For the plane that passes through (−4,1,5), (−7,−3,1), and (−2,3,9), the implicit equation is:

Q: ) How many ways can Mary split up 12 hamburgers and 16 hot dogs among 4 kids (R, P, C, and J) in a…

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Q: Consider an object D bounded by y = 0, y = x², and x = 3 with density p(x, y) = In(y). Compute the…

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Q: Find the coordinates of M = [M]B = -7 9 173] 0 -3 with respect to this basis.

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Q: Find fourier series 0 f(x) = {x² ≤ x ≤ 0. 0 ≤x≤ TT.

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Q: Question 3 X= Find the values of x, y and z that correspond to the critical point of the function:…

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Q: 1 (x-3)² True False is always positive.

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Q: (a) Prove that the function f is well-defined; that is, the value f(q) of the function at a rational…

A: Given the notation , and using this defining the set . Then the function  defined as:.It is well…

Q: Let u(æ, y, z) = Vr +y + z? where æ = 8re', y = 2te & z = et, du ду dw E Ər ot Әх ду дz Әх or ' or '…

A: Given:      where We have to calculate and  by using the chain rule.

Q: Find parametric equations for line that is tangent to the curve x = cost, y = sint, z = t at the…

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Q: Let z(x, y) = x³y where x = t³ & y = tº. dz dx dy by first finding & and using the chain rule. dt dt…

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Q: Consider the functional S[y] = =ffdx [₁ = dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant…

A: The functional  S[y] is given by an integral that depends on the function y and its derivative y′…

Q: you're done (as modeled in class videos); you do not need to actually do the complete proof. 1.…

A: Using mathematical induction,we can prove the given problem.

Q: 1. Prove that 35121 (mod 1024).

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Q: Let 5 (x² + y²)³ be a one-form on U = R² \ {(0,0)}, and : V → U be the smooth function (r, t) = (r…

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Q: For the function f(x, y) = 5e³ sin(y), find a unit tangent vector to the level curve at the point…

A: For the function f(x, y) = 5e3xsin(y), we have to find out a unit tangent vector to the level curve…

Q: Set up the simplex tableau for the exercise. Do not solve. Gina eats a meal of steak, baked potato…

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Q: Find and classify the critical points of z = = (x² − 7x) (y² – 6y). Local maximums: Local minimums:…

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Q: How do you know the region in polar coordinates? How to find the polar coordinates?

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Q: Let P denote the path that goes in straight lines from (1, 1, 1) to (-1,-1,1) to (-1,-1,-1) to…

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Q: Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S…

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Q: 3. Find an equation of the plane parallel to the plane 4x -z- 3y -4 = 0 and passes through the point…

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Q: Find the absolute maximum and minimum of f(x, y) = 4x + 4y within the domain x² + y² ≤ 1. Please…

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Q: 1.9. Consider the CES technology f(x1,x2) = [a₁x² + a₂x2]. Show that we can always write this in the…

A: To show that it can write the CES technology function in the form f(x1,x2)=A(ρ)[bx1ρ+(1−b)x2ρ]1/ρ,…

Q: dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y =…

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Q: ercise 3. (i) Show that 9(x) = ▶ cos(kx) Σ 3k k=1 defines a continuous function g: [0, ½] → R. (ii)…

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Q: Sketch the region of integration and convert the polar sum of integrals to a Cartesian integral or…

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Q: Let w(x, y, z) = √x2 + y² + 2² where x = -8ret, y = 2ter & z = ert. дw дw Oz Әх ду дz Әх ду…

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Q: 3. Show that every arithmetic progression is clopen in (N, 7). 4. Let B be a collection of all…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 16. Find an interval representation for the poset in Figure 6.38 or give a reason why one does not…

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Q: In how many ways can one distribute ten distinct prizes among 4 students with exactly two students…

A: According to the question, To distribute ten distinct prizes among 4 students with exactly two…

Q: 3. Let T: P3 → M2x2 be the linear transformation defined by a+d b. с b + c a d T(a + bx + cx² + da³…

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Q: A national census bureau predicts that a certain population will increase from 35.3 million in 2000…

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Q: Exercise 4 (The max norm ||· ||). Recall from class that the max norm ||· ||∞ is defined on Rn as…

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Q: Find the differential of the function f(x, y) 77 dz Now find Az and compare it to your answer above…

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Q: Solve the linear programming problem. Minimize C= 8x +9y Subject to 5x+7y 2 35 x, y 20 What is the…

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Q: 9. If 90° ≤ 0 ≤ 180° for which sinė = 5 13 Determine the exact value of tan 0 10. State the period…

A: (For ,  is negative.)Hence,

Q: w is the orthogonal projection of the vector v upon the vector u where v:=vector([1,-1,1]);…

A: The orthogonal complement If w is the orthogonal projection of the vector v upon the vector u is .

Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

A: Let the given triangular matrix be Find the eigenvalues corresponding to the given matrix.

Q: 7.22 Let in Australia k(t) be the number of kangaroos at time t (the prey) and p(t) be the number of…

A: According to the question,

Q: 2xy²e(xv)² + 2x² ye(xy)² y² = 0

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Q: Compute the order of 2 with respect to the prime moduli 3, 5, 7, 11, 13, 17, and 19.

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Q: You may use modular arithmetic to solve the following. (a) Prove that for all n ≥ 2, 14+1 +8" is…

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Q: Solve the following linear programming problem, using the Simplex Method. maximize P= 4x + 6y…

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Q: 3. Prove that A x B=Ax B. Exercise 10 Hausdorff product topology Prove that the product of two…

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Q: Let z(x, y) = xey where x = Calculate = t³ & y = 3 + 4t. dx dt dz dx dy by first finding & and using…

A: We have givenThen derivatives of x and y

Q: For a prime p suppose that n = 2º − 1 is not a prime. that n is a pseudoprime base 2. how every…

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Q: Let V be an inner product space over the field of real numbers with the inner product defined as (u,…

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Q: = Exercise 12. |Diagonal Show that X is Hausdorff if and only if the diagonal A {(2,1); z X) is…

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Q: Draw the diagram of the interval order represented in Figure 6.34. d 8 Hi re 6.34. An interval…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the remainder when 2108 is divided by 31.

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