Help and hurry fast you get 75 points HELP

To solve the boundary-value ordinary differential equation,  _d2u +6 -u = 2_  with boundary conditions (0) = 10 and u(2) =1 using centered finite difference, the discretization h=0.5 is used.

Thomas algorithm will be applied to solve the resulting system of equations.

The equation to be solved is

_d2u +6 -u = 2_.

Using centered finite difference, it can be represented as:

\(_ui+1 + ui-1 - 2ui_  =  _h2(f(xi) - 6ui + ui)_  , where  _f(xi) = 2_,  _xi_  =  _ih_ , and  _h_  =  _0.5_.\)

Expanding the above equation gives:  \(_-ui-1 + 2ui - ui+1 = -h2(f(xi) - 6ui + ui)_  ...\)equation (1)The boundary conditions given are  _(0) = 10_  and  _u(2) =1_. These can be discretized as follows:

\(_(1) = u0_  _(3) = u4_  _(1) = 10_  _(3) = 1_   ... equation (2)\)

Equation (1) can be written in the form of the matrix equation:  _Au = b_ , where  _u_  is the column matrix of  _(1), (1.5), (2), (2.5), (3)_ ,  _A_  is the coefficient matrix, and  _b_  is the column matrix obtained by discretizing  _f(xi)_  and including the boundary values. After solving the system of equations using Thomas algorithm, we obtain the values of  _u_.

To solve the boundary-value ordinary differential equation,  _d2u +6 -u = 2_  with boundary conditions (0) = 10 and u(2) =1 using centered finite difference, we first obtain the discretization h=0.5. The second-order derivative in the equation is discretized using centered finite difference to obtain equation (1).

The boundary conditions given are then discretized to obtain equation (2).The matrix equation  _Au = b_  is then obtained by combining equations (1) and (2).

Using Thomas algorithm, the system of equations is solved to obtain the values of  _u_.

To solve the boundary-value ordinary differential equation,  _d2u +6 -u = 2_  with boundary conditions (0) = 10 and u(2) =1 using centered finite difference, we obtain the discretization h=0.5.

Centered finite difference is then used to discretize the second-order derivative in the equation, and the boundary conditions are discretized as well.

By combining these equations, we obtain the matrix equation  _Au = b_. We then apply Thomas algorithm to solve the system of equations and obtain the values of  _u_.

To know more about Thomas algorithm :

brainly.com/question/28724722

#SPJ11

Answer:

to find domain just take the first values of each ordered pairs

to find the range just take the second values of each ordered pairs.

Answer:

try this

Step-by-step explanation:

Make a straight cut through the center, cutting the cake in half.

Stack the two halves, one on top of the other and then cut them all in half #2. stack these 4 pieces of cake on top of each other and make your third cut, cutting them all in half for 8 equal, but messy, pieces of cake with 3 cuts.

Answer:

the figure is in cuboidal shape.

volume of cuboid=length ×width ×height

volume of cuboid=12mi×5mi×4mi

volume of cuboid=240mi³

Answer: 12/18

Step-by-step explanation:

For a quick explanation, all you need to do is multiply 1/6 by 6 to get 1 whole and do the same to 2/3 so it’s proportional again.

The number of cups of water she needs to mix is 4.

Given that,

Based on the above information, the calculation is as follows:

\(= \frac{2}{3} \div \frac{1}{6} \\\\= \frac{2\times 6}{3\times 1 }\)

= 4

Learn more: brainly.com/question/17429689

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

Learn more about SAS ,ASA ,AAS, SSS from the link below

https://brainly.com/question/29617415

#SPJ4

Answer:

18 - x

Step-by-step explanation:

f(x) = 6 - x

g(x) = x/3 + 8

f(2x) = 6 - (2x) => 6 - 2x

g(3x + 9) = (3x+9)/3 + 9 = x + 3 + 9 => x + 12

(6 - 2x) + (x + 12)

Simplified:

18 - x

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

Learn more about production

brainly.com/question/31859289

#SPJ11

Answer:

5&1

7&3

8&4

Step-by-step explanation:

The Relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

The relationship between the points D(6, 9) and A(8, 12) can be described in terms of dilations. In mathematics, a dilation is a transformation that changes the size of an object while keeping its shape intact. It involves scaling the object by a certain factor, either enlarging or reducing it.

To understand the relationship between D and A, we can calculate the dilation factor. The dilation factor, denoted by 'k', is the ratio of the corresponding side lengths or distances between the pre-image (original object) and the image (transformed object).

The dilation factor between D(6, 9) and A(8, 12):

First, we need to find the change in x-coordinates and y-coordinates:

Δx = 8 - 6 = 2

Δy = 12 - 9 = 3

Next, we calculate the dilation factor:

k = Δy / Δx = 3 / 2 = 1.5

The dilation factor of 1.5 indicates that the image point A is 1.5 times as far from the origin (point D) compared to the pre-image. This means that A is located at a greater distance from the origin than D, both horizontally and vertically.

Moreover, since the dilation factor is positive, the dilation is an enlargement. This means that A is enlarged with respect to D. The ratio of the corresponding side lengths will also be 1.5.

the relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

For more questions on Relationship .

https://brainly.com/question/28003064

#SPJ8

The power of a that makes it equal to b is x = 5/6

The square root of a number is a number when multiplied by itself gives another number.

The cube root of a number is a number when multiplied by itself three times gives another number.

The power of a number is the exponent of that number

Since two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. It follws that

4√a = 9∛b

⇒∛b = 4√a/9

⇒ b = ∛[4√a/9]

Since we require the  of x is a, to the x power equal to b if a = 2/3.

This implies that

aˣ = b

Substituting b into the equation, we have

aˣ =  ∛[4√a/9]

Since a = 2/3, we have

(2/3)ˣ =  ∛[4√(2/3)/9]

(2/3)ˣ =  ∛[4/9 × √(2/3)]

(2/3)ˣ =  ∛[2²/3² × √(2/3)]

(2/3)ˣ =  ∛[(2/3)² × √(2/3)]

(2/3)ˣ =  ∛[2/3)

\((\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{2 + \frac{1}{2}} } \\(\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{\frac{5}{2}} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{2} \times \frac{1}{3} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{6}\)

Equating both powers, we see that x = 5/6

So, the power of a is x = 5/6

Learn more about powers of exponents here:

https://brainly.com/question/26130878

#SPJ1

Answer:

-8/4 or -2

Step-by-step explanation:

First of all notice the graph is negative. Meaning that this will be a negative slope.

Now we can use rise over run, counting up 8 spaces, and to the left 4.

Since the graph is negative make the rise negative. -8/4.

To simplify this fraction divide -8 by 4, and receive an answer of -2.

-Hope this helped

Answer:

The y-intercept is 7

Step-by-step explanation:

y = slope(x) + y-intercept

Answer:

4 > x

Step-by-step explanation:

-30 < -5(2x - 2)

Multiply the -5 into the numbers inside of the parenthesis

-30 < -10x + 10

Subtract the number without the variable to the other side

-30 < -10x + 10

-10             - 10

-40 < -10x

Divide -10 into -40

-40 / -10 = 4

4 < x

Flip the less than sign to greater than

*(because you divided a number with a negative number)*

4 > x

4 is greater than x

or x < 4

Answer: 240inches

Step-by-step explanation: 100% sorry if it’s incorrect but if you convert 75% into a decimal and multiply 180x.75 you get 240. Which if your using a basic calculator you haft to divide 180/.75 and it gives you the same answer.

Answer:

40

Step-by-step explanation:

The value of the double integral is 0.

We are given the double integral:

\(\int \int x^2 2y\) da,

where d is bounded by y=x and y=x³.

To evaluate this integral, we first need to find the limits of integration for x and y.

Since d is bounded by y=x and y=x³, the limits of integration for y are from y=x to y=x³.

For a fixed value of y, the limits of integration for x are from\(x=y^(^1^/^3^)\)to \(x=y^(^1^/^2^)\), since \(y^(^1^/^3^)\) is the smaller x-value on the curve y=x³ and \(y^(^1^/^2^)\) is the larger x-value on the curve y=x.

Therefore, the integral becomes:

∫ from \(x=y^(^1^/^3^)\) to \(x=y^(^1^/^2^)\) ∫ from y=x to y=x³ x² 2y dy dx

Integrating with respect to y first, we get:

∫ from \(x=y^(^1^/^3^)\) to \(x=y^(^1^/^2^) [(y^4^/^2^) - (y^2^/^2^)] x^2 dx\)

Simplifying, we get:

∫ from \(x=y^(1^/^3^) to x=y^(^1^/^2^) [(y^4^/^2^) - (y^2^/^2^)] x^2 dx\)

\(= (1/10) [y^(^5^/^2^) - y^(^7^/^2^)] [y^(^4^/^3^) - y^(^1^/^2^)]\)

\(= (1/10) [(y^3)^(^5^/^6^) - (y^3)^(^7^/^6^)] [(y)^(^4^/^3^) - (y)^(^1^/^2^)]\)

\(= (1/10) [y^(^5^/^3^) - y^(^7^/^3^)] [(y)^(^4^/^3^) - (y)^(^1^/^2^)]\)

Integrating this expression with respect to x, we get:

\(= (1/30) [y^(^5^/^3^) - y^(^7^/^3^)] [(y^2)^(^4^/^3^) - (y^2)^(^1^/^2^)]\)

\(= (1/30) [y^(^5^/^3^) - y^(^7^/^3^)] [(y^(^8^/^3^) - y)^(^1^/^2^)]\)

Now we can evaluate the integral by plugging in the limits of integration for y:

\(= (1/30) [(y^(^5^/^3^) - y^(^7^/^3^))] [(y^(^8^/^3^) - y)^(^1^/^2^)]\) evaluated from y = 0 to y = 1

\(= (1/30) [(1 - 1/1)] [(1 - 0)^(^1^/^2^)] - (1/30) [(0 - 0)] [(0 - 0)^(^1^/^2^)]\)

= 0

Therefore, the value of the double integral is 0.

Learn more about double integral

brainly.com/question/31404551

#SPJ11

To prove that if R is a well-order on A, then R is a total order which has the least upper bound, and the greatest lower bound properties, we need to show the following:

R is a total order: For R to be a total order, it must satisfy three conditions: reflexivity, antisymmetry, and transitivity. Since R is a well-order on A, it already satisfies these conditions.

R has the least upper bound property: To prove that R has the least upper bound property, we need to show that for any non-empty subset S of A, there exists a least upper bound (supremum) of S in R.

Suppose S is a non-empty subset of A. Since R is a well-order on A, every non-empty subset of A has the least element.

Let x be the least element of S. Then, for any element y in S, we have x <= y.

Therefore, x is an upper bound of S. Moreover, x is the least upper bound of S in R, because if there were another upper bound z in R, we would have

x <= z and z <= x (by reflexivity and transitivity), which implies x = z.

R has the greatest lower bound property: To prove that R has the greatest lower bound property, we need to show that for any non-empty subset S of A, there exists a greatest lower bound (infimum) of S in R.

Suppose S is a non-empty subset of A. Since R is a well-order on A, every non-empty subset of A has the least element.

Let x be the greatest element of the set A\ S (complement of S in A). Then, for any element y in S, we have y <= x.

Therefore, x is a lower bound of S. Moreover, x is the greatest lower bound of S in R, because if there were another lower bound z in R, we would have z <= x and x <= z (by reflexivity and transitivity), which implies x = z.

Therefore, R is a total order which has the least upper bound, and the greatest lower bound properties if R is a well-order on A.

For more such answers on an upper bound

https://brainly.com/question/28725724

#SPJ11

If R is a well order on A, then it means that every non-empty subset of A has a least element under R. This implies that R is a total order, as for any two elements a, b in A, either aRb or bRa holds, and either a ≤ b or b ≤ a holds.

Now, for any non-empty subset S of A that has an upper bound, let B be the set of all upper bounds of S under R. Since B is a non-empty subset of A, it has a least element, which we call the least upper bound of S under R. This shows that R has the least upper bound property.

Similarly, for any non-empty subset S of A that has a lower bound, let B be the set of all lower bounds of S under R. Since B is a non-empty subset of A, it has a greatest element, which we call the greatest lower bound of S under R. This shows that R has the greatest lower bound property.

Therefore, we have shown that if R is a well order on A, then R is a total order which has the least upper bound, and the greatest lower bound properties.

To learn more about subset click here, brainly.com/question/24138395

#SPJ11

Answer:

19/25

Step-by-step explanation:

7/10 + 6/100

= 70/100 + 6/100

= 76/100

= 19/25

So, the answer is 19/25

Answer:

0

Step-by-step explanation:

The slope is zero because if you put it on a graph the line looks like this

_______________________________

Hope this helps!

And also if the equation is like x = 4 the slope would be undefined.

Bye!!

The measure of angle subtended by the arc CEB is 210⁰.

The value of m∠CDB is 30⁰.

The measure of angle subtended by the arc CEB is calculated by applying the following formula.

The sum of angles in a circle = 360⁰, so the value of arc CEB is calculated as;

arc CEB = 360 - 150⁰

arc CEB = 210⁰

Based on the angle of intersecting chord theorem, we will have the following equation to determine the value of m∠CDB.

m∠CDB = ¹/₂ (210 - 150)

m∠CDB = 30⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer: 5.7 (rounded)

Step-by-step explanation: The formula to find the diagonal of a square is \(\sqrt{2\) * a, where a is a side length on the square. Since we are solving for half of a diagonal, we use this formula and divide our result by two. We start by multiplying root 2 by 8 and we get 11.31371, next we divide by two and we get 5.656855 which is 5.7 when rounded.

Considering their slopes, these two lines, Line 1 and Line 2, are perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the slopes are given as follows:

The multiplication is given by:

3 x -1/3 = -1.

Hence they are perpendicular.

More can be learned about the slope of a line at brainly.com/question/12207360

#SPJ1

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

For more questions on Values .

https://brainly.com/question/843074

#SPJ8

Answer:

48 hours

Step-by-step explanation:

which can be 48000 minutes

Divide price by quantity:

3.00 / 12 = $0.25 per can.

Answer:

D

Step-by-step explanation:

simplified is 1 1/2, 1.5 or 3/2

The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.

The given sum can be written as:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],

where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,

where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.

Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

To learn more about definite integral refer to:

brainly.com/question/24353968

#SPJ11