(q15) A supply of soaps available at different prices is given by the supply curve s(x)= 180+0.3x^3/2 , where x is the product quantity. If the selling price is $250, find the producer surplus.

Answer:

I assume you mean what they are called, if not please clarify

<1 and <5 = corresponding angles

<3 and < 6 = alternate interior angles

<4 and <6 =  consecutive interior angles

Step-by-step explanation:

Answer:

Approximately 2.5% of the data is greater than 34.

Step-by-step explanation:

To solve this problem, we need to use the empirical rule (also known as the 68-95-99.7 rule) for a normal distribution. This rule states that about 68% of values lie within 1 standard deviation of the mean, about 95% of the values lie within 2 standard deviations of the mean, and about 99.7% of the values lie within 3 standard deviations of the mean.

The mean of the dataset is 27, and the standard deviation is 3.5.

34 is exactly 2 standard deviations away from the mean (since 27 + 2*3.5 = 34). According to the empirical rule, about 95% of the data falls within this range. This means that about 5% of the data is outside of this range.

Since the normal distribution is symmetrical, the data outside of 2 standard deviations is equally split between values that are too large and too small. Hence, about half of this 5%, or 2.5%, is greater than 34.

Therefore, approximately 2.5% of the data is greater than 34.

To find the range of a data set, we subtract the minimum value from the maximum value.

Given the data set: 47, 38, 72, 56, 40, 64, 30, 80, 66, 51

The minimum value is 30, and the maximum value is 80.

Range = Maximum value - Minimum value

= 80 - 30

= 50

Therefore, the range for the data set is 50.

To find the interquartile range (IQR), we need to determine the values of the first quartile (Q1) and the third quartile (Q3) and then calculate the difference between them.

First, we need to order the data set in ascending order:

30, 38, 40, 47, 51, 56, 64, 66, 72, 80

To find Q1, we take the average of the values at the 25th and 26th positions (since it falls between 38 and 40):

Q1 = (38 + 40) / 2

= 78 / 2

= 39

To find Q3, we take the average of the values at the 75th and 76th positions (since it falls between 66 and 72):

Q3 = (66 + 72) / 2

= 138 / 2

= 69

Now, we can calculate the interquartile range (IQR):

IQR = Q3 - Q1

= 69 - 39

= 30

Therefore, the interquartile range (IQR) for the given data set is 30.

About 95% of the housing Prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

Given that housing prices in a small town are normally distributed with a mean of µ. We are to use the empirical rule to complete the following statement.

The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean,

and approximately 99.7% of the data falls within three standard deviations of the mean.Since we do not have information about the standard deviation of the housing prices,

we cannot provide exact values for the empirical rule. However, we can make some general statements:

About 68% of the housing prices are between (µ - σ) and (µ + σ).

About 95% of the housing prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

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Answer:

B. $5.99

Step-by-step explanation:

Let's start by finding the total cost of the sodas. We know that there were 5 sodas and each cost $0.75, so the total cost of the sodas is:

5 * $0.75 = $3.75

Next, we need to subtract the cost of the sodas from the total cost before tax to find the cost of the pizzas:

$33.70 - $3.75 = $29.95

Finally, we can divide the cost of the pizzas by the number of pizzas to find the cost of each pizza:

$29.95 ÷ 5 = $5.99

Therefore, the cost of each pizza pie was $5.99. Answer choice B is correct.

The yield on 1-year T-bonds one year from now, based on the pure expectations Theory, is approximately 0.0349 or 3.49%. the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

The pure expectations theory, which suggests that the yield on a bond for a particular period is determined by the market's expectation of future interest rates. The theory assumes that investors are indifferent between investing in shorter-term bonds and rolling over their investments or investing in longer-term bonds.

A.) To calculate the yield on 1-year T-bonds one year from now, we need to find the geometric average of the current yield on 1-year T-bonds and the expected yield on 1-year T-bonds two years from now. Let's assume the current yield on 1-year T-bonds is 3% and the expected yield on 1-year T-bonds two years from now is 4%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

     = sqrt((1 + 0.03) * (1 + 0.04)) - 1

     = sqrt(1.03 * 1.04) - 1

     ≈ sqrt(1.0712) - 1

     ≈ 0.0349

Therefore, the yield on 1-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0349 or 3.49%.

B.) To calculate the yield on 2-year T-bonds one year from now, we need to find the geometric average of the current yield on 2-year T-bonds and the expected yield on 2-year T-bonds two years from now. Let's assume the current yield on 2-year T-bonds is 4% and the expected yield on 2-year T-bonds two years from now is 5%.

Using the geometric average formula, we can calculate the yield as follows:

Yield = sqrt((1 + Current Yield) * (1 + Expected Yield)) - 1

     = sqrt((1 + 0.04) * (1 + 0.05)) - 1

     = sqrt(1.04 * 1.05) - 1

     ≈ sqrt(1.092) - 1

     ≈ 0.0443

Therefore, the yield on 2-year T-bonds one year from now, based on the pure expectations theory, is approximately 0.0443 or 4.43%.

C.) To calculate the yield on 1-year T-bonds two years from now, we need to find the expected yield on 1-year T-bonds two years from now. Let's assume the expected yield on 1-year T-bonds two years from now is 5%.

The yield on 1-year T-bonds two years from now, based on the pure expectations theory, is equal to the expected yield, which is 5%.

Therefore, the yield on 1-year T-bonds two years from now, based on the pure expectations theory, is 5%.

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Answer:

161.67 square feet

Step-by-step explanation:

The explanation is attached below.

Area of rectangle = length * width

=> Area of ABIJ = (7 * 6)ft^2 = 42 ft^2

=> Area of IJHG = (5 * 7)ft^2 = 35 ft^2
=> Area of HGCD = (7.81 * 7)ft^2 = 54.67 ft^2

=> Area of triangle = (EIH) = JFG = 1/2 * Base * height

EIH = 1/2 * 6 * 5 = 15 ft^2

JFG = 1/2 * 6 * 5 = 15 ft^2

Total area = (42 + 35 + 54.67 + 15 + 15)ft^2 = 161.67 ft^2

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The debt will be cleared in approximately 158 months.

The monthly installment starts at Rs. 10,000 and increases by Rs. 100 each month. We can set up an arithmetic progression to represent the installment amounts:

10,000, 10,100, 10,200, ...

The nth term of this arithmetic progression can be calculated using the formula:

an = a1 + (n-1)d

where:

an = nth term of the sequence

a1 = first term of the sequence

d = common difference between the terms

In this case, a1 = 10,000 and d = 100.

Now we need to find the value of n such that the sum of the first n terms of the sequence exceeds or equals Rs. 622,500.

The sum of the first n terms of an arithmetic sequence can be calculated using the formula:

Sn = (n/2)(2a1 + (n-1)d)

We need to solve the equation:

Sn >= 622,500

Substituting the values, we have:

(n/2)(2*10,000 + (n-1)*100) >= 622,500

Simplifying the equation, we can solve for n:

n^2 + 199n - 614000 = 0

Using the quadratic formula, we find that:

n ≈ 157.37 or n ≈ -356.37

Since we cannot have a negative number of months, we take n ≈ 157.37. Therefore, it will take approximately 158 months (rounded up) to clear the debt.

Hence, the debt will be cleared in approximately 158 months.

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Answer:

(x - 1/8) * 1/4 = 1/16

x - 1/8 = 1/16

x = 1/16 + 1/8

x = 3/8

Mean: also known as the average is a measure of central tendency in a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values.

Standard deviation: The standard deviation is a measure of the dispersion of data around the mean in a dataset.t quantifies the average amount by which each data point in the dataset varies from the mean. A higher standard deviation indicates greater variability or dispersion of the data points, while a lower standard deviation suggests that the data points are closer to the mean. The standard deviation is typically represented by the symbol σ (sigma).

Z-Score: The z-score (also known as the standard score) is a statistical measurement that indicates how many standard deviations an individual data point is from the mean of a distribution. It allows you to compare and understand the relative position of a particular data point within a dataset.

The formula to calculate it is:  Z = (x - μ) / σ where:

Z = Z-score

x = data point

μ = mean

σ =  standard deviation

To calculate the z-score for Luis's exam grade, we can use the formula:

z = (x - μ) / σ

Where:

x = Luis's exam grade (84)

μ = Mean (81)

σ = Standard deviation (2.5)

Substituting the given values into the formula, we have:

z = (84 - 81) / 2.5

z = 3 / 2.5

z = 1.20

Rounding to two decimal places, the z-score for Luis's exam grade is 1.20.

Here's a table of values for the equation y = 8x - 4:

The table below show the input and output values of the equation.

x y

0 -4

1 4

2 12

3 20

4 28

5 36

6 44

7 52

8 60

9 68

10 76

These values represent the corresponding values of y when you substitute different values of x into the equation y = 8x - 4.

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Answer:

(a) x² + 6x + 8 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 6, and c = 8

Substituting the values, we get:

x = (-6 ± sqrt(6² - 4(1)(8))) / 2(1)

x = (-6 ± sqrt(36 - 32)) / 2

x = (-6 ± sqrt(4)) / 2

x = (-6 ± 2) / 2

x = -4 or -2

Therefore, the solutions are x = -4 or x = -2.

(b) x² + 7x + 12 = 0

We can factorize this quadratic equation as:

x² + 7x + 12 = (x + 3)(x + 4)

Therefore, the solutions are x = -3 or x = -4.

(c) y² + 7y + 10 = 0

We can factorize this quadratic equation as:

y² + 7y + 10 = (y + 2)(y + 5)

Therefore, the solutions are y = -2 or y = -5.

(d) y² + 3y - 4 = 0

We can factorize this quadratic equation as:

y² + 3y - 4 = (y + 4)(y - 1)

Therefore, the solutions are y = -4 or y = 1.

(e) x² - 2x - 8 = 0

We can factorize this quadratic equation as:

x² - 2x - 8 = (x - 4)(x + 2)

Therefore, the solutions are x = 4 or x = -2.

(f) m² - 7m + 12 = 0

We can factorize this quadratic equation as:

m² - 7m + 12 = (m - 3)(m - 4)

Therefore, the solutions are m = 3 or m = 4.

(g) y² - 10y + 25 = 0

We can factorize this quadratic equation as:

y² - 10y + 25 = (y - 5)²

Therefore, the only solution is y = 5.

(h) y² - 4y - 45 = 0

We can factorize this quadratic equation as:

y² - 4y - 45 = (y - 9)(y + 5)

Therefore, the solutions are y = 9 or y = -5.

(k) x² + 9x + 18 = 0

We can factorize this quadratic equation as:

x² +9x + 18 = (x + 3)(x + 6)

Therefore, the solutions are x = -3 or x = -6.

(m) y² - 13y + 22 = 0

We can factorize this quadratic equation as:

y² - 13y + 22 = (y - 2)(y - 11)

Therefore, the solutions are y = 2 or y = 11.

(n) x² + x - 12 = 0

We can factorize this quadratic equation as:

x² + x - 12 = (x + 4)(x - 3)

Therefore, the solutions are x = -4 or x = 3.

(p) x² - 11x + 18 = 0

We can factorize this quadratic equation as:

x² - 11x + 18 = (x - 2)(x - 9)

Therefore, the solutions are x = 2 or x = 9.

(q) y² - 14y + 48 = 0

We can factorize this quadratic equation as:

y² - 14y + 48 = (y - 6)(y - 8)

Therefore, the solutions are y = 6 or y = 8.

(s) m² - m - 56 = 0

We can factorize this quadratic equation as:

m² - m - 56 = (m- 8)(m + 7)

Therefore, the solutions are m = 8 or m = -7.

(t) y² + 22y + 96 = 0

We can factorize this quadratic equation as:

y² + 22y + 96 = (y + 12)(y + 8)

Therefore, the solutions are y = -12 or y = -8.

(v) x² - 38x + 72 = 0

We can factorize this quadratic equation as:

x² - 38x + 72 = (x - 2)(x - 36)

Therefore, the solutions are x = 2 or x = 36.

(w) x² + 14x - 51 = 0

We can factorize this quadratic equation as:

x² + 14x - 51 = (x + 17)(x - 3)

Therefore, the solutions are x = -17 or x = 3.

(y) g² - 12g - 64 = 0

We can factorize this quadratic equation as:

g² - 12g - 64 = (g - 8)(g - 4)

Therefore, the solutions are g = 8 or g = 4.

(z) y² + 22y + 121 = 0

We can factorize this quadratic equation as:

y² + 22y + 121 = (y+ 11)²

Therefore, the only solution is y = -11.

(1) y² + 10y + 24 = 0

We can factorize this quadratic equation as:

y² + 10y + 24 = (y + 4)(y + 6)

Therefore, the solutions are y = -4 or y = -6.

(1) x² - x - 56 = 0

We can factorize this quadratic equation as:

x² - x - 56 = (x - 8)(x + 7)

Therefore, the solutions are x = 8 or x = -7.

(1) x² + 23x + 22 = 0

We can factorize this quadratic equation as:

x² + 23x + 22 = (x + 1)(x + 22)

Therefore, the solutions are x = -1 or x = -22.

(0) m² - 6m - 27 = 0

We can factorize this quadratic equation as:

m² - 6m - 27 = (m - 9)(m + 3)

Therefore, the solutions are m = 9 or m = -3.

(r) x² - 15x + 56 = 0

We can factorize this quadratic equation as:

x² - 15x + 56 = (x - 7)(x - 8)

Therefore, the solutions are x = 7 or x = 8.

(u) k² - 18k - 88 = 0

We can factorize this quadratic equation as:

k² - 18k - 88 = (k - 2)(k - 16)

Therefore, the solutions are k = 2 or k = 16.

(x) y² + 32y + 240 = 0

We can factorize this quadratic equation as:

y² + 32y + 240 = (y + 12)(y + 20)

Therefore, the solutions are y = -12 or y = -20.

Hope this helps!

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B).

Explanation:  

In the given scenario, we are given that Leandra is renting a car for one week. The total cost to rent the car includes a weekly rate plus an additional charge per mile driven.

We can make the following points to obtain the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week

Let, x = Number of miles driven y = Total costLeandra is renting a car for one week.

Hence, we have the following given information:Total cost is a function of number of miles driven. Thus, the dependent variable is y, the Total cost.Weekly rate is a fixed cost and additional charge per mile driven is variable cost.

Hence, independent variable is x, the number of miles driven. Thus, x represents the number of miles driven and y represents the total cost to rent the car for one week.

The graph should show the number of miles driven on the x-axis and the corresponding total cost on the y-axis.The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B) which is given as follows:

x-axis represents the number of miles driven in the car during one week, and y-axis represents the total cost Leandra will pay to rent the car for one week.

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note the full question maybe:

Which graph correctly labels the axes for the total cost (y-axis) Leandra will pay to rent a car for one week based on the number of miles driven (x-axis)?

The Puyer Corporation has budgeted fixed selling and administrative expenses of $73,860 for February.

This includes advertising of $51,960, executive salaries of $21,900, and other expenses of $9,900.

The variable cost per Deb sold is $2.50. If the company sells 16,900 Debs in February, then the total budgeted selling and administrative expenses will be $89,760.

The total budget spending is given as:

$73,860 + (16,900 * $2.50) = $89,760

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If x = -2 is a zero with a multiplicity of one, x = 3 is a zero with a multiplicity of two, and x = 1 is a zero with a multiplicity of one, then the polynomial can be written in factored form as:

[tex]f(x) = (x + 2)(x - 3)^2(x - 1)[/tex]

To find the polynomial in expanded form, we can use the distributive property and the rules of exponents:

[tex]f(x) = (x + 2)(x - 3)(x - 3)(x - 1)\\= (x^2 - x - 6)(x - 3)(x - 1)\\= (x^3 - 4x^2 + 3x + 18)(x - 1)\\= x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

Therefore, the polynomial that has a lead coefficient of one and exactly three distinct zeros, with x = -2 as a zero with multiplicity of one, x = 3 as a zero with multiplicity of two, and x = 1 as a zero with multiplicity of one, is:

[tex]f(x) = x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

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Answer:

Among them 4/5 Is correct answer.

Answer:

3/4

Step-by-step explanation:

..,...............

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Answer:

A

Step-by-step explanation:

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

To form a polynomial with degree 5 and the given zeros, we can start by writing the factors corresponding to each zero.

The zero 3 gives us the factor (x - 3).

The zero -i gives us the factor (x + i) since complex zeros always come in conjugate pairs.

The zero 9+i gives us the factor (x - (9+i)).

Now, we can multiply these factors together to obtain the polynomial:

f(x) = (x - 3)(x + i)(x - (9+i))

Next, we simplify the expression:

f(x) = (x - 3)(x + i)(x - 9 - i)

Expanding the product, we have:

f(x) = (x^2 + xi - 3x - 3i)(x - 9 - i)

Multiplying further:

f(x) = (x^3 - 9x^2 - ix^2 + xi - 3x^2 + 27x + 3ix - 3xi - 27i - 3x + 27 + 3i)

Combining like terms:

f(x) = x^3 - (9 + i)x^2 - 3x^2 + (x - 3 - 3i)x + 27x + (27 + 3i)

Simplifying:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

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Answer:  C  200 times larger

Step-by-step explanation:

If you want to compare Edmond to Tulsa

Edmond = 1.6 x 10^3

Tulsa  = 3.3 x 10^5

10 to the power of anything means 1 and what ever that power is, that's how many 0's you put on.

Ex. 10^3 = 1000

10^5 = 100000

So Edmond = 1.6 x 1000

Tulsa = 3.3 x 100000

If you multply by 10's 100's etc.  the amount of 0's you have is how many you will move your decimal point

So Edmond = 1600

Tulsa = 330000

You can see that when comparing edmond to tulsa it got a lot larger.  200 times larger.

Answer:

18.2 grams

Step-by-step explanation:

Since the base diameter of the cylindrical container is d=11 cm, so its radius r is:

[tex]r=\frac{d}{2}=\frac{11}{2}=5.5[/tex]

Then, the volume V of the cylindrical container with radius r=5.5 cm and height h=12 cm is:

[tex]V=\pi r^{2}h=\pi \times 5.5^{2}\times 12=363\pi[/tex]

Since the water sample contains 0.016g of trace element for every cubic centimeter of water, so amount of trace element collected by the container of volume [tex]V=363\pi[/tex] cubic centimeters is:

[tex]0.016 g/cm^{3}\times 363\pi~cm^{3}=18.2g[/tex]

Approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

Let's denote the number of quarts of whipping cream that needs to be mixed as "x". We know that the whipping cream has a butterfat percentage of 36% and the half and half has a butterfat percentage of 12%. We want to determine the quantity of whipping cream needed to create a mixture with a butterfat percentage of 18%.

To solve this problem, we can use the concept of weighted averages. The amount of butterfat contributed by the whipping cream is 0.36x, and the amount contributed by the half and half is 0.12 * 4 = 0.48.

The total amount of butterfat in the resulting mixture is 0.18 * (x + 4) since we are aiming for an 18% butterfat content in the final mixture.

Setting up an equation based on the butterfat content, we have:

0.36x + 0.48 = 0.18(x + 4)

Simplifying the equation:

0.36x + 0.48 = 0.18x + 0.72

0.36x - 0.18x = 0.72 - 0.48

0.18x = 0.24

x = 0.24 / 0.18

x = 1.33...

Therefore, approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

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The volume of the solid figures are:

1. 480 cm³

2. 1000 m³

3. 141.43 cm³

4. 60.48 cm³

5. 16971.43 mm³

1. The volume of a cuboid is given by the formula:

V = l * w * h

where l is the length, w is the width and h is the height

We have:

l = 12 cm

w = 5 cm

h = 8 cm

V = 12 * 5 * 8

V = 480 cm³

2. The volume of a cube is given by the formula:

V = l³

where l is the side length

We have:

l = 10m

V = 10³

V = 1000 m³

3. The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height

We have:

r = 3 cm

h = 5 cm

V = 22/7 * 3² * 5

V = 141.43 cm³

4. This is also a cuboid.

We have:

l = 4.5 cm

w = 3.2 cm

h = 4.2 cm

V = 4.5 * 3.2 * 4.2

V = 60.48 cm³

5. This is also a cylinder.

We have:

r = 30/2 = 15 mm

h = 24 mm

V = 22/7 * 15² * 24

V = 16971.43 mm³

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Answer:

The bottom one

Step-by-step explanation:

Notice that the graph is an upward opening parabola and passes through the x-axis at the x-intercepts x=1 and x=-4. These are our zeroes that allow f(x)=0 by the Zero Product Property.

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

We have,

To solve the given integrals using integration by parts, we follow the formula:

∫u dv = uv - ∫v du

Let's solve each integral step by step:

∫xe^(7x) dx ; u = x, dv = e^(7x) dx

Taking the derivatives and integrals:

du = dx

v = ∫e^(7x) dx = (1/7) * e^(7x)

Applying the integration by parts formula:

∫xe^(7x) dx = uv - ∫v du

= x * (1/7) * e^(7x) - ∫(1/7) * e^(7x) dx

= (1/7) * xe^(7x) - (1/49) * e^(7x) + C

And,

∫x cos(8x) dx ; u = x, dv = cos(8x) dx

Taking the derivatives and integrals:

du = dx

v = ∫cos(8x) dx = (1/8) * sin(8x)

Applying the integration by parts formula:

∫x cos(8x) dx = uv - ∫v du

= x * (1/8) * sin(8x) - ∫(1/8) * sin(8x) dx

= (1/8) * x * sin(8x) + (1/64) * cos(8x) + C

Therefore,

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

Learn more about integrations here:

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[tex](\sin \theta)^2+\left(\dfrac{9}{10}\right)^2=1\\\\(\sin \theta)^2+\dfrac{81}{100}=1\\\\(\sin \theta)^2=\dfrac{19}{100}\\\\\sin\theta=\sqrt{\dfrac{19}{100}}=\dfrac{\sqrt{19}}{10}[/tex]