(8) Suppose that a is algebraic over F, and [F(a): F] = 7. What is [F(a): F?

Q: For the matrix A = (3+4)A=3A+4A (3+4)A = 3A + 4A = 4 3 5 -5 True False evaluate each side of the…

A: For given A we have to determine whether  (3 + 4) A = 3A + 4A  is true or false.

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Q: Let f: [a, b] → R be Riemann integrable and g: [a, b] → R be such that f(x) = g(x) for all x € (a,…

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Q: Question 1: Find the equation of the plane passing through the points A: (-2,-3,4), B: (1,2,7), and…

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Q: (e) Given that the general solution of the partial differential equation and boundary conditions may…

A: From the given equation find the general solution:

Q: Two tanks are interconnected. Tank A contains 70 grams of salt in 50 liters of water, and Tank B…

A: Given that Two tanks are interconnected. Tank A contains 70 grams of salt in 50 liters of water, and…

Q: Azad sold some books at $12 each and used the money to buy some concert tickets at $60 each. He had…

A: We have to find least number of books he could have sold and  least amount of money he could have…

Q: -{··} Let B₁ = 0 and B₂ = { {[2].0} (D) - and let T : R³ → R² be the linear transformation defined…

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Q: Find the Laplace transform of the following function. t f(t) = [ 0 COS s (t — 7)e² sin 7 dt.

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Q: Evaluate y² - x² where E is the region outside the region enclosed by the ellipse (22 +y2) diedy E…

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Q: The temperature distribution 0(x, t) along an insulated metal rod of length L is described by the…

A: From the given equation find the general solution and lembda= mu(symbol).

Q: Question 9 Andy, Bernard and Charlie were running on a 400 m circular track. Andy started running at…

A: (a) Since Andy and Bernard are moving in opposite directions, they will meet when the distance they…

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Q: 11. Calculate F.ds where F = (3xy, xe², z³) and S is the surface of the solid bounded by the…

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Q: Find bases for the following subspaces of F5: and W₁ = {(a₁, a2, a3, a4, a5) € F5 : a₁ a3 a4 = 0}…

A: Basis : A basis of a vector space is a minimal spanning set but a maximal linearly independent set…

Q: Solve the differential equation below by undetermined coefficients: y" + 2y' = x + e²x

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Q: In Exercises 11 and 12, find the closest point to y in the subspace W spanned by V₁ and v2. 11. y =…

A: The objective is to find the closest point to y=3151 in the subspace W spanned by v1=31-11 and…

Q: Specify the sets by description. Letters that occur in both words Kalgoorlie and Irkutsk…

A: The letters that occur in "Kalgoorlie" are k,a,l,g,o,r,i,e The letters that occur in "Irkutsk" are…

Q: Find a basis B for the T domain such that the T matrix relative to B is diagonal. T: R^3 → R^3: T(x,…

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Q: Z Prove that the residue of functions and 2³ - 7² +1 Z3 (z-a) (z-b) at infinity are -1 and 1…

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Q: Find a parametric representation for the surface. The part of the plane z = x + 2 that lies inside…

A: According to Bartleby guidelines I have solved first one. For next question you can repost the…

Q: 3. Given that (X, d) is a mtric space. Suppose p is another metric on X such that d(x, y) ≤ kp(x, y)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: From the following table, find x correct to two decimal places, for which y is maximum and find this…

A: Given table, x 1.2 1.3 1.4 1.5 1.6 y 0.9320 0.9636 0.9855 0.9975 0.9960  So, from above table,…

Q: Problem 5. Find the eigenvalues and a basis for the eigenspace of the matrix associated with each…

A: Our objective is given below:

Q: Find the transpose of the matrix. - 1 21 23 5 13 19 8 9 - 2 14 24 18

A: Given that the matrix is                                   -121235131989-2142418. To find the…

Q: Given v = -7i- 6j and w=5i - j, find the angle between v and w What is the angle between v and w? 口。…

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Q: (-1)"x" (n+1)! Consider the series n=0 (a) Find the series' radius and interval of convergence. (b)…

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Q: [1 0 1 0 -2 2 0 -2 -2 Enter the matrices Q and R below. Any empty entries are assumed to be 0. Find…

A: The given problem is to find the QR decomposition for the given matrix A. Given matrix A = [ 1 0 1 ;…

Q: Use proof by contradiction to show that √3 is irrational.

A: We will use contradiction method

Q: 15 The following data defines the sea-level concentration of dissolved oxygen for fresh water as a…

A: Trapezoidal Rule The formula to calculate the area under the curve using the Trapezoidal rule is…

Q: a. Determine on (1) for an arbitrary value of n. Gb. Ploton(t) for n = 1, ..., 4. Observe whether…

A: (a) Given differential equation is y' = t y + 1 ,  y(0)=0 .  Take integral from 0 to t , we get  ∫0t…

Q: A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold…

A: The number of units of product A, B, and C sold by x, y, and z, respectively.

Q: Find, by the method of Lagrange multipliers, the critical points of the function, subject to the…

A: I have explained everything with in the solution, please go through that.

Q: Integrate G(x,y,z)=z-x over the portion of the graph of z= x + y² that lies above the triangle in…

A: Given that G  x, y, z  = z - x              The portion of the graph a curve z = x + 3y2 above…

Q: Explain how rise run and Уг - У1 X₂ - X₁ both represent the slope formula.

A: Slope Definition:  The slope of a line refers to its direction and steepness. The slope of a…

Q: Solve: y""+3y"-4y-12y = 0 y(0) = −3, y'(0) = 0, y″(0) = −22 y(t) =

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Q: Find the x- and y-intercepts for the functions. (Enter ordered pairs (x, y), using commas to…

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Q: (a) Color the graph below. That is, using the smallest number of colors possible, color the vertices…

A: Now we have the given graph First, we will start at A, and fill it with the first color violet. Then…

Q: If $2,400 is deposited at the end of each quarter in an account that earns 4% compounded quarterly,…

A: $2, 400 deposited at end of each quarter.  Rate of interest - 4% Future value at end - $46, 000. We…

Q: A = {1, 2, 3, 4) and S4 = {f | f : A A, one-to-one and orten} group (S4, ) be given. In the S4 k…

A: The question can be transformed as follows. We have to find all elements of order 2 in S_4

Q: (a) Yk+2 - 2yk+1 + y = 0 subject to y₁ = 0, y₁ = 1 (b) yn+2-8yn+1-9y=0 subject to yo = 2, y₁ = 1 (c)…

A: The Z- transform:

Q: The parametric equations and parameter interval for the motion of a particle in the xy-plane are…

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Q: Suppose a bank draws its venture capital funds annually from three sources of income: business…

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Q: The following table gives the scores of 30 students in a mathematics examination. 90-99 80-89 70-79…

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Q: Prove that a polynomial in z is continuous. That is, prove that the following polynomial is…

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Q: Suyin has 56 pennies and 196 nickels. She wants to place them all in stacks so that each stack has…

A: Given that, Suyin has 56 pennies and 196 nickels. She wants to place them all in stacks so that each…

Q: A student is allowed to check out 3 books from the library. All of the books must come from one…

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Q: Compute the quadratic form x Ax for the given matrix A and vector x. X1 ¹1) A- [89]-x-[x2] = X = 07…

A: Any symmetric matrix A can be converted to quadratic form by using the standard form  Quadratic…

Q: Solve: y"+7y"+27y'+85y = 0 y(0) = −4, y'(0) = 0, y″(0) = 4 y(t) =

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Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, Y2, Y3, and y4 of the…

A: The given initial value problem is:y'=-1-2x+2y, y0=-2, and h=0.5. To Find:y1y2y3y4