8.17π m²

25.68 m²

Let's find the length of the arc of the circle as follows:

Therefore,

length of an arc = ∅ / 360 × 2πr

where

Hence,

∅ = 180 - 88 = 92 degrees

r = 16 m

length of an arc MA = 92 / 360 × 2 × π × 16

length of an arc MA = 2944π / 360

length of an arc MA = 8.17π

Therefore,

length of an arc MA = 25.68 m²

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Answer:

f(0) = 1

f(1) = 21.1

Step-by-step explanation:

Do as the problem says:

[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]

Answer:

-9 is less than x, which is less than or equal to 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Domain is where the function exists for x.

The functions domain goes in terms of x goes from -9 to 11 not including -9 and including 11.

Interval notation:

-9 < x ≤ 11

Set notation:

(-9, 11]

Answer:

The recursive formula for an=1/8(2)n-1 is:

a1=1/8 an+1=1/8(2)(n)

This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.

Step-by-step explanation:

The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.

To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.

Let's calculate the ratio for each model:

Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.

Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.

Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.

Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.

From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.

Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.

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The correct statement regarding the relative extremas of F(x) is given as follows:

F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.

Hence the extremas for this problem are given as follows:

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Answer:

the solution would be X=3 as 3.1 represents 3×1.

11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.

12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.

In Mathematics and Geometry, a perpendicular bisector divides or bisects a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.

Question 11.

By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector of AB because CE bisects AB:

AC ≅ BC

CD ≅ CD

AE ⊥ EC

Question 12.

By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.

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Missing information:

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

The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.

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Step-by-step explanation:

The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.

In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):

68 = 2πr

To find the radius, we can divide both sides of the equation by 2π:

r = 68 / (2π)

Using an approximate value of π ≈ 3.14159, we can calculate the radius:

r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm

Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.

Therefore, The Radius of the Circle is 10.8 cm.

The distance from the given city to the South Pole is 125 degrees of latitude.

To determine the distance from the given city to various locations, we need to consider the latitude and longitude coordinates.

Distance to the North Pole:

The North Pole is located at 90°N latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the North Pole.

Distance to the North Pole = 90° - 35° = 55°

The distance from the given city to the North Pole is 55 degrees of latitude.

Distance to the Equator:

The Equator is located at 0° latitude. To determine the distance from the city to the Equator, we need to calculate the absolute value of the latitude of the city.

Distance to the Equator = |35°| = 35°

The distance from the given city to the Equator is 35 degrees of latitude.

Distance to the South Pole:

The South Pole is located at 90°S latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the South Pole.

Distance to the South Pole = 35° - (-90°) = 35° + 90° = 125°

The distance from the given city to the South Pole is 125 degrees of latitude.

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Answer:

Step-by-step explanation:

(a) To find the linear cost function C(x), we need to consider the fixed cost and the marginal cost. The fixed cost is $100, and the marginal cost is $8 per pair of earrings.

The linear cost function can be represented as C(x) = mx + b, where m is the slope (marginal cost) and b is the y-intercept (fixed cost).

In this case, the slope (m) is $8, and the y-intercept (b) is $100. Therefore, the linear cost function is:

C(x) = 8x + 100.

(b) The average cost function (AC) can be found by dividing the total cost (C(x)) by the number of units produced (x):

AC(x) = C(x) / x.

Substituting the linear cost function C(x) = 8x + 100, we have:

AC(x) = (8x + 100) / x.

(c) To find C(5), we substitute x = 5 into the linear cost function:

C(5) = 8(5) + 100

= 40 + 100

= 140.

Interpretation: C(5) = 140 means that when the artist produces 5 pairs of earrings, the total cost (including fixed and variable costs) is $140.

(d) To find C(50), we substitute x = 50 into the linear cost function:

C(50) = 8(50) + 100

= 400 + 100

= 500.

Interpretation: C(50) = 500 means that when the artist produces 50 pairs of earrings, the total cost (including fixed and variable costs) is $500.

(e) The horizontal asymptote of C(x) represents the cost as the number of units produced becomes very large. In this case, the marginal cost is constant at $8 per pair of earrings, indicating that as the number of units produced increases, the cost per unit remains the same.

Therefore, the horizontal asymptote of C(x) is $8, indicating that the average cost per pair of earrings approaches $8 as the number of units produced increases indefinitely.

In practical terms, this means that for every additional pair of earrings produced beyond a certain point, the average cost will stabilize and remain around $8, regardless of the total number of earrings produced.

Answer:

3071.6 ft

Step-by-step explanation:

In this situation,

We can use sine law,

in which Sin angle = opposite side/ hypotenuse

Similarly

In triangle ABC

SIn A=BC/AC

Sin 19°=1000/AC

Doing criss cross multiplication:

AC= 1000/(Sin 19°)

AC=3071.55 ft

Therefore, the distance I ski down the mountain is 3071.6 ft

The diagram is below.

==============================================

Work Shown:

sin(angle) = opposite/hypotenuse

sin(19) = 1000/x

xsin(19) = 1000

x = 1000/sin(19)

x = 3071.553487

x = 3071.6

Refer to the diagram below.

Note that the angle of depression ACD is equal to the angle of elevation BAC because of the alternate interior angles theorem.

(a) The average cost in 2011 is  $2247.64.

(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.

(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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The line that intersects two of the planes is : Line X

The line that intersects one of the planes is : Line Z

The line that that has points on three of the planes shown is Line Y

From this figure you can see that there are 3 different levels and 3 different lines. One line intersects two planes (line X), another line intersects only one plane (line Z). Line Y, on the other hand, has points in all three planes.

A line y has points A and B in all three planes.

A plane is simply a plane that can be intersected by a straight line connecting any two points on the plane.

Therefore, we can conclude from the figure

A line that intersects two planes is: line x

A line that intersects one of the planes is: line Z

A line with points on the three planes shown is Line Y. 

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The expression equivalent to -x--xy is 4x(3 + y).

To simplify the expression -x--xy, we can apply the rules of combining like terms and distribute the negative sign.

-x - (-xy)

Removing the double negative:

-x + xy

Factoring out the common factor of x:

x(-1 + y)

Now, let's compare the simplified expression with the given options:

Option 1: 2x - xy

This expression is not equivalent to -x - (-xy) as it includes an additional term of 2x.

Option 2: x(3 - y)

This expression is equivalent to the simplified expression x(-1 + y), as it represents the distribution of x over the terms inside the parentheses.

Option 3: 4x(3 - y)

This expression is not equivalent to -x - (-xy) as it includes the constant term 4.

Option 4: x(3 + y)

This expression is not equivalent to -x - (-xy) as it includes the positive sign before the y term.

Option 5: 4x(3 + y)

This expression is not equivalent to -x - (-xy) as it includes the constant term 4 and the positive sign before the y term.

From the given options, the expression that is equivalent to -x - (-xy) is:

Option 2: x(3 - y).

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Answer:

See below

Step-by-step explanation:

Domain would be all the x-values, so this is {3, 8, 8, 9}
Range would be all the y-values, so this is {0, 3, p, q}

The square root of m^6 is always positive.

The square root of m^6 can be calculated by dividing the exponent 6 by 2, since taking the square root is equivalent to raising a number to the power of 1/2.

In this case, m^6 divided by 2 gives us m^3.

Thus, the square root of m^6 is m^3.

This means that if we square m^3, the result will be m^6.

It is important to understand that the square root operation yields the positive root, so the square root of m^6 is always positive.

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The three arithmetic means between 10 and 130 are 40, 70, and 100.

To find the three arithmetic means between 10 and 130, we need to calculate the common difference between consecutive terms.

The common difference (d) can be found using the formula:

d = (last term - first term) / (number of terms - 1)

In this case, the first term is 10, the last term is 130, and we need to find three arithmetic means.

d = (130 - 10) / (3 + 1) = 120 / 4 = 30

Now, we can calculate the three arithmetic means by adding the common difference to the previous term:

First arithmetic mean = 10 + 30 = 40

Second arithmetic mean = 40 + 30 = 70

Third arithmetic mean = 70 + 30 = 100

So 40, 70, and 100 are the three arithmetic means between 10 and 130.

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Answer:

Step-by-step explanation:

12 14 33 35========1,234,000,124,581.