Using the generalised triangle inequality, show that |d(x, y) − d(z, w)| ≤ d(x, z) + d(y, w).

Q: If f(x) = 5 – x and g (x) = vx + 3, the range of the graph of is O a) {y]y > –11, y E R} O b) {y]y >…

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Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: Minimize: subject to: z = x - y 4x - 3y 20 3x - 4y ≤ 0 x, y ≥ 0

A: The given problem is to solve the given linear programming problem. Given linear programming…

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

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Q: 10. Maximize the Function P(r, y) = 35x – 27y on the set: 6x + 8y < 96 2 3

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Q: If Iz – 2| < 2, then find (x,y) * arg(z),r i5

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Q: If f(x,y,z) = x2 + y2, what is the locus of points in space for which grad f is parallel to the…

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Q: In the figure, find the value of c in the interval [0, 4] on the x-axis that maximizes angle

A: Redraw the figure as shown below.

Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: a) Compute the absolute extrema of f(x, y) = y² on D = {(x, y) : 0 ≤ y ≤4-x²,-2 ≤ x ≤ 2}.…

A: In the following solutions, we will compute the absolute extrema of the function on the domain , and…

Q: P = (x, y) = x + 4y ≤ 13 3x + y ≤ 6 x ≥ 0, y ≥ 0.

A: Let us first find the feasible region.

Q: Faith observed that her product sales in a certain town is given by the function of M(u, v) = u²v²…

A: The given function is M(u,v)=u2v2 for (u,v)∈ℝ. The given region is bounded by lines passing through…

Q: If a is costructible,then evaluate that x=x and y=x are constructible lines. |

A: Claim :  If a is costructible, then x=a and y=a are constructible lines

Q: Using Baye's Theorem, show that if X⊥Y, then I(X;Y|Z)=I(X;Y,Z

A: Using Baye's theorem, show that if X⊥Y, then  IX, Y/Z=IX, Y, Z.

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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Q: The distance between the points P(0, 0,4) and Q(7,6, 8) is V102 Select one: True False

A: According to question,Given points,P0, 0, 4 and Q7, 6, 8

Q: 4) Evaluate f(x) = Vx + 3 a) x = 1 b) x = a – 1

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Q: ✓ 3.11 Find M+. 292 (a) M = { (c) M = { (e) M = { { (₁) |x=0} () (f) M={y|-x+3y+z=0} (g) M={y | x =…

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Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: 1. Consider the following three domains in the space: {(x,y,z) E R³:1 ≤|x+y+z<4}, {(x,y,z) € R³ : 2…

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution:

Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ∞), where a > 0. b > 0 , c > 0 Find the condition if…

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