can someone plz help me plz plz

The solution is the zero function for all values of x and t.

To solve the heat equation u_t = 60u_xx with the given boundary and initial conditions, we can use separation of variables. We assume that u(x, t) can be written as a product of two functions, X(x) and T(t), such that u(x, t) = X(x)T(t).

Substituting this into the heat equation, we have:

X(x)T'(t) = 60X''(x)T(t)

Dividing both sides by 60X(x)T(t), we get:

T'(t)/T(t) = 60X''(x)/X(x)

The left side of the equation only depends on t, while the right side only depends on x. Since both sides are equal to a constant, we can set them equal to -λ², where λ is the constant.

T'(t)/T(t) = -λ²

X''(x)/X(x) = -λ²

Now, let's solve these two equations separately:

T'(t)/T(t) = -λ²

This is a separable ordinary differential equation. Integrating both sides with respect to t, we get:

∫ T'(t)/T(t) dt = ∫ -λ² dt

ln|T(t)| = -λ²t + C₁

Taking the exponential of both sides, we have:

T(t) = e^(-λ²t + C₁)

T(t) = e^(C₁) * e^(-λ²t)

T(t) = A * e^(-λ²t), where A = e^(C₁)

Now, let's solve the second equation:

X''(x)/X(x) = -λ²

This is also a separable ordinary differential equation. Integrating both sides with respect to x, we get:

∫ X''(x)/X(x) dx = ∫ -λ² dx

∫ (X''(x)/X(x)) dx = -λ²x + C₂

Using the fact that X''(x) = d²X(x)/dx², we can rewrite the equation as:

∫ (d²X(x)/dx²)/X(x) dx = -λ²x + C₂

∫ (d²X(x)/dx²) / X(x) dx = ∫ -λ² dx

∫ (1/X(x)) d²X(x)/dx² dx = -λ²x + C₂

Integrating both sides again, we have:

ln|X(x)| = -λ²x + C₂x + C₃

Taking the exponential of both sides, we get:

X(x) = e^(-λ²x + C₂x + C₃)

X(x) = e^(-λ²x) * e^(C₂x) * e^(C₃)

X(x) = B * e^(-λ²x) * e^(C₂x), where B = e^(C₃) * e^(C₂x)

Putting the solutions for T(t) and X(x) together, we have:

u(x, t) = X(x)T(t)

u(x, t) = (B * e^(-λ²x) * e^(C₂x)) * (A * e^(-λ²t))

We can combine the constants A and B into a single constant C:

u(x, t) = C * e^(-λ²x) * e^(C₂x) * e^(-λ²t)

Applying the boundary condition u(0, t) = 0, we have:

u(0, t) = C * e^(-λ²0) * e^(C₂0) * e^(-λ²t) = 0

This implies that C * e^(-λ²t) = 0. Since e^(-λ²t) is never zero, we must have C = 0.

Therefore, the solution to the heat equation with the given boundary and initial conditions is: u(x, t) = 0

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Answer:

Convert the decimal to a percentage by multiplying the decimal by  

100 .

500%

700%

900%

400%

Answer:

Yes it is possible. Start at (0,0) which is the orgin and go right on the x-axis 3 spaces, and go up on the y-axis 7 spaces to get to the ordered pair of (3,7).

Step-by-step explanation:

Answer:

t < 7

Step-by-step explanation:

52 > 5t + 17

52 - 17 > 5t

35 > 5t

35/5 > t

t < 7

Answer:

I would need to see the attached lesson to answer this question.

Answer:

A. x = -2, x = 1.25

Step-by-step explanation:

Use the quadratic formula

x = [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

4x² + 3x - 10 = 0

a = 4

b = 3

c = - 10

x = [tex]\frac{-3+\sqrt{3^{2}-4x4(-10) } }{2x4}[/tex]

Simplify

Evaluate the exponent

x = [tex]\frac{-3+\sqrt{9-4x4(-10)} }{2x4}[/tex]

Multiply the numbers

x = [tex]\frac{-3+\sqrt{9+160} }{2x4}[/tex]

Add the numbers

x = [tex]\frac{-3+\sqrt{169} }{2x4}[/tex]

Evaluate the square root

x = [tex]\frac{-3+13}{2x4}[/tex]

Multiply the numbers

x = [tex]\frac{-3+13}{8}[/tex]

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = [tex]\frac{-3+13}{8}[/tex]

x = [tex]\frac{-3-13}{8}[/tex]

Solve

Rearrange and isolate the variable to find each solution

x = - 2

x = 1.25

Answer:

A. x = -2, x = 1.25

Step-by-step explanation:

Use the sum-product pattern

4x² + 3x - 10 = 0

4x² + 8x - 5x - 10 = 0

Common factor from the two pairs

(4x² + 8x) + (-5x - 10) = 0

4x (x + 2) - 5 (x + 2) = 0

Rewrite in factored form

4x (x + 2) - 5 (x + 2) = 0

(4x - 5)(x + 2) = 0

Create separate equations

(4x - 5)(x + 2) = 0

4x - 5 = 0

x + 2 = 0

Solve

Rearrange and isolate the variable to find each solution

x = 1.25

x = - 2

1000 meters are there in a kilometer.

Answer:

Answer is NOT 126 CORRECT answer is 628

Step-by-step explanation

First you divide 40 by 2 which equals 20 . Then you do pi which equals 3.14 and you multiply it by 20^(2) which equals 1256 . After that you take 1256 and divide it by 2 which equals 628 .

Answer:

1st, 3rd, and 4th box.

Step-by-step explanation:

9^5=59049

9^2=81   9^3=729    729*81=59049              yes

9^5=59049   59049x9=531441                     no

9^4=6561    6561*9=59049                           yes

9^2=81      81x81=6561     6561*9=59049     yes

9^3=729   729x729=531441                          no

Answer:

The answer is the third one or (9^(4) (9)  

Step-by-step explanation:

Answer:

(3,-1)

Step-by-step explanation:

The given equations are :

x = 3 ..(1)

y+1 = 0 ....(2)

We need to solve the equations graphically. x = 3 means draw a line parallel to y axis.

For y+1=0

y = -1

Draw a line parallel to the negative x axis. The attached figure shows the graph for the given equations. The solution is (3,-1).

Answer:

I think the answer is 54.2, but it may not be correct.

Step-by-step explanation:

To find the mean of something, you're supposed to find the sum of all the numbers and the divide it by how many numbers are in the set. Hope this helped!

The equations of values of x and y =0 that will maximize the revenue.

The marginal revenue equations, to calculate the partial derivatives of the revenue function with respect to each variable, x and y.

Given the revenue function:

t(x, y) = 110x + 180y + 3x² - 4y² - xy

The marginal revenue with respect to x, rx(x, y), the partial derivative of t(x, y) with respect to x, while treating y as a constant:

rx(x, y) = ∂t/∂x = 110 + 6x - y

Similarly, the marginal revenue with respect to y, ry(x, y),the partial derivative of t(x, y) with respect to y, while treating x as a constant:

ry(x, y) = ∂t/∂y = 180 - 8y - x

The production levels that will maximize revenue, both marginal revenue equations equal to zero and solve as a system of equations.

Setting rx(x, y) = 0:

110 + 6x - y = 0

Setting ry(x, y) = 0:

180 - 8y - x = 0

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Answer:  -7

Step-by-step explanation:

In order to find rate of change, we use two points (0,70) and (3,49).

rate of change = (y2 - y1)/ (x2 - x1)

                         = (49 - 70) / (3 - 0)

                         = -21/3

                         = -7

Answer:

hi

Step-by-step explanation:

hi

Answer:

..

Step-by-step explanation:

First, you need to make sure that you know a few things.

1. A line is 180 degrees

2. Angles with the small boxes on them are right angles.

3. Angles that are across from each other are the same amount of degrees...

For example, look at angle 2, you can see that directly across from it is the angle 35 degrees, this makes angle 2 35 degrees as well.

In order to find angle 1, you need to subtract 35 from 180, to see how much is needed to fill the line, in this case it is 145.

So, angle 1 is 145 degrees, and angle two is 35.

One more thing, angles 1 and 7 are the same and so are 2 and 6 because they are on the same line, I can't remember why, but they are.

Answer:

1/4 or 25%

Step-by-step explanation:

Out of 12 students, 3 liked Hamlet 3/12 is 1/4 simio lidies and 1/4 can be 25%

Answer:

1/4 would be the answer

Step-by-step explanation:

There are 12 total students in the class, and 3 of them liked Hamlet best. So the chances of randomly picking a Shakespeare student that likes Hamlet best is 3/12. If we simplify this answer, we would get 1/4.

Answer:

F=45

Step-by-step explanation:

G is 90 degrees and FC angles combined is 90 and divided is 45 each

To predict a linear regression score, you first need to train a linear regression model using a set of training data.

Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,

A higher regression score indicates a better fit, while a lower score indicates a poorer fit.

To predict a linear regression score, follow these steps:

1. Gather your data: Collect the data p

points (x, y) for the variable you want to predict (y) based on the input variable (x).

2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).

3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)]  Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.

4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.

5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.

6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging in the x value into the equation. The resulting y value is your predicted linear regression score.

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Answer:

145

Step-by-step explanation:

Answer:

19 + 13 = 32 x 10 = 320 divided by 2 = 160yd2

Formula of a trapezoid:

B1 (base 1) + B2 (base2) x Height x 1/2 (basically dividing by 2).

Base 1 was 19

Base 2 was 13

and 10 was your height

And then divide by 2. ( x 1/2)

Answer:

c,h is a 90 degree angle and so is a,k,c

a,k,c is half of the 12cm

so the answer is c,h is 6cm

Step-by-step explanation:

Answer:

CH = 6

BAH = 96

Step-by-step explanation:

BC = 12, so BK = 6, and ABK = ACH, so BK = CH = 6

BAK = 32, KAC = 32, CAH = 32

BAK + KAC + CAH = BAH = 96

Evaluating this expression will give us the value of f(3).

To find the value of f(3), we need to integrate the second derivative of f(x) twice and use the given initial conditions to determine the constants of integration.

Step 1: Integrate the second derivative f''(x) with respect to x to find the first derivative f'(x):

∫(f''(x)) dx = ∫(9x + 5sin(x)) dx

f'(x) = (9/2)x^2 - 5cos(x) + C1

Step 2: Use the given initial condition f'(0) = 2 to find the constant C1:

f'(0) = (9/2)(0)^2 - 5cos(0) + C1

2 = 0 - 5 + C1

C1 = 7

Step 3: Integrate f'(x) with respect to x to find the function f(x):

∫(f'(x)) dx = ∫[(9/2)x^2 - 5cos(x) + 7] dx

f(x) = (9/6)x^3 - 5sin(x) + 7x + C2

Step 4: Use the given initial condition f(0) = 3 to find the constant C2:

f(0) = (9/6)(0)^3 - 5sin(0) + 7(0) + C2

3 = 0 - 0 + 0 + C2

C2 = 3

Now we have the function f(x):

f(x) = (9/6)x^3 - 5sin(x) + 7x + 3

To find f(3), substitute x = 3 into the function:

f(3) = (9/6)(3)^3 - 5sin(3) + 7(3) + 3

Therefore, Evaluating this expression will give us the value of f(3).

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0 -18 is the answer to your question

The collected information is:

a) 1. House_ID and 2. Neighborhood: Categorical (Nominal) 3. Mail_Zip: Categorical (Ordinal) 4. Acres, 5. Yr_Built, 6. Full_Market_Value, 7. SFLA: Quantitative (Continuous)

b) House_ID: Categorical and nominal, serves as an identifier variable.

c) Neighborhood: Categorical and nominal, represents different neighborhood categories.

a) For each variable:

1. House_ID: Categorical and nominal. House_ID is a unique identifier for each house, and there is no inherent order to the values.

2. Neighborhood: Categorical and nominal. Neighborhood is a categorical variable that can be divided into different categories, such as "Greenfield Manor", "Dublin", and "Arcady". There is no inherent order to the values.

3. Mail_Zip: Categorical and ordinal. Mail_Zip is a categorical variable that can be divided into different categories, such as "12859", "12801", and "12309". The values are ordered in ascending order, with 12859 being the smallest value and 12309 being the largest value.

4. Acres: Quantitative and continuous. Acres is a quantitative variable that can take on any value between 0 and infinity. The units of measurement are acres.

5. Yr_Built: Quantitative and discrete. Yr_Built is a quantitative variable that can take on any value between 1955 and 1997. The units of measurement are years.

6. Full_Market_Value: Quantitative and continuous. Full_Market_Value is a quantitative variable that can take on any value between $67,100 and $190,000. The units of measurement are dollars.

7. SFLA: Quantitative and continuous. SFLA is a quantitative variable that can take on any value between 900 and 1620 square feet. The units of measurement are square feet.

b) Describe the variable House_ID. Choose the correct answer below.

A. The variable House_ID is categorical and ordinal. Incorrect

B. The variable House_ID is categorical and nominal. Correct

C. The variable House_ID is an identifier variable. Correct

D. The variable House_ID is quantitative, with units house number. Incorrect

c) Describe the variable Neighborhood. Choose the correct answer below.

A. The variable Neighborhood is categorical and ordinal. Incorrect

B. The variable Neighborhood is quantitative, with units neighborhood name. Incorrect

C. The variable Neighborhood is categorical and nominal. Correct

D. The variable Neighborhood is quantitative, with units number of neighborhoods. Incorrect

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Answer:

x, y) → (1.5x, 1.5y)

Step-by-step explanation:

Answer:

10,603 cu in

Step-by-step explanation:

For a pipe use its length instead of height: pipe volume = π * radius² * length , where radius = inner diameter/2 . The volume of a pipe is equal to the volume of a liquid inside.

Therefore,

radius = 1 inch ÷ 17 = 5 inch

length = 15 × 5 inches = 75 inches

volume = π (pi) × radius squared × length

volume = 15× (.5 x .5) × 75

volume = 15 × 5 × 2

volume = 10,603 in³

The volume of fluid in a pipe can be found given the inner diameter of the pipe and the length. To estimate pipe volume, use the following formula:

volume = π ×  

d2

4

× h

Thus, the volume of a pipe is equal to pi times the pipe diameter d squared over 4, times the length of the pipe h.

This formula is derived from the cylinder volume formula, which can also be used if you know the radius of the pipe.

volume = π × r2 × h

Answer:

[tex]178.98\ \text{m}^2[/tex]

Step-by-step explanation:

d = Diameter of flower bed = 16 m

Thickness of sidewalk = 3 m

r = Radius of flower bed = [tex]\dfrac{d}{2}=\dfrac{16}{2}=8\ \text{m}[/tex]

R = Radius of flower bed with sidewalk = [tex]8+3=11\ \text{m}[/tex]

The required area is given by

[tex]A=\pi(R^2-r^2)\\\Rightarrow A=3.14\times (11^2-8^2)\\\Rightarrow A=178.98\ \text{m}^2[/tex]

The radius of the sidewalk is [tex]178.98\ \text{m}^2[/tex].

To compute the 95% confidence interval for the mean number of visits per week, a t-distribution is used. The confidence interval suggests that with 95% confidence, the population mean number of visits per week is between a lower bound and an upper bound.

(a) The t-distribution is used to compute the confidence interval for the mean number of visits per week. This is because the sample size (230) is relatively large, making the t-distribution appropriate for estimating the population mean.

(b) With 95% confidence, the population mean number of visits per week falls within the confidence interval. To calculate the interval, the sample mean (3.5) and the standard deviation (2.7) are used. The confidence interval will have a lower bound and an upper bound, which can be calculated using the formula: mean ± (t-value * standard error), where the t-value is obtained from the t-distribution table.

(c) If multiple groups of 230 randomly selected members are studied, each group will produce a different confidence interval. Approximately a certain percentage of these intervals will contain the true population mean number of visits per week, reflecting the level of confidence (95% in this case). The remaining percentage of intervals will not contain the true population mean. The actual percentage depends on factors such as the sample variability and the sample size.

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Answer:

The closest measurement is 69 meters.

Step-by-step explanation:

We already know that 22 meters is the diameter and to find the circumference you need to multiply the diameter with π. We don't know π, so we are going with 3.14. When you multiply 22 and 3.14 together, you get 69.08 meters. You round the answer to the nearest meter, so it's 69 meters. So, the closest measurement is 69 meters.

Answer:

volume = 80 in³

Step-by-step explanation:

base area = 8 x 6 x 0.5 = 24 in²

volume = 24 x 10 x 1/3 = 80 in³