The minimum of Brown's badly scaled function, f(x) = (x₁ - 10^6)² + (x₂ − 2 × 10^-6)² + (x₁x₂ - 2)², can be found using Powell's method.
Powell's method is an optimization algorithm used to find the minimum of a function. It is an iterative method that searches for the minimum by successively approximating the direction of the minimum along each coordinate axis.
To apply Powell's method to find the minimum of Brown's badly scaled function, we start with an initial guess for the minimum point. Then, we iteratively update the guess by evaluating the function at different points and adjusting the guess based on the obtained results.
The iterative process continues until a convergence criterion is met, indicating that the minimum has been sufficiently approximated. The final guess represents the minimum point of the function.
By applying Powell's method to Brown's badly scaled function, we can determine the coordinates of the minimum point, which correspond to the values of x₁ and x₂ that minimize the function. The specific values of x₁ and x₂ will depend on the initial guess and the convergence criteria used in the optimization process.
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The
ratio of votes in favor to votes against in an election is 5 to 4.
How many total votes were cast if there are 2,620 votes in
favor?
Total votes were casted in election are 4716
Given: The ratio of votes in favor to votes against in an election is 5 to 4. 2,620 votes are in favor.
To find: The total number of votes cast.
Let the number of votes against is 4x.
Given the ratio of votes in favor to votes against is 5 : 4
Then, the number of votes in favor is 5x.
According to the question, 2,620 votes are in favor.
So, 5x = 2,620x = 2,620/5x = 524
The number of votes against = 4x = 4 × 524 = 2096
The total number of votes cast = votes in favor + votes against= 2620 + 2096= 4716
Therefore, there were 4716 votes cast in the
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A polygon has the following coordinates: A(-5,2), B(-2,-2), C(2,3), D(6,3), E(6,-5), F(-5,-5). Find the length of EF.
A.
12 units
B.
9 units
C.
11 units
D.
10 units
Answer:
C
Step-by-step explanation:
got it right on edg
Please just give me the answer
9514 1404 393
Answer:
8
Step-by-step explanation:
The Pythagorean theorem tells you of the relation ...
x² + 6² = 10² . . . . . . . . . squares of sides total to the square of hypotenuse
x² = 100 -36 = 64 . . . . . subtract 6²
x = √64 = 8 . . . . . . . . . . square root
The length of side x is 8 units.
The manager of the City of Industry Electronics store is concerned that his supplier has been giving him TV sets with lower than average quality. His research shows that replacement times for TV sets have a mean of 7.5 years and a standard deviation of 5 years. He then randomly selects 64 TV sets sold in the past and found that the mean replacement time is 6 years. Determine the probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or less. Find the z score (round to two decimals) QUESTIONS 2b. What do you get from Table A? QUESTION 6 20. Determine the probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or loss. (round to a percent with two decimals)
The probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or less is approximately 0.0048, or 0.48%.
To calculate this probability, we need to standardize the sample mean using the z-score formula and then find the corresponding probability from the standard normal distribution.
The formula for the z-score is:
z = (x - μ) / (σ / √n)
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, x = 6, μ = 7.5, σ = 5, and n = 64. Substituting these values into the formula, we get:
z = (6 - 7.5) / (5 / √64)
Simplifying the expression:
z = -1.5 / (5 / 8)
z = -1.5 * 8 / 5
z = -2.4
From Table A (standard normal distribution table), the area to the left of z = -2.4 is approximately 0.0082.
However, since we are interested in the probability of obtaining a mean replacement time of 6 years or less, we need to find the area to the right of z = -2.4. This is given by:
1 - 0.0082 = 0.9918
Therefore, the probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or less is approximately 0.0048, or 0.48%.
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Find the diagonalization of A by finding an invertible matrix P and a diagonal matrix D such that PAP= D.
To diagonalize a matrix A, we need to find an invertible matrix P and a diagonal matrix D such that PAP^(-1) = D. Here's how to find the diagonalization of matrix A
1. Find the eigenvalues of A:
- Calculate the characteristic polynomial by subtracting λI from A, where λ is a scalar variable and I is the identity matrix of the same size as A.
- Set the characteristic polynomial equal to zero and solve for λ to find the eigenvalues.
2. Find the eigenvectors corresponding to each eigenvalue:
- For each eigenvalue, substitute it back into the equation (A - λI)x = 0, where x is a vector, and solve for x.
- Repeat this step for each eigenvalue to obtain a set of linearly independent eigenvectors.
3. Construct the matrix P:
- Arrange the eigenvectors found in Step 2 as columns to form the matrix P.
4. Construct the diagonal matrix D:
- Place the eigenvalues obtained in Step 1 on the diagonal of a matrix of the same size as A, with zeros elsewhere.
5. Verify the diagonalization:
- Calculate PAP^(-1) and check if it equals D. If PAP^(-1) = D, then A is diagonalizable.
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Find the absolute maximum and minimum of f (x, y) = x^2 + 2y^2 − 2x − 4y +1 on D = {(x, y) 0 ≤ x ≤ 2, 0 ≤ y ≤ 3} .
Absolute maximum of f (x, y) = 19 and Absolute minimum of f (x, y) = −3.
To find the absolute maximum and minimum of f (x, y) = x² + 2y² − 2x − 4y + 1 on D = {(x, y) 0 ≤ x ≤ 2, 0 ≤ y ≤ 3}, we need to follow these steps:Step 1: We need to find the critical points of f (x, y) in the interior of D. Step 2: We then need to evaluate f (x, y) at the critical points. Step 3: We need to find the maximum and minimum of f (x, y) on the boundary of D. Step 4: Compare the values obtained in steps 2 and 3 to get the absolute maximum and minimum values of f (x, y) on D.1. To find the critical points of f (x, y) in the interior of D, we need to find the partial derivatives of f (x, y) with respect to x and y respectively, and solve the resulting system of equations for x and y:fx = 2x − 2fy = 4y − 4Solving for x and y, we obtain (1, 1) as the only critical point in the interior of D.2. To evaluate f (x, y) at the critical point (1, 1), we substitute x = 1 and y = 1 into f (x, y) to get:f (1, 1) = (1)² + 2(1)² − 2(1) − 4(1) + 1 = −3.3. To find the maximum and minimum of f (x, y) on the boundary of D, we use the method of Lagrange multipliers. We set up the equations:g(x, y) = x² + 2y² − 2x − 4y + 1 = k1h1(x, y) = x − 0 = 0h2(x, y) = 2 − x = 0h3(x, y) = y − 0 = 0h4(x, y) = 3 − y = 0Solving for x and y, we obtain the critical points on the boundary of D: (0, 0), (0, 3), (2, 0), and (2, 3).4. Comparing the values obtained in steps 2 and 3, we have the following:f (1, 1) = −3f (0, 0) = 1f (0, 3) = 19f (2, 0) = −3f (2, 3) = 13The absolute maximum of f (x, y) on D is 19 at (0, 3), while the absolute minimum is −3 at (2, 0). Therefore, we have:Absolute maximum of f (x, y) = 19 and Absolute minimum of f (x, y) = −3.
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Populations of aphids and ladybugs are modeled by the equations dA = 2A 0.01AL dt dL = -0.5L + 0.0001AL. dt (a) Find an expression for dL/dA. dL dA 0.5L + 0.0001AL 2A – 0.01AL
The expression for dL/dA, which represents the rate of change of ladybugs (L) with respect to aphids (A), is 0.5L + 0.0001AL - 2A + 0.01AL.
To find the expression for dL/dA, we need to differentiate the equation dL/dt with respect to A. The given equations are:
dA/dt = 2A - 0.01AL
dL/dt = -0.5L + 0.0001AL
To find dL/dA, we differentiate dL/dt with respect to A:
dL/dA = (dL/dt) / (dA/dt)
Substituting the given equations into this expression, we have:
dL/dA = (-0.5L + 0.0001AL) / (2A - 0.01AL)
Simplifying further, we can rearrange the terms:
dL/dA = -0.5L / (2A - 0.01AL) + 0.0001AL / (2A - 0.01AL)
Combining the terms with a common denominator, we get:
dL/dA = (0.0001AL - 0.5L) / (2A - 0.01AL)
So, the expression for dL/dA is (0.0001AL - 0.5L) / (2A - 0.01AL), which represents the rate of change of ladybugs with respect to aphids in the given model.
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Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,800 per month for twenty years. She must deposit $218,437.048 and the total amount that Holly will receive from her payout annuity will be $432,000.
A. How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity, which she sets up thirty years before her retirement?
B. how large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement?
A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.
B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.
What is the monthly payment required for an ordinary annuity set up 30 years before retirement?To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.
How much must be paid monthly for an ordinary annuity set up 20 years before retirement?For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.
It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.
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Diane has $334 in her checking account. She writes a check for $112, makes a deposit of $100, and then writes another check for $98. Find the amount left in her account.
Select one:
a. $444
b. $214
c. $224
d. $86
Answer:
334 - 112 + 100 - 98
Step-by-step explanation:
Please answer if your know
Answer:
52 pounds
Step-by-step explanation:
52 pounds
Find mZR
R
120°
140°
S
Need help with this question?
Answer:
[tex] m\angle R = 50 \degree[/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle R = \frac{1}{2} [360 \degree - (120 \degree + 140 \degree)] \\ \\ m\angle R = \frac{1}{2} [360 \degree -260 \degree] \\ \\ m\angle R = \frac{1}{2} \times 100 \degree \\ \\ m\angle R = 50 \degree \\ \\ [/tex]
The sixth grade art students are making a mosaic using tiles in the shape of triangles.Each tile Hans leg measures of 7cm and 4cm. If there are 84 tiles in the mosaic,what I sent the area of the mosaic
Answer:
1,176 square centimeters
Step-by-step explanation:
The computation of the area of the mosaic is shown below:
As we know that
The Area of the triangle is
= 1 ÷ 2 × base × height
= 1 ÷ 2 × 7 × 4
= 14
Now 1 tile would be 14 square centimeters
And, there are 84 tiles in the mosaic
So, the total area is
= 84 × 14
= 1,176 square centimeters
At a particular restaurant, each mini hotdog has 100 calories and each slider has 200 calories. A combination meal with mini hotdogs and sliders is shown to have 1200 total calories and 4 times as many mini hotdogs as there are sliders. Graphically solve a system of equations in order to determine the number of mini hotdogs in the combination meal, x,x, and the number of sliders in the combination meal, yy.
Answer:
The number of sliders is 2 and the number of hot dogs is 8.
Step-by-step explanation:
Since at a particular restaurant, each mini hotdog has 100 calories and each slider has 200 calories, and a combination meal with mini hotdogs and sliders is shown to have 1200 total calories and 4 times as many mini hotdogs as there are sliders, in order to determine the number of mini hotdogs in the combination meal, X, and the number of sliders in the combination meal, Y, the following calculation must be performed:
2X + Y = 1200
800 + 400 = 1200
800/100 = 8
400/200 = 2
Thus, the number of sliders is 2 and the number of hot dogs is 8.
I’m not sure how to do this someone explain please
Pictures listed in order... from A-C
solve the system of differential equations. = 2x 3y 1 = -x - 2y 4
The given system of differential equations is:
dx/dt = 2x + 3y
dy/dt = -x - 2y + 4
To solve this system, we can use various methods such as substitution, elimination, or matrix methods. Let's use the matrix method.
First, we can rewrite the system in matrix form:
d/dt [x y] = [2 3] [x] + [1]
[-1 -2] [y] + [4]
Next, we define A as the coefficient matrix [2 3; -1 -2], X as the column matrix [x; y], and B as the column matrix [1; 4]. The system can now be written as:
dX/dt = AX + B
To find the solution, we can calculate the eigenvalues and eigenvectors of matrix A. From the eigenvalues, we determine the corresponding eigenvectors and use them to construct the general solution. However, without the specific values of matrix A, it is not possible to provide the exact solution.
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6. Brandon and Charlotte Snifflesworth are visiting three of Americas top tourist attractions. The Snifflesworths
live close to Disney World in Orlando, Florida. They decided to start their trip at Disney World before traveling to
San Francisco, California to see the Golden Gate Bridge and then to Minneapolis, Minnesota to go shopping at the
Mall of America. The bearing from Disney to the Golden Gate Bridge is North 65° West. The bearing from the
Golden Gate Bridge to the Mall of America is North 80° East. The bearing from Disney to the Mall of America is
North 30° West and the distance traveled is 1,320 miles. Find all missing interior angles and distances created from
their triangular trip to America's top tourist attractions. Also find the bearing from the Mall of America to
Disneyland.
Answer:
The distance from Disney to the Golden Gate Bridge is 2,162.56 miles
The distance from Mall of America to The Golden Gate Bridge is 1,320 miles
The interior angle at The Golden Gate Bridge is 35°
The interior angle at Mall of America is 110°
The interior angle at Disney is 35°
The direction from Mall of America to Disney is South 30° East
Step-by-step explanation:
The bearing from Disney to the Golden Gate Bridge = North 65° West
The bearing from the Golden Gate Bridge to the Mall of America = North 80° East
The bearing from Disney to the Mall of America = North 30° West
The distance from Disney to the Mall of America = 1,320 miles
Let 'A', 'B', and 'C' represent the interior angles at Disney, The Golden Gate bridge and Mall of America respectively
From the drawing of the triangular trip, we find that the interior angle at C = The sum angles complementary to the bearings at B and at C
Therefore, the interior angle at C = (90° - 65°) + (90° - 80°) = 35°
The interior angle at B = The bearing of C from B - The bearing of A from B
∴ The interior angle at B = 65° - 30° = 35°
B = 35°
∠C = 35° and ∠B = 35°, therefore, the triangle is an isosceles triangle
The interior angle at A = 180° - (∠B + ∠A) = 180° - (35° + 35°) =110°
CA = AB = 1.320
By sine rule, a = sin(110) × 1320/sin(35) ≈ 2,162.56 miles
a = CB = 2,162.56 miles
Therefore, we have;
The distance from Disney to the Golden Gate Bridge = 2,162.56 miles
The distance from Mall of America to The Golden Gate Bridge = 1,320 miles
The interior angle at The Golden Gate Bridge = 35°
The interior angle at Mall of America = 110°
The interior angle at Disney = 35°
The magnitude of the bearing of Mall of America to Disney = The magnitude of the alternate angle to the bearing of Disney to Mall of America = 30°
∴ The direction from Mall of America to Disney = South 30° East
Tell whether the ordered pair is of liner equations (5,-6) 6x+3y=12 4x+y=14
Answer:
The ordered pair is one of the solution to the system of equations. See below.
Step-by-step explanation:
To tell if the ordered pair is the solution to the system of equations or not, we can do by substituting the ordered pair in both equations.
(x, y) = (5,-6)
Substitute x = 5 and y = -6 in both equations.
First Equation
6x+3y=12
6(5)+3(-6)=12
30-18=12
12=12
Second Equation
4x+y=14
4(5)-6=14
20-6=14
14=14
Because both equations have same sides which mean that both equations are true for (5,-6). Therefore (5,-6) is part of the equations.
Will mark brainliest !!!
Answer:
27
Step-by-step explanation:
Length * width * height to find the volume so it is 3*3*3=27
how do you determine if a relation is a function
Answer:
Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
Step-by-step explanation:
QUICK! Giving Brainliest to whoever gives the correct answer
Answer:
taco bell
Step-by-step explanation:
per one taco at taco bell $0.53
per one taco at los comales $0.62
A cylinder containing water is fitted with a piston restrained by an external force that is proportional to cylinder volume squared (P = cvc is constant). Initial conditions are 120°C, 90% quality and a volume of 200 L. A valve on the cylinder is opened and additional water flows into the cylinder until the mass inside has doubled. If at this point the pressure is 300 kPa. What is the final temperature, show your solution
The final temperature of the cylinder is -148.68 °C .
To find the final temperature
Let the final temperature be T₂.
Let the final volume be V₂.
The mass of water inside the cylinder at initial conditions, m₁ = ρV₁
On opening the valve, the water enters the cylinder until the mass doubles. So the mass of water inside the cylinder after the valve is opened, m₂ = 2ρV₁
The pressure and mass are related by the equation, PV = mRT
On simplifying the equation we get,
P = (m/ρ) * RTSo Pρ = mRT ………… (1)
From equation (1),
P₁ρ₁ = m₁R T₁
Substituting the values in equation (1) for final conditions,
P₂ρ = m₂R T₂
We need to find T₂
So, T₂ = (P₂ρ/m₂) * R = (300000 N/m² * 1000 kg/m³)/[2 * 1000 kg] * 8.314 J/(mol K)
= 124.47 K or -148.68 °C
So, -148.68 °C is the final temperature approximately.
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Will mark brainliest for the **CORRECT** answer!
Answer:
4x + 12x = 320
16x = 320
x = 20
Step-by-step explanation:
This is because the diagram shows 4x + 12x and the total being, 320.
4x + 12x = 16x
and 320/16 = 20
so x = 20
hope this helped :)
HW: using trigonometric identities, show that the solution of the damped forced oscilla from can be written as: (24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2 Hint: ure the identifies for addition and Substraction of angles.
Hence, the required equation is `(24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2`.
Given damped forced oscillation equation is,`m d²x/dt² + c dx/dt + kx = Fo sin(wt)`Using trigonometric identities, we can write solution for the given damped forced oscillation equation as,X(t) = Acos(wt + Φ) + Xpwhere Xp = (Fo/k) sin(wt - δ)Let's substitute X(t) in the given equation to get the required equation.```
X(t) = Acos(wt + Φ) + Xp
=> dX(t)/dt = -Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)
=> d²X(t)/dt² = -Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)
```Now, substitute these values in the given damped forced oscillation equation.`md²X(t)/dt² + cdX(t)/dt + kX(t) = Fo sin(wt)`⇒ `m(-Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)) + c(-Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)) + k(Acos(wt + Φ) + (Fo/k)sin(wt - δ)) = Fo sin(wt)`Grouping the terms of sines and cosines, we get⇒ `{-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + (Fo/k)w²sin(δ) + kAcos(wt + Φ) + (Fo/k)wcos(δ)} = Fo sin(wt) - c(Fo/k)wcos(wt - δ)`Let's solve these equations for `δ` and `A`.```
-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + kAcos(wt + Φ) = 0 .....................(1)
(Fo/k)w²sin(δ) + (Fo/k)wcos(δ) = Fo sin(wt) - c(Fo/k)wcos(wt - δ) .....(2)
```Squaring and adding both equations, we get,`(Aw)²m + kA² = (Fo/k)²`or `A = Fo/(k² - mω²)^(1/2)`From equation (1), we have,`(Aw)²m + kA² = 0`or `δ = tan⁻¹(Aw/k)`Substitute values of A and δ in equation (2), we get,`Xp = (Fo/k) sin(wt - δ) = Fo/(k² - mω²)^(1/2) sin(wt - tan⁻¹(Aw/k))`Therefore, solution for the given damped forced oscillation equation is,`X(t) = Acos(wt + Φ) + Xp`= `12 Fo/m Sin (wo-w)t sin (wotw)t / (wo² - w²)²`
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You are charged $16. 05 after tax for a meal. Assume sales tax is 7%, what was the menu price for the meal
Answer:
$15
Step-by-step explanation:
107% is the price of $16.05
so, 107% = $16.05
Divide both sides by 107:
1% = $0.15
Multiply both sides by 100:
100% = $15.00
A submarine began at sea level and descended toward the ocean floor at a rate of −0.015 km per minute. Its final depth was −0.3675 km. Estimate how long it took the submarine to reach its final depth by rounding the dividend and divisor to the nearest hundredth.
Estimate of the quotient:
Answer:
Around 24.5 minutes
Step-by-step explanation:
Answer:
Estimate of the dividend: -0.37
Estimate of the divisor: -0.02
Estimate of the quotient: 18.5
Step-by-step explanation:
I did the test and it was right and I dubble checked it to
5 x 100 = ? for easy points
Answer:
500! Just multiply 5 x 1 then add the remaining 2 zeros :)
Step-by-step explanation:
Thank you!
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
[tex]5 \times 100 \\ = 500[/tex]
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Given the following function, find the integral s voix by substitution : integral 3 (x-2 ] 3 +4 dx by substitution sinhy=3(x-2)
The simplified expression of integral 3 (x-2 ] 3 +4 dx is (A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B
How to find the integral ∫3(x-2)³+4 dx using the substitution sinh(y) = 3(x-2)?To find the integral ∫3(x-2)³+4 dx using the substitution sinh(y) = 3(x-2), we can start by differentiating both sides of the equation with respect to x to find the differential of y:
d(sinh(y))/dx = d(3(x-2))/dx
cosh(y) * dy/dx = 3
dy/dx = 3/cosh(y)
Now, let's solve for dx in terms of dy:
dx = (cosh(y)/3) dy
Substituting this value of dx in the integral:
∫3(x-2)³+4 dx = ∫(3/cosh(y)) * (3(x-2)³+4) dy
Now, we need to substitute the expression for x in terms of y using the given substitution:
3(x-2) = sinh(y)
x - 2 = sinh(y)/3
x = sinh(y)/3 + 2
Substituting this in the integral:
∫(3/cosh(y)) * (3((sinh(y)/3 + 2) - 2)³+4) dy
Simplifying:
∫(3/cosh(y)) * (sinh(y)³+4) dy
To integrate the expression ∫(3/cosh(y)) * (sinh(y)³+4) dy, we can simplify it first:
∫(3/cosh(y)) * (sinh(y)³+4) dy = 3∫(sinh(y)³/cosh(y)) dy + 12∫(1/cosh(y)) dy
To integrate the first term, we can use the substitution u = cosh(y), which implies du = sinh(y) dy:
3∫(sinh(y)³/cosh(y)) dy = 3∫(u³/u) du = 3∫(u²) du = u³/3 + C
For the second term, we can directly integrate 1/cosh(y) using the identity sech²(y) = 1/cosh²(y):
12∫(1/cosh(y)) dy = 12∫sech²(y) dy = 12tanh(y) + D
Now, substituting back y = [tex]sinh^{(-1)}(3(x-2))[/tex]:
u = cosh(y) = cosh[tex](sinh^{(-1)}(3(x-2))[/tex]) = √(3(x-2)² + 1)
Thus, the integral becomes:
∫(3/cosh(y)) * (sinh(y)³+4) dy = (u³/3 + C) + 12tanh(y) + D
Substituting back u = √(3(x-2)² + 1):
= (√(3(x-2)² + 1)³/3 + C) + 12tanh(y) + D
= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh(y) + D
= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh[tex](sinh^{(-1)}(3(x-2)))[/tex] + D
To simplify the expression and combine constants, let's assume (√(3(x-2)² + 1)³ + 3C)/3 = A, and 12D = B.
The simplified expression becomes:
(A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B
Since [tex]sinh^{(-1)}(3(x-2))[/tex] is the inverse hyperbolic sine function, we can simplify it using the identity sinh[tex](sinh^{(-1)}(x))[/tex] = x:
(A/3) + 12tanh(3(x-2)) + B
This is the simplified form of the integral ∫(3/cosh(y)) * (sinh(y)³+4) dy after combining constants and simplifying the expression.
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If y varies inversely with x, and y= 12 when x = 16, what is the constant of variation k?
Answer:
k = 192
Step-by-step explanation:
Given that,
y varies inversely with x. It can be written as :
[tex]y=\dfrac{k}{x}[/tex]
Where
k is the constant of variation
Put x = 16 and y = 12 in the above formula.
[tex]k=yx\\\\k=16\times 12\\\\k=192[/tex]
So, the value of the constant of variation is equal to 192.
You know this??????????????
Answer:
y=x+15
Step-by-step explanation:
help me find the surface area!
Answer:
62
Step-by-step explanation:
find the area of each side
(3 * 5) + (2 * 3) + (2 * 5) + (2 * 5) + (2 * 3) + (3 * 5)
add them all
15 + 6 + 10 + 10 + 6 + 15 = 62