2. If the equation is the polynomial curve on affine planef (x, y) = xy? – y3 + xy + 3 = 0a. Find the homogenous polynomial F(x, y,z) with property:F(x, y,1) = f(x, y).b. Does the above homogenous polynomial F(x, y, z) have ideal points? Perform the analysisby intersecting the polynomial to the equation z=0!

Answered: Image /qna-images/answer/8e1d3b4e-4048-41ba-9c42-70c507ab1b1c.jpg

Answered: 2. If the equation is the polynomial…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the maximum value that f(x, y, z) = x² + 9y − z² can have on the line of intersection of the planes 8x - y = 0 and y + 3z = 0.
C is the semicircular curve drawn in the ground (the xy-plane) joining the points (0, - 2), (2, 0), (0, 2). A fence is to be built along the curve planted at each point of C, going up in the positive z-direction, with a height at the point (x, y) given as h(x,y)= 1 + Find the area of the fence that will be built. In other words, work out the line integral h(x,y) ds The area of the fence is
Find the maximum of f (x, y) = 5y² + 5xy - 5x² on the square domain 0 ≤ x ≤ 6,0 ≤ y ≤ 6. (Give an exact answer. Use symbolic notation and fractions where needed.) fmax = 180 Incorrect
Find the vertical trace of the function h(x, y) = COS x + y) for = = 2. h = The plane below represents the plane parallel to the zy-plane where a = 2. Assume the vertical axis is the z-axis. -3T -5x/2 -2n -37/2 -n -/2 t/2 1 31/2 2n 5n/2 3n -2+ Clear All Draw:
3. Consider a closed storage tank S with walls given by the curved surfaces x = y, z > 0 and a = 2 – y', z > 0, floor at z = :0, and roof is part of the plane x + 2y + 2z 6. (a) Sketch S, clearly labelling any intercepts. (b) Find the area of the roof of the tank. (c) Write down an expression for the volume of the tank as a triple integral. (d) Evaluate the integral in part (c) using the MATLAB symbolic toolbox.
Q3.If f(x,y)=sin²(x-3y)+sin(xy find: Q4. Use Lagrange multipliers to find the shortest distance between the origin and the plane contains the points (1,2,-1), (3,5,9), and (-1,2,-5). af and and aj
On a dark night, two ships, Saga and Hero, sail parallel to a straight coastline on which there are two lights of equal brightness, 16 kilometres apart. P(x, b) (-8, 0) (8, 0) x Suppose the coastline is represented by the x axis where the origin O is chosen to be the midpoint of the light sources. It is known that the (total) brightness from the lights on a ship at point P(x, b) is 1 I = b² +(x+8)² 'b² +(x-8)² + dI (i) Show that dx 2P where P= (x+8)(3² +(x – 8)*)* +(x -8)(s² +(x + 8)*)* | and Q = (3° +(x +8)*)} (s? +(x-87)'. To answer parts (ii) and (iii), you may assume the following factorisation, given by a computer package, that P= 2x(x² + 64 + b? +16/64 + b² (x² + 64 + b² –16/64 + b²). (ii) Saga sails parallel to the coast at a distance 15 km from the coast. dI show that, as Saga sails from left to right, the brightness By considering on Saga increases to a maximum when x= 0 and then decreases. dx (iii) Hero sails parallel to the coast at a distance 6 km from the coast. Describe…

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