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Question 4 < > Find the volume of the solid obtained by rotating the region bounded by y 4x2, 1 = 1, and y = 0, about the x-axis. V Submit Question

The contribution margin for braised greens is $2.68.

The contribution margin is a financial metric that helps businesses determine the profitability of a product or service. It represents the amount of revenue that is left over after deducting the variable costs of producing that product or service.

In this case, the ingredients for the braised greens cost $1.32, and the selling price is $4, so the contribution margin would be $2.68 ($4 - $1.32 = $2.68).

This means that for every sale of the braised greens, the business earns $2.68 towards covering fixed costs and generating profit. By calculating the contribution margin, businesses can determine the pricing strategy that is necessary to achieve their desired profit margins while remaining competitive in the market.

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Polar coordinates for rectangular coordinates if x<0: r=√(x²+y²) and θ=tan⁻¹(y/x)+π if y≥0 or θ=tan⁻¹(y/x)−π if y<0, For x≥0: r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.

The polar coordinates of a point with rectangular coordinates (x,y) depend on the sign of x.

If x<0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2. If x≥0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2.

If x<0, t

hen r=√(x²+y²) and

θ=tan⁻¹(y/x)+π if y≥0

or θ=tan⁻¹(y/x)−π if y<0.

The value of r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment from the origin to the point.

If x≥0, then r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.

In this case, θ is the angle between the positive x-axis and the line segment from the origin to the point, measured counterclockwise.

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The magnitude and direction of the vector u = <-4, 7> are |u| ≈ √65 and θ ≈ 119.74°.

To find the magnitude and direction of the vector u = <-4, 7>, we will use the following steps:

1. Calculate the magnitude using the Pythagorean theorem.
2. Calculate the direction using the arctangent function.

Step 1: Calculate the magnitude.
Magnitude (|u|) = √((-4)^2 + (7)^2) = √(16 + 49) = √65

Step 2: Calculate the direction (angle θ).
θ = arctan(opposite/adjacent) = arctan(7/-4) ≈ -60.26° (in degrees)
Since the vector is in the second quadrant, we need to add 180°.
θ = -60.26° + 180° ≈ 119.74°

So, the magnitude and direction of the vector u = <-4, 7> are |u| ≈ √65 and θ ≈ 119.74°.

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Answer:

The truck can deliver up to 209 boxes without exceeding a mass of 4700.

Step-by-step explanation:

To solve this problem, we need to use the formula:

[tex]\sf:\implies Total_{(Mass)} = Number_{(Boxes)} \times Weight_{(Per\: Box)}[/tex]

We know that each box weighs 22.5, so the formula becomes:

[tex]\sf:\implies Total_{(Mass)} = 22.5 \times Number_{(Boxes)}[/tex]

We want to find the maximum number of boxes that the truck can deliver without exceeding a mass of 4700. So we set up an inequality:

[tex]\sf:\implies 22.5 \times Number_{(Boxes)} \leqslant 4700[/tex]

To solve for number of boxes, we isolate it by dividing both sides by 22.5:

[tex]\sf:\implies Number_{(Boxes)} \leqslant 4700 \div 22.5[/tex]

[tex]\sf:\implies Number_{(Boxes)} \leqslant 209.33[/tex]

Since we can't have a fraction of a box, we round down to the nearest integer:

[tex]\sf:\implies \boxed{\bold{\:\:Number_{(Boxes)} \leqslant 209\:\:}}\:\:\:\green{\checkmark}[/tex]

Therefore, the truck can deliver up to 209 boxes without exceeding a mass of 4700.

The carbon dioxide level in the atmosphere is modeled using two possible derivative functions. Using Model I, the level in 2050 is approximately 426.25 ppm, and using Model II, it is approximately 522.73 ppm.

Using Model I

We need to integrate the derivative function C'(t) = 0.5 + 0.025t to get C(t).

∫C'(t) dt = ∫0.5 + 0.025t dt

C(t) = 0.5t + (0.025/2)t^2 + C

Using the initial condition that C(0) = 370, we get

370 = 0 + 0 + C

C = 370

So, C(t) = 0.5t + (0.025/2)t^2 + 370

To find the carbon dioxide level in 2050 using Model I

C(50) = 0.5(50) + (0.025/2)(50)^2 + 370

C(50) = 25 + 31.25 + 370

C(50) = 426.25 ppm

Using Model II

We need to integrate the derivative function C'(t) = 0.5e^(0.025t) to get C(t).

∫C'(t) dt = ∫0.5e^(0.025t) dt

C(t) = (20e^(0.025t))/ln(10) + C

Using the initial condition that C(0) = 370, we get

370 = (20e^(0))/ln(10) + C

C = 370 - (20/ln(10))

So, C(t) = (20e^(0.025t))/ln(10) + (370 - (20/ln(10)))

To find the carbon dioxide level in 2050 using Model II

C(50) = (20e^(0.025(50)))/ln(10) + (370 - (20/ln(10)))

C(50) = 522.73 ppm (rounded to two decimal places)

Therefore, the carbon dioxide level in 2050 is approximately 426.25 ppm using Model I, and approximately 522.73 ppm using Model II.

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Answer:

x=7

Step-by-step explanation:

Because all the bases are the same you can ignore the 8's.

Instead solve for 15=x+8

in which you would subtract the 8 to the left side, and 15-8=7

The investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

Let's denote the amount invested in Swan Peak as x and the amount invested in Riverside Community as y.

According to the given information:

1. The return on investment in Swan Peak was a 110% increase, which means the total return was 100% + 110% = 210% of the initial investment.

2. The return on investment in Riverside Community was 50% over the initial investment, which means the total return was 100% + 50% = 150% of the initial investment.

We are also given that the investor earned $1 million in profits.

Based on the above information, we can set up the following equations:

1.1 million = 2.1x + 1.5y  (equation 1)    [This equation represents the total profits earned by the investor.]

x + y = 1.1 million  (equation 2)    [This equation represents the total amount invested.]

To solve these equations, we can use substitution or elimination method. Let's use the elimination method:

Multiply equation 2 by 2.1 to make the coefficients of x in both equations equal:

2.1x + 2.1y = 2.31 million   (equation 3)

Now, subtract equation 1 from equation 3 to eliminate x:

(2.1x + 2.1y) - (2.1x + 1.5y) = 2.31 million - 1.1 million

0.6y = 1.21 million

Divide both sides by 0.6:

y = 2.01 million / 0.6

y ≈ 3.35 million

Substitute the value of y into equation 2:

x + 3.35 million = 1.1 million

x ≈ 1.1 million - 3.35 million

x ≈ -2.25 million

Since the amount invested cannot be negative, we discard the negative value.

Therefore, the investor invested approximately $500,000 in Swan Peak (x) and approximately $600,000 in Riverside Community (y).

Hence, the investor invested $500,000 in Swan Peak and $600,000 in Riverside Community.

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Blue color of clay weighs exactly twice the number of pounds of another color of clay. The correct option is a.

We need to find the color of clay that weighs exactly twice the number of pounds of another color of clay. We can start by comparing the amounts of clay for each color:

- Blue: 11 pounds

- Green: 8 pounds

- Yellow: 2 pounds

- Red: 15 pounds

To find the answer, we need to see if any of these values is exactly twice another value. We can start by dividing each amount by 2:

- Blue: 11 ÷ 2 = 5.5

- Green: 8 ÷ 2 = 4

- Yellow: 2 ÷ 2 = 1

- Red: 15 ÷ 2 = 7.5

From this, we can see that the amount of blue clay (11 pounds) is exactly twice the amount of green clay (5.5 pounds). Therefore, the answer is A. Blue.

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r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

a. To test whether there is a significant reduction in mental alertness after consuming tryptophan versus before, we can use a paired samples t-test. The null hypothesis is that there is no difference in mental alertness scores before and after the meal, and the alternative hypothesis is that the scores are lower after the meal:

H0: μd = 0 (no difference)

Ha: μd < 0 (lower scores after the meal)

Here, μd is the mean difference score in mental alertness before and after the meal. We will use a one-tailed test with α = .05, since we are only interested in the possibility of lower scores after the meal.

The t-statistic for a paired samples t-test is calculated as:

t = (Md - μd) / (sd / sqrt(n))

Where Md is the mean difference score, μd is the hypothesized mean difference (in this case, 0), sd is the standard deviation of the difference scores, and n is the sample size.

We are given that Md = 14, and the standard deviation of the difference scores (sd) is:

sd = sqrt(SSd / (n - 1)) = sqrt(1152 / 8) = 12

Substituting these values, we get:

t = (14 - 0) / (12 / sqrt(9)) = 3.5

Using a one-tailed t-distribution table with 8 degrees of freedom and α = .05, the critical value is -1.86. Since our calculated t-value (3.5) is greater than the critical value, we reject the null hypothesis and conclude that there is a significant reduction in mental alertness after consuming tryptophan versus before.

b. To compute r2 to measure the size of the effect, we can use the formula:

r2 = t2 / (t2 + df)

Where t is the calculated t-value for the test, and df is the degrees of freedom, which is n-1 in this case.

Substituting the values , we get:

r2 = (3.5)2 / ((3.5)2 + 8) = 0.523

Therefore, r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.

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Answer:

b+24

Step-by-step explanation:

the sum of a number represented by variable b

-- b+

and 24

-- b+24

Answer: b + 24

Step-by-step explanation:

The sum of .. and ➜ addition between two values

a number b ➜ b (represented by a variable)

24 ➜ the number 24

         The sum of a number b and 24 ➜ b + 24

The problem involves finding the derivative of a given function at a specified point.

Specifically, we are given the function f(x) = -8x^(-1) + 5x^(-2), and we need to find the value of the derivative f'(2) at x = 2. To find the derivative of f(x), we need to apply the rules of differentiation, which involve taking the derivative of each term separately and applying the power rule and chain rule as needed.

Once we have the derivative function f'(x), we can evaluate it at x = 2 to find the value of f'(2). Differentiation is a fundamental concept in calculus, and is used extensively in many areas of mathematics, science, and engineering. The ability to find derivatives allows us to analyze the behavior of functions and solve a wide variety of problems, from optimization to modeling physical systems.

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The interval where y increases for the function f(x) = (4x² - 1)/(x² + 1) is (-∞, -0.5) U (0.5, ∞) is 0.5-(-∞) = ∞.

To find the intervals where the function f(x) = (4x² - 1)/(x² + 1) increases, we need to find its derivative and determine its sign. The derivative of f(x) can be found using the quotient rule:

f'(x) = [(8x)(x² + 1) - (4x² - 1)(2x)]/(x² + 1)²

Simplifying this expression, we get:

f'(x) = (12x - 4x³)/(x² + 1)²

To find the critical points, we need to solve the equation f'(x) = 0:

12x - 4x³ = 0

4x(3 - x²) = 0

This gives us the critical points x = 0 and x = ±√3. We can now test the intervals between these critical points to determine the sign of f'(x) in each interval.

Testing x < -√3, we choose x = -4, and we get f'(-4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.

Testing -√3 < x < 0, we choose x = -1, and we get f'(-1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.

Testing 0 < x < √3, we choose x = 1, and we get f'(1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.

Testing x > √3, we choose x = 4, and we get f'(4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.

Hence, the interval where f(x) increases is (-∞, -0.5) U (0.5, ∞). Therefore, the answer is 0.5 - (-∞) = ∞.

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The data set is 2, 7, 7, 8, 9, and 9, with a mean of 7. The outlier is 2, and the mean without the outlier is 6.6. The outlier pulls the mean lower than the center, but once removed, the mean becomes more representative of the data set.

To find the mean of a set of values, we add up all the values and divide by the total number of values.

In this case, we know that the mean of six values is 7, so we can set up the following equation

(2 + 7 + 7 + 8 + 9 + 9) / 6 = 7

Simplifying the equation, we get

42 / 6 = 7

So, the sum of the six values is 42.

Now, we know that there is one outlier that pulls the mean higher than the center. In other words, one of the values is much larger than the others. Let's assume that the outlier is 20.

So, the new sum of the six values would be

2 + 7 + 7 + 8 + 9 + 20 = 53

To find the mean without the outlier, we need to subtract the outlier from the sum and divide by the remaining number of values. In this case, there are five values remaining. So, we get

(2 + 7 + 7 + 8 + 9) / 5 = 33 / 5 = 6.6

Therefore, the possible data set is 2, 7, 7, 8, 9, and 9, and the mean without the outlier is 6.6.

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--The given question is incomplete, the complete question is given

" The mean of six values is 7. There is one outlier that

pulls the mean higher than the center. What could the

data set be? What is the mean without the outlier?  

The possible data set is 2, 7, 7, 8, 9, and 9. "--

The most appropriate conclusion that can be made when the null hypothesis is rejected for the chi-square test of independence is: There is a significant association between fear of crime and one's perception of their neighborhood as a high crime area or not.

If the null hypothesis is rejected in a chi-square test of independence, it means that there is a significant association between the two variables being studied. In this case, the fear of crime is dependent on one's perception of whether their neighborhood is a high crime area or not.

Therefore, the most appropriate conclusion that can be made is that there is a significant relationship between the two variables, and one's perception of their neighborhood being a high crime area or not is a predictor of fear of crime. However, the chi-square test of independence does not determine causality, so it is not possible to conclude which variable is causing the other. Further research would be required to determine the direction and nature of the relationship between the two variables.

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Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.

Let's assume that x is the number of bottles of cherry soda sold and y is the number of bottles of grape soda sold. We can set up a system of equations to represent the given information:

x + y = 210 (equation 1: the total number of bottles sold is 210)

1.15x + 0.99y = 230.30 (equation 2: the total cost of the sodas is $230.30)

We can use the first equation to solve for y in terms of x:

y = 210 - x

Substituting this expression for y into the second equation, we get:

1.15x + 0.99(210 - x) = 230.30

Simplifying and solving for x, we get:

1.15x + 207.9 - 0.99x = 230.30

0.16x = 22.4

x = 140

So Bill sold 140 bottles of cherry soda. Substituting this value into equation 1, we get:

140 + y = 210

y = 70

Therefore, Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.

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The markup on retail is 47%. The correct option is c.

he markup on retail price is calculated to determine the percentage increase from the wholesale price to the retail price. In this case, the wholesale price is $17 and the retail price is $25. By subtracting the wholesale price from the retail price ($25 - $17),

we find that the markup is $8. Dividing this markup by the wholesale price ($8 / $17) gives us a ratio. Multiplying this ratio by 100 converts it to a percentage, which is approximately 47.06%.

This means that the retail price is approximately 47% higher than the wholesale price. Option c, 47%, correctly represents the calculated markup on the retail price.

Therefore, the markup on retail is 47%, so the answer is (c).

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Answer:

Obtuse

Step-by-step explanation:

Right angles are 90° so incorrect

Acute angles are less than 90°, also incorrect

Obtuse angles are between 90 and 180. And this is the range which 137 is found

So angle S is obtuse

Answer:

B) Obtuse

Step-by-step explanation:

Let's look at the definitions for each answer choice:

Acute: An acute angle is an angle that measures less than 90°.

Obtuse: An obtuse angle is an angle that measures more than 90°.

Right: A right angle is an angle that measures exactly 90°.

Given that Angle S is 137°, we can classify this angle as an obtuse angle, as 137>90.

Hope this helps! :)

The correct answer is 9% interest rate and 25 years.

To find the correct answer, we can use the mortgage payment formula:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:
M = monthly mortgage payment ($629.81)
P = principal loan amount ($70,000)
r = monthly interest rate (annual interest rate / 12)
n = total number of payments (years * 12)

We can test each option to see which one fits the given mortgage payment.

1) 9%, 20 years:
r = 0.09 / 12 = 0.0075
n = 20 * 12 = 240

M = 70000 * (0.0075(1 + 0.0075)^240) / ((1 + 0.0075)^240 - 1)
M ≈ $629.29 (close but not exact)

2) 9%, 25 years:
n = 25 * 12 = 300

M = 70000 * (0.0075(1 + 0.0075)^300) / ((1 + 0.0075)^300 - 1)
M ≈ $629.81 (matches the given mortgage payment)

Based on our calculations, the correct answer is 9% interest rate and 25 years.

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Answer:

f(-2) = 9

Step-by-step explanation:

f(x) = -3x + 3                       Solve for f(-2)

f(-2) = -3(-2) + 3

f(-2) = 6 + 3

f(-2) = 9

(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.

The given function is: C(x) = -10x^2 + 500x + 110

To find the derivative, we will apply the power rule:

C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)

For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500

(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.

To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360

The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.

Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard

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Answer:

54

Step-by-step explanation:

9x 3 x2 =54

Therefore, the molarity of the sugar solution is 0.3704 M at 25°C. Therefore, the molality of the NaCl solution is 1.8994 mol/kg.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=). The expressions on either side of the equal sign may contain variables, constants, coefficients, and mathematical operations.

Here,

1. To calculate the molarity of a sugar solution, we need to first determine the number of moles of solute (glucose, C6H12O6) present in the solution. We can then divide this number of moles by the volume of the solution in liters to obtain the molarity. The number of moles of glucose in the solution can be calculated as follows:

Number of moles = mass of solute / molar mass of solute

Number of moles = 100.0 g / 180 g/mol

Number of moles = 0.5556 mol

Next, we can calculate the molarity of the solution using the following formula:

Molarity = number of moles / volume of solution (in L)

Molarity = 0.5556 mol / 1.50 L

Molarity = 0.3704 M

2. To calculate the molality of a solution, we need to know the number of moles of solute (NaCl) per kilogram of solvent (water).

First, let's calculate the number of moles of NaCl:

Number of moles = mass of NaCl / molar mass of NaCl

Number of moles = 200.0 g / 58.5 g/mol

Number of moles = 3.4188 mol

Next, we need to calculate the mass of the solvent (water) in kilograms:

Mass of solvent = 2.00 kg - 0.200 kg

Mass of solvent = 1.80 kg

Note that we subtracted the mass of the NaCl from the total mass of the solution to obtain the mass of the solvent.

Finally, we can calculate the molality of the solution using the following formula:

Molality = number of moles of solute / mass of solvent (in kg)

Molality = 3.4188 mol / 1.80 kg

Molality = 1.8994 mol/kg

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The 95% CI for the genuine proportion of this bank's checking account customers who also have savings accounts is (0.3666, 0.4976).

To construct a 95% confidence interval for the true proportion of checking account customers who also have savings accounts, we can use the following formula:

CI = p ± z*√(p*(1-p)/n)

where:

We are given that the sample size is n = 243 and that 105 of the customers had both checking and savings accounts. Therefore, the sample proportion is:

p = 105/243 = 0.4321

The critical value z for a 95% confidence interval is approximately 1.96 (obtained from a standard normal distribution table or calculator).

We get the following results when we plug these values into the formula:

CI = 0.4321 ± 1.96*√(0.4321*(1-0.4321)/243)

CI = 0.4321 ± 0.0655

CI = (0.3666, 0.4976)

Therefore, we can say with 95% confidence that the true proportion of checking account customers who also have savings accounts at this bank is between 0.3666 and 0.4976.

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Conducting a survey among the students would be the best way to determine the most popular type of vending machine.

In order to accurately determine the most popular type of vending machine, it is important to gather data from the intended audience - the students. By conducting a survey, the administrator can gather information on the types of snacks and drinks that the students prefer, as well as their pricing preferences.

This will allow the administrator to make an informed decision on which type of vending machine will be most popular and profitable for the school.

Additionally, by involving the students in the decision-making process, they may feel more invested in the vending machines and be more likely to use them, ultimately leading to a successful vending program.

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Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.

The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.

Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.

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To differentiate x^6y^9 with respect to x, we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function multiplied with the second function, plus the first function multiplied with the derivative of the second function.

Step 1: Identify the functions
Function 1 (u): x^6
Function 2 (v): y^9

Step 2: Find the derivatives
u' (du/dx): Differentiate x^6 with respect to x, which gives 6x^5
v' (dv/dx): Differentiate y^9 with respect to x, which gives 9y^8 * (dy/dx) = 9y^8D (since D = dy/dx)

Step 3: Apply the product rule
d/dx (x^6y^9) = u'v + uv'
= (6x^5)(y^9) + (x^6)(9y^8D)
= 6x^5y^9 + 9x^6y^8D

So, the derivative of x^6y^9 with respect to x is 6x^5y^9 + 9x^6y^8D.

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The volume of the cylinder is 3811.7 cubic units when the radius is 9 and the width is 15.

Volume = π × radius² × height

Substitute the given values:
Volume = π × (9)² × 15

Squaring the radius:
Volume = π × 81 × 15

Multiplying the values together:
Volume = π × 1215

Calculating the volume using the approximate value of π (3.14):
Volume ≈ 3.14 × 1215

Calculating the final volume:
Volume ≈ 3811.7 cubic units

So, the volume of the cylinder with a radius of 9 and a height of 15 is approximately 3811.7 cubic units.

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When m = 50 and v = 2, the value of T is -200 according to Equation 1 and 200 according to Equation 2.

In the given equations, T represents a variable and m and v are constants.

We need to find the value of T when m = 50 and v = 2.

Let's evaluate each equation separately.

Equation 1: T = -mv²

Substituting the given values, we have:

T = -(50)(2)²

T = -(50)(4)

T = -200

Equation 2: T = my²

Substituting the given values, we have:

T = (50)(2)²

T = (50)(4)

T = 200

Thus, when m = 50 and v = 2, Equation 1 gives T = -200 and Equation 2 gives T = 200.

These equations represent two different relationships between the variables.

Equation 1 has a negative sign in front of the result, indicating that T will have a negative value.

On the other hand, Equation 2 does not have a negative sign, resulting in a positive value for T.

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Answer:

Step-by-step explanation:

25x3x15