(a) By drawing a suitable diagram, prove the triangle inequality |z1 – 2| > |21| – |2|-

Q: The minimum value of J.y,Z) = 6x - y – óZ subject to the constraints *+y -Z=0 and ? + 2? = 1 is?

A: Given,          The minimum value of fx,y,z=6x-y-6z subject to the constraints x+y-z=0 and x2+2z2=1.

Q: x (q 43 ソ-1; 13. Represent the solution set of the following inequalities in the Cartesian plane. b)…

A:

Q: Find the minimum value of q(x) = x" x subject to the condition ||x|| = 1. %3D Select one: O A. 2 -…

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Q: QUESTION 23 Find the maximum value of Q(x) subject to the constraint x'x= 1. Q(x) = 2x,? + 9x,? +…

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Q: Consider the problem min x + 2x + 2x1x2 + X1 – X2 – x3 s.t. x1 +x2 + x3 < 1 X3 < 1 (i) Is the…

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Q: Let for a two-category one-dimensional problem with &#160; (a) Show that the minimum probability of…

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Q: 2] a) If Á. B = AB cos(0), then show that |A. B| < |A]. |B|.(Cauch-Schwarz inequality).

A: I am solving question 1 if you want second question then repost.

Q: Express Constraint 1 to mathematical statement. 0.8x1 + 0.2x2 + 0.2x3 + 0.2x4 = 0 0.8x1 - 0.2x2 -…

A:

Q: 6. Use Cauchy-Schwartz Inequality, Ju· v| < ||u|| |v||, to prove the Triangle Inequality: ||u+ v|| <…

A: To Determine: Use Cauchy-Schwartz inequalities,                                  u.v≤u  v To prove…

Q: Sketch the region that corresponds to the given inequalities. 4x + 5y s 4 4x - 5y 2 4 -y 2 2

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Q: For A C Cmxn, n=dim(R(A))+dim(N(A)).

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Q: Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1)…

A: To find the largest interval on which existence and uniqueness guarantees a unique solution. For…

Q: 2. Solve the fóllówing inequalities: (a) {x: x-3x 0} 2x 2-1 (c) {x: 20} (x-2)(x+1) (d) {x20} X+1

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Given that a is a parameter, which region provided below is part of the solution to the following…

A: For the inequality |x|&gt;a x&gt;a or x&lt;-a

Q: Solve the following inequality graphically in two-dimensional plane: x + y &lt; 5

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Q: Describe the set of all points in 3- space whose coordinates satisfy the inequality Y² + z² + 6y −4z…

A: Sphere: A three-dimensional shape like a round ball. A sphere has one curved surface and no corners…

Q: Graph the solution region of each of the following systems of inequal- ities. (a) 6x + 12y 2x – 3…

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Q: Sketch the region that corresponds to the given inequalities. 8x 7y 2 0 x - 6y s 0 x 2 0, y 2 0

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Q: (c) Let z1 = 2+ 2i and let 22 =1+i. Prove that the triangle inequality |21 + z2| < |21| + |22|…

A: Left hand side is equal to, z1+z2=2+2i+1+i=3+3i=32+32=32 Right hand side is equal to,…

Q: 4. Prove the Triangle Inequality: If v, weV, then || v + w ||<|| v || + | w || -

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Q: Solve the following inequality graphically in two-dimensional plane:x – y ≤ 2

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Q: kimum and minimum r3 9y +1

A: Given as, f(x)=x3 -9x+1, -∞,∞

Q: Verify the discrete metric d2 satises the triangle inequality.

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Q: 6 Find the minimum of –x + 2y on the feasible set given by x 2 0, x5 4, y 2 2, and x+y24. a) 0 b) 2…

A: We graph x≥0, x≤4, y≥2 and x+y≥4 using a graphing calculator.

Q: If the conditions of the fixed point theorem are not satisfied, then there exist no unique fixed…

A: The ciric theorem states that, Let X be a complete metric space, and let f : X → X be such that,…

Q: From the graph of the function f (z) =-|z+ 3| + 5, Desi found the solution of {z|z S-6 or z2 0} for…

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Q: Consider the following polyhedron P = {x € R³ : 2.x1–x2+x3 -1, –2x1+x2+x3 = 0, x2+x3 > -1}. Decide,…

A: We are given the following polyhedron.        P=x∈ℝ3 : 2x1-x2+x3≤-1, -x1+2x2≤2, x1+x3≥-1,…

Q: =: |2| = 1 on closed curve -dz < 2ne, show that inequality exists.

A: Let fz=ez+4z2 Then f has singularity at z=0 of multiplicity 2 Resf;0=limz→0ddzz2×ez+4z2…

Q: Which of the followings are the extreme values of f(x, y) = e¬#Y subject to the constraint a? + y² =…

A: Recall: Lagrange method: Lagrange method is used for maximizing or minimizing a general function…

Q: Sketch the region that corresponds to the given inequality. 6x + y s 8 y 15 15 10 10 5A Solution Set…

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Q: 4. Write the standard primal and dual for each of the following problems: (a) Minimum z = 5x1 – 3x2…

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Q: 1 Consider two nonnegative numbers x and y such that x+y= 10 . Maximize and minimize y -

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Q: Find the extreme values of f(x, y) = 12x + 3y, subject to the constraints xy = 4, x > 0, and y > 0.…

A: Solve the following

Q: Solve the following LP in three different ways (use TORA for convenience). Which method appears to…

A: Given: Minimize    z=6x1+7x2+3x3+5x4 subject to    5x1+6x2-3x3+4x4≥12…

Q: Solve the following inequality graphically in two-dimensional plane:2x + y ≥ 6

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Q: 1. Sketch the regions associated with the following inequalities. Determine if the region is open ,…

A: soln:The equation,z-a=r ,represents a circle with  centre at a and radius…

Q: 3. yA -12- -10- 8- 6- 4- 2- -2 -2- -4- -6- -8- -10- On the grid, label the region that satisfies all…

A: We need to plot region of given inequalities.

Q: 38. Using the Cauchy-Schwartz Inequality, the MINIMUM value of the function a? +y subject to the…

A:

Q: Consider the set X E R? defined by the system of inequalities X = {R² : -x1+ x2 0, x2 > 0}. (a) In…

A: (a) We have the set, X={ℝ2 : -x1+x2≤2, x1+x2≤5, 2x1+x2≤4, x1≥0, x2≥0}The set is represented in the…

Q: 1). If r is not equal to one, show that a + ar + ar^2+ ....+ ar^n= a( r^n+1 -1)/( r-1).2).…

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Q: Solve the following constrained optimization problem using the method of Lagrang 1 - 2y + 6z,…

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Q: 14.) Sketch the graph of the solution set the system of inequalities. Label the vertices. of the…

A: Given: The system of inequalities  2x-6y&gt;4-x+3y≥5 To Graph: The solution set of the given system…

Q: Prove that Ix I - I y I &lt; Ix - y 1-Hint: Apply the triangle inequality to y and x - y.

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Q: Solve the following inequality graphically in two-dimensional plane:3x + 4y ≤ 12

A: We first graph 3x+4y=12 line We make a table for it x 4 0 y 0 3

Q: Sketch the region that corresponds to the given inequality. XS 4y 1아 1아 1아 Solution Set 5- Solution…

A: Given the inequality . Let us consider the inequality as an equation. that is x = 4y. Now to graph…

Q: 38. Using the Cauchy-Schwartz Inequality, the MINIMUM value of the function a + y subject to the…

A: 38 Given function is fx,y=x2+y2 We have to find the minimum value of fx,y=x2+y2 subject to condition…

Q: Solve the following inequality graphically in two-dimensional plane:3y – 5x &lt; 30

A: We first graph 3y-5x=30 using a table  x 0 -6 y 10 0

Q: (a) Let f(x, y) = x² + 2y². Find the extreme values of f(x,y) subject to the constraint equation x²…

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Q: 10. Let f(x, y) = x²y + y. Find the minimum and maximum values of f subject to the constraint x² +…

A: Given: fx,y=x2y+y The constraint equation is: gx,y=x2+y2=5   Now apply the Lagrange's multiplier;…