The height of the outside is given as 17.44 meters
How to solveThe equation of hyperbola is :
[tex]y^2 - x^2 = 38[/tex]
=>[tex]y^2/38 - x^2/38 = 1[/tex]
(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)
Here, [tex]a^2 = b^2 = 38[/tex]
[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]
( a is the distance of vertices from the center and c is the distance of foci from the center.)
Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center
and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining
end points of the wall on one side is through the foci point.
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2n-1/3=n+2/2 please help me
[tex] \sf \longrightarrow \: \frac{2n - 1}{3} = \frac{n + 2}{2} \\ [/tex]
[tex] \sf \longrightarrow \: 2( 2n - 1) = 3(n + 2) \\ [/tex]
[tex] \sf \longrightarrow \: 4n - 2 = 3n +6 \\ [/tex]
[tex] \sf \longrightarrow \: 4n = 3n +6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: 4n - 3n= 6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: 1n= 6 + 2\\ [/tex]
[tex] \sf \longrightarrow \: n= 8\\ [/tex]
[tex] \longrightarrow { \underline{ \overline{ \boxed{ \sf{\: \: \: n= 8 \: \: \: }}}}} \: \: \bigstar\\ [/tex]
Solve (d-8) (6d-3) using the box method show work
6d^2 - 51d + 24
that's it
...............................
The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −3≤x≤8?
The average rate of change of the function f(x) in the interval [tex]-3 \leq x\leq -2[/tex] is -15.
We are given an interval in which we have to find the average rate of change of the function f(x) based on the graph given in the question. The interval given is -3 [tex]\leq[/tex] x [tex]\leq[/tex] -2. We are going to apply the formula for an average rate of change to find the rate of change of the given function in the given interval.
The formula we will use is
The average rate of change = [tex]\frac{f(b) - f(a) }{b - a}[/tex]
Identifying the points in the graph,
a = 3, f(a) = -10
b = -2, f(b) = -25
We will substitute these values in the formula for the average rate of change.
The average rate of change = [tex]\frac{-25-(-10)}{-2-(-3)}[/tex]
The average rate of change = ( -25 + 10)/(-2 +3)
= -15/1
= -15.
Therefore, the average rate of change of the function in the interval [tex]-3 \leq x \leq -2[/tex] is -15.
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The complete question is "The function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval -3\le x \le -2 −3≤x≤−2? "
Please help me this and can you write answer in box!!!!!
Use the gradient to find the directional derivative of the function at P in the direction of PQ. . f(x, y) = 3x2 - y2 + 4, = P(3, 1), Q(2, 4)
The directional derivative of the function f(x, y) = 3x^2 - y^2 + 4 at P(3, 1) in the direction of PQ is -24/sqrt(10).
To find the directional derivative of the function f(x, y) = 3x^2 - y^2 + 4 at point P(3, 1) in the direction of PQ, follow these steps:
Step 1: Compute the gradient of the function. The gradient of f(x, y) is given by the partial derivatives with respect to x and y: ∇f(x, y) = (df/dx, df/dy) = (6x, -2y)
Step 2: Calculate the gradient at point P(3, 1). ∇f(3, 1) = (6(3), -2(1)) = (18, -2)
Step 3: Calculate the unit vector in the direction of PQ. First, find the difference vector PQ = Q - P = (2-3, 4-1) = (-1, 3). Next, find the magnitude of PQ: |PQ| = sqrt((-1)^2 + (3)^2) = sqrt(10). Then, calculate the unit vector uPQ = PQ / |PQ| = (-1/sqrt(10), 3/sqrt(10)).
Step 4: Compute the directional derivative of f at P in the direction of PQ. The directional derivative, D_uPQ f(P), is given by the dot product of the gradient at P and the unit vector uPQ: D_uPQ f(P) = ∇f(P) • uPQ = (18, -2) • (-1/sqrt(10), 3/sqrt(10)) = 18(-1/sqrt(10)) - 2(3/sqrt(10)) = -18/sqrt(10) - 6/sqrt(10) = -24/sqrt(10)
So the directional derivative of the function f(x, y) = 3x^2 - y^2 + 4 at P(3, 1) in the direction of PQ is -24/sqrt(10).
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Lindsey wears a different outfit every day. Her outfit consists of one top, one bottom, and one scarf.
How many different outfits can Lindsey put together if she has 3 tops, 3 bottoms, and 3 scarves from which to choose? (hint: the
counting principle)
3 outfits
B9 outfits
24 outfits
D) 27 outfits
7. quentin has 45 coins, all dimes and quarters. the total value of the coins is $9.15.
how many of each coin does he have?
number of dimes =
number of quarters =
Quentin has 14 dimes and 31 quarters.
Let x be the number of dimes, and y be the number of quarters. According to the problem, we have two equations: x + y = 45 (equation 1) 0.10x + 0.25y = 9.15 (equation 2)
To solve for x and y, we can use substitution or elimination method. Here, we'll use the elimination method:
Multiplying equation 1 by 0.10, we get: 0.10x + 0.10y = 4.50 (equation 3)
Subtracting equation 3 from equation 2, we get: 0.15y = 4.65, y = 31
Substituting y=31 in equation 1, we get: x + 31 = 45, x = 14
Therefore, Quentin has 14 dimes and 31 quarters.
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Newton’s Method!!!!!!
The approximate value of x using the newton method is 0.7
Calculating the value of x using the newton methodFrom the question, we have the following expression that can be used in our computation:
[tex]\frac{x}{x^2+1}-\sqrt{1-x}[/tex]
Also, we have the function f(x) to be
[tex]f(x) = x(x^2+1)^{-1} -\sqrt{1-x}[/tex]
And we have the differentiated function to be
[tex]f'(x) = \frac{1}{x^2+1} - \frac{2x^2}{(x^2 + 1)^2} + \frac{1}{2\sqrt{1-x}}[/tex]
The value of x using the newton method is given as
[tex]x_n = x_{n-1} - \frac{f(x_{n-1})}{f'(x_{n-1})}[/tex]
Set [tex]x_{n-1}[/tex] = 0
So, we have
x₁ = 0 - -1/1.5 = 0.67
x₂ = 0.67 - undefined = undefined
So, we have
x₁ = 0.67
When approximated, we have
x = 0.7
This means that the value of x using the newton method is 0.7
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Median & IQR Question: The data shows the number of hours a part-time waiter works each week. Tell whether each statement about the data is True or False. Statements and numbers are listed in the picture.
The statements regarding the median and the quartiles are given as follows:
a. True.
b. True.
c. False.
What are the median and the quartiles of a data-set?The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The ordered data-set in this problem is given as follows:
7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.
Hence:
The first quartile is of 8. -> option b is true.The median is of 9. -> option a is true.The third quartile is of 11.More can be learned about median and quartiles at https://brainly.com/question/3514929
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A movie studio surveyed married couples about the types of movies they prefer. In the survey, the husband and wife were each asked if they prefer action, comedy, or drama. The summary of the data the studio got after asking 225 couples
Suppose the movie studio will ask 150 more couples about their movie preference. How many of these 150 couples will have exactly one spouse prefer action movie?
Out of the 150 new couples, we can expect about:
45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.
30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.
What is probability?
Probability is a measure of the likelihood of an event occurring.
Based on the given data from the survey of 225 couples, we can construct a contingency table as follows:
Husband Wife Total
Action 45 30 75
Comedy 30 45 75
Drama 45 45 90
Total 120 120 240
From the contingency table, we can see that:
Out of 240 respondents, 75 (45 from husbands and 30 from wives) preferred action movies.
Out of 240 respondents, 60 (30 from husbands and 30 from wives) preferred comedy movies.
Out of 240 respondents, 90 (45 from husbands and 45 from wives) preferred drama movies.
To answer the question of how many of the 150 couples will have exactly one spouse who prefers action movie, we can use the information that:
Out of 240 respondents, 45 husbands preferred action movies but their wives did not.
Out of 240 respondents, 30 wives preferred action movies but their husbands did not.
Therefore, out of the 150 new couples, we can expect about:
45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.
30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.
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A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y'' = 2y + 12 cot^3 x, yp(x) = 6 cotx The general solution is y(x) =
The general solution is then [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]
To find the general solution for the nonhomogeneous equation [tex]y'' = 2y + 12 cot^3x[/tex] with particular solution
yp(x) = 6 cotx, we can use the method of undetermined coefficients.
First, we need to find the complementary function, which is the general solution to the homogeneous equation y'' = 2y. The characteristic equation is r² - 2 = 0, which has roots r = ±√2.
Therefore, the complementary function is[tex]y_c(x) = c1 e^√2x + c2 e^-√2x.[/tex]
Next, we need to find a particular solution yp(x) to the nonhomogeneous equation. Since the right-hand side is 12 cot^3 x, we can guess a solution of the form [tex]yp(x) = a cot^3 x.[/tex] Taking the first and second derivatives of this, we get
[tex]yp''(x) = -6 cotx - 18 cot^3 x and yp'''(x) = 54 cot^3 x + 54 cotx.[/tex]
Substituting these into the original equation, we get:
[tex](-6 cotx - 18 cot^3 x) = 2(a cot^3 x) + 12 cot^3 x-6 cotx = 2a cot^3 x[/tex]
a = -3/2
Therefore, the particular solution is[tex]yp(x) = -3/2 cot^3 x.[/tex]
The general solution is then [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]
So the final answer is [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]
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Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #13
The value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
∵ ΔJLM is a right triangle, as ∠MJL=90°
∴ tan(∠JML)= JL/JM [∵ tan∅=perpendicular/hypotenuse]
⇒ tan(51°)=JL/14
⇒ JL=14×tan(51°)
= 14×1.23
= 17.29
∴ JL=17.29
Again, ΔJKL is a right triangle, with ∠JKL=90°
∴ cos(∠JLK)=KL/JL [∵ cos∅=base/hypotenuse]
⇒cos(72°)= KL/17.29
⇒KL=17.29×cos(72°)
= 17.29×0.309
= 5.34
∴ KL=5.34
Hence, the value of KL is 5.34.
Also, tan(∠JLK)=KJ/KL
⇒tan(72°)=JK/5.34
⇒JK=5.34×tan(72°)
= 5.34×3.077
= 16.434
∴ JK=16.434
And, cos(∠JML)=JM/ML
⇒cos(51°)=14/ML
⇒ML=14/cos(51°)
=14/.629
=22.25
∴ ML=22.25
Hence, the value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
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Write a function rule for the statement.
the output is eight less than the input
The function rule for the statement "the output is eight less than the input" is a simple mathematical expression that represents a relationship between the input and output values.
In this case, it can be expressed as Output = Input - 8. The function takes the input value, subtracts 8 from it, and returns the result as the output value. This rule ensures that the output will always be eight units smaller than the input. For example, if the input is 15, the output will be 7. This function rule can be used to perform calculations or model various scenarios where the output is consistently eight units less than the input.
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celine ordered a set of beads. she received 10,000 beads in all, 9,100 of the beads were brown. what percentage of the beads were brown?
Answer:
91%
Step-by-step explanation:
Malia had 15 lb of birdseed. She fed her birds 5 lb of birdseed every day until all the birdseed was gone. For how many days did Malia feed the birdseed to her birds? A.20 days B. 3 days C.90 days D.75 days
Answer:
B
Step-by-step explanation:
15 pounds and 5 pounds per day so to figure out how many days you do division. The equation is 15÷5=3 so the answer is 3 days.
Reddy
algebraic expressions with exponents - instruction - level f
) amelia stores her gardening supplies in two cube-shaped boxes. the smaller box has a
volume of 100 in.. amelia wants to know the total volume of both boxes.
s = length (in) of one side of the larger box.
6) write an expression to show the total
volume of the two boxes.
The expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] ([tex]in^3[/tex])
We can start by finding the volume of the smaller box using the formula for the volume of a cube:
Volume of smaller box = (length of one side)^3 = 100 in^3
Taking the cube root of both sides, we get:
Length of one side = ∛100 in ≈ 4.64 in
Now, we can use this value to find the volume of the larger box:
Volume of larger box = (length of one side)[tex]^3 = s^3[/tex]
The total volume of both boxes is the sum of the volume of the smaller box and the volume of the larger box:
Total volume = Volume of smaller box + Volume of larger box
Total volume = 100 in [tex]^3 + s^3[/tex]
Therefore, the expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] (in[tex]^3[/tex])
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Does anyone know the answer?
Answer:
B. ∠FBG
Step-by-step explanation:
When an angle is in the three letter form, the first letter is the first line that forms the angle, the second letter is where the angle is located, and third letter is the line that forms the angle with the first line.
Thus, we can see that line E combines with line F, and the actual angle is located at point B.
The two angles adjacent to ∠EBF are ∠DBE and ∠FBG. Only ∠FBG is one of the answer choices so this is our final answer.
A flat screen television costs $1600. It may be purchased for $100 down and 24 easy monthly payments of $80 each. What simple interest rate was charged on the purchase per monthly payment?
The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.
To determine the simple interest rate charged per monthly payment on the flat screen television, please follow these steps:
1. Calculate the total amount paid in monthly payments: 24 payments * $80 = $1920.
2. Subtract the down payment: $1920 - $100 = $1820.
3. Subtract the original cost from the total amount paid: $1820 - $1600 = $220. This is the total interest paid.
4. Divide the total interest by the number of monthly payments: $220 / 24 = $9.1667 interest per month.
5. Calculate the interest rate per monthly payment: ($9.1667 / $1600) * 100 = 0.5735% per month.
The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.
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HELP! In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 703. 27
and a standard deviation of 34. 14. A score of 700 is needed to earn 3 points
To find the probability of scoring at least 700 points on the Algebra EOC, we calculate the z-score, which is -0.122, and then find the area under the standard normal curve using a z-table. The probability is 54.98%. Since this is higher than the significance level of 0.05, we can conclude that the student has met the requirement to earn 3 points on the EOC.
Identify the mean, standard deviation, and score needed to earn 3 points
Mean (μ) = 704.39
Standard deviation (σ) = 36.18
Score needed for 3 points = 700
Calculate the z-score for the score needed to earn 3 points
z = (score - μ) / σ
= (700 - 704.39) / 36.18
= -0.122
Look up the area to the left of the z-score in the standard normal distribution table
The area to the left of -0.122 is 0.4502.
Subtract the area found in step 3 from 1 to find the area to the right of the z-score
Area to the right = 1 - 0.4502 = 0.5498
Convert the area to the right into a percentage
Percentage = 0.5498 x 100% = 54.98%
Interpret the percentage as the probability of earning 3 points or more on the Algebra EOC exam:
The probability of earning 3 points or more on the Algebra EOC exam is 54.98%.
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--The given question is incomplete, the complete question is given
" In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39
and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.
a. Fill in the values of each standard deviation above and below the mean, and make sure to add in the value
of the mean. Answers only are fine. "--
How to simplify radical expressions with variables?.
To simplify radical expressions with variables, identify perfect square factors, simplify the radical by taking out the largest possible integer factor that is a perfect square, and then multiply by the remaining factor outside the radical. Repeat the process until no more simplification is possible.
To simplify radical expressions with variables, follow these steps
Factor the expression under the radical sign into its prime factors.
Identify any perfect squares within the factors.
Rewrite the expression with the perfect squares outside the radical sign and the remaining factors inside.
Simplify any remaining radicals if possible.
Combine any like terms if necessary.
For example, to simplify the expression √(12x²y), you would first factor 12x²y into 2 * 2 * 3 * x * x * y. Then, you would identify the perfect square of x² and rewrite the expression as 2x√(3y). Finally, you could simplify further if possible, but in this case, the expression is already in its simplest form.
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Calculate the lenght of the shadow cast on level groundby a radio mast 90m high when the elevationof the sun is 40degree
The length of the shadow cast on level ground by a radio mast 90m high when the elevation of the sun is 40 degrees is approximately 85.3 meters.
To calculate the length of the shadow, we need to use trigonometry. We can imagine a right-angled triangle, where the height of the mast is the opposite side, the length of the shadow is the adjacent side, and the angle of elevation is 40 degrees.
Using the trigonometric function tangent (tan), we can find the length of the shadow, which is equal to the opposite side (90m) divided by the tangent of the angle of elevation (40 degrees). Therefore, the length of the shadow is approximately 85.3 meters.
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15. It is given that X~B(5,p) and P(X=3) = P(X=4)
Find the value of p, given that 0 < p < 1
[3 marks]
Given that 0 < p < 1 for X~B(5,p) and P(X=3) = P(X=4), so the value of p is 2/3.
We know that X~B(5,p) and P(X=3) = P(X=4).
Using the probability mass function of a binomial distribution, we can write:
P(X=3) = (5 choose 3) * p³ * (1-p)²
P(X=4) = (5 choose 4) * p⁴ * (1-p)¹
Since P(X=3) = P(X=4), we can set these two expressions equal to each other and simplify:
(5 choose 3) * p^3 * (1-p)² = (5 choose 4) * p⁴ * (1-p)¹
10p^3(1-p)^2 = 5p^4(1-p)
Dividing both sides by [tex]p^{3(1-p)[/tex] and simplifying, we get:
10(1-p) = 5p
10 - 10p = 5p
10 = 15p
p = 2/3
Therefore, the value of p is 2/3, given that 0 < p < 1.
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A sample of 60 Grade 9 students' ages was obtained to estimate the mean age of all Grade 9 students. Consider that
X
= 15. 3 years and the population variance is 16. (Note: Standard Deviation is the square root of variance). Assume that the distribution is normal.
Answer the following questions:
1. What is the point estimate for
μ
?
2. Find the 95% confidence interval for
μ
.
3. Find the 99% confidence interval for
μ
.
4. What conclusions can you make based on each interval estimate ?
The point estimate for μ is 15.3 years, based on the sample of 60 Grade 9 students.
How to find the age of all Grade 9 of students?Based on the statistical techniques given information, the point estimate for the population mean age of all Grade 9 students is 15.3 years. This means that if we assume that the sample is representative of the entire population of Grade 9 students, then we estimate that the average age of all Grade 9 students is 15.3 years.
To estimate the precision of this point estimate, we can calculate confidence intervals. For a 95% confidence interval, we can use the formula:
CI = X ± (Zα/2) * (σ/√n)
where X is the point estimate, Zα/2 is the critical value of the standard normal distribution for a 95% confidence level (1.96), σ is the population standard deviation (which we assume to be known as 4), and n is the sample size (which is 60).
Substituting the values, we get the 95% confidence interval as:
CI = 15.3 ± (1.96) * (4/√60) = (14.33, 16.27)
This means that we can be 95% confident that the true population mean age of Grade 9 students lies between 14.33 and 16.27 years.
For a 99% confidence interval, we can use the same formula with a different value of Zα/2 (2.58 for a 99% confidence level). Substituting the values, we get the 99% confidence interval as:
CI = 15.3 ± (2.58) * (4/√60) = (13.94, 16.66)
This means that we can be 99% confident that the true population mean age of Grade 9 students lies between 13.94 and 16.66 years.
Based on the confidence intervals, we can conclude that the sample provides evidence that the true mean age of all Grade 9 students is likely to be between 14.33 and 16.27 years with a 95% confidence level, and between 13.94 and 16.66 years with a 99% confidence level. However, we cannot be completely certain that the true population mean falls within these intervals as there is always some level of uncertainty associated with sample-based estimates.
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A function f(x) = 3x^4 dominates g(x) = x^4. True False
The given statement "A function f(x) = 3x^4 dominates g(x) = x^4" is True, which means that as x gets larger, the value of f(x) will increase much more rapidly than the value of g(x).
As x increases or decreases, the 3x^4 term in f(x) will grow faster or be larger in magnitude than the x^4 term in g(x). Since f(x) grows faster or has a larger magnitude than g(x), we can conclude that f(x) dominates g(x).
Therefore, the function f(x) = 3x^4 has a higher degree than g(x) = x^4
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A 2-quart carton of pineapple juice costs $8.08. What is the price per cup?
$
Answer:
$1.01
Step-by-step explanation:
We Know
A 2-quart carton of pineapple juice costs $8.08
1 quart = 4 cups
2 quarts = 8 cups
So, 8 cups of pineapple juice cost $8.08.
What is the price per cup?
We Take
8.08 / 8 = $1.01
So, the price per cup is $1.01
find the volume of the solid obtained by rotating the region bounded by 2 =8 32? and 2 = -2y about the line x= 9. round to the nearest thousandth.
The volume of the solid obtained by rotating the region about the line x=9 is approximately 201.06 cubic units.
To find the volume of the solid obtained by rotating the region bounded by 2 =8 32? and 2 = -2y about the line x= 9, we can use the cylindrical shell method.
First, we need to sketch the region and the line of rotation:
| +---------+
8 | | |
| | |
| +---------+ x=9
|
0 +---------------+
0 4 8
The region is a rectangle with height 4 and width 8, centered at the origin. The line of rotation is x=9.
Now, we can express the volume of the solid as a sum of cylindrical shells:
V = ∫[0,4] 2πr h dx
where r is the distance between x=9 and the boundary of the region at height x, and h is the thickness of the shell.
Since the region is symmetric about the y-axis, we can consider only the right half of the region and multiply the result by 2 to get the total volume.
The equation of the boundary at height x is:
2 = -2y
y = -x/2
The distance between x=9 and this line is:
r = 9 - (-x/2) = 9 + x/2
The thickness of the shell is dx.
Substituting these values into the integral, we get:
V = 2 ∫[0,4] 2π(9 + x/2) dx
V = 2π ∫[0,4] (18 + x) dx
V = 2π [18x + (1/2)[tex]x^2[/tex]] from x=0 to x=4
V = 2π [(18*4 + (1/2)[tex]4^2[/tex]) - (180 + (1/2)*[tex]0^2[/tex])]
V = 64π ≈ 201.06
Therefore, the volume of the solid obtained by rotating the region about the line x=9 is approximately 201.06 cubic units.
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Question 3 Next ſsin"" e cos"" Evaluate the indefinite integral xdu
But there seems to be some missing information in your question. Please provide more context or details so that I can assist you accurately.
Hi! I'd be happy to help you evaluate the indefinite integral. Based on the provided terms and information, it seems like you want to evaluate the following integral:
∫x * sin(e * cos(x)) dx
To solve this integral, we can use integration by parts, which is defined as:
∫u dv = u * v - ∫v du
Let's choose u = x and dv = sin(e * cos(x)) dx. Then, we need to find du and v:
du = dx
v = ∫sin(e * cos(x)) dx
Unfortunately, the integral for v does not have a simple closed-form expression. However, you can use numerical methods or software (like Wolfram Alpha) to approximate it. Once you have an approximation for v, you can plug it back into the integration by parts formula to obtain an approximation of the original integral:
∫x * sin(e * cos(x)) dx ≈ x * v - ∫v dx
Keep in mind that this is an indefinite integral, so don't forget to add the constant of integration, C, to your final answer.
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Qn2. Two functions f and g are defined as follows: f(x) = 2x – 1 and g(x) = x +4. Determine: i) fg(x) ii) value of x such that fg(x) = 20
The value of x such that fg(x) = 20 is 6.5.
Find the value of f(x)g(x) by substituting g(x) into f(x):f(x)g(x) = f(x)(x+4) = 2x(x+4) - 1(x+4) = 2x^2 + 8x - 4To find the composite function fg(x), we need to substitute the expression for g(x) into f(x), as follows:
fg(x) = f(g(x)) = f(x + 4) = 2(x + 4) - 1 = 2x + 7
So, fg(x) = 2x + 7
ii) To find the value of x such that fg(x) = 20, we can substitute fg(x) into the equation and solve for x, as follows:
fg(x) = 2x + 7 = 20
2x = 13
x = 6.5
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Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 3x^4 – 4x^3-12x^2 + 1, {-2, 3] absolute minimum value
absolute maximum value
The absolute maximum value of f(x) on the interval [-2,3] is 201 and occurs at x = -2, and the absolute minimum value of f(x) on the interval [-2,3] is -79 and occurs at x = 2.
To find the absolute maximum and absolute minimum values of f(x) on the interval [-2,3], we need to first find the critical points of the function and evaluate the function at these points as well as at the endpoints of the interval.
To find the critical points, we need to find where the derivative of the function equals zero or does not exist. Taking the derivative of f(x), we get:
f'(x) = 12x^3 - 12x^2 - 24x
Setting this equal to zero and factoring out 12x, we get:
12x(x^2 - x - 2) = 0
Using the quadratic formula to solve for x^2 - x - 2 = 0, we get:
x = -1, 0, 2
These are our critical points.
Now we evaluate f(x) at the critical points and the endpoints of the interval:
f(-2) = 201
f(-1) = 6
f(0) = 1
f(2) = -79
f(3) = 16
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Eric’s dad asks him to figure out the tax on the meal his family just finished eating at their favorite restaurant. The total bill for the meal is $57. 60. The tax is 7. 5%. What is the tax amount for this meal?
The tax amount for this meal is $4.32.
To calculate the tax amount on the meal, you'll need to multiply the total bill by the tax rate. In this case, the total bill is $57.60 and the tax rate is 7.5%.
To find the tax amount, use this formula: Tax Amount = Total Bill × Tax Rate
Tax Amount = $57.60 × 0.075
Tax Amount = $4.32
The tax amount for this meal is $4.32.
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What is the difference between factored form and non-factored form?
Factored form is a way of expressing a polynomial as a produce of factors, place each factor is a polynomial accompanying a degree of 1 or greater.
Factored form, on the other hand, is the polynomial terms written in polynomial expanded form, outside any universal factors.
What is the difference?Factored and non-factored forms are ways to express polynomial expressions, which involve variables raised to non-negative integer powers with constant coefficients. X² + 3x + 2 is a polynomial expression.
Factored form is expressing it as a product of factors with a degree of 1 or greater. The polynomial x² + 3x + 2 can be factored as (x + 1)(x + 2). Non-factored form is the expanded expression without common factors. The polynomial (x + 1)(x + 2) can be expressed as x² + 3x + 2 in non-factored form. Factored form is a product of factors, while non-factored form is the expanded form without common factors.
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