A bird is hunting for fish in a pond. She swoops down from a height and picks up a fish from the water surface and flies back up, all along a path y=4x2−(2k+2)x+1, where k≥0, y is its height from the water surface, and x is the horizontal distance from a fixed origin which is in the plane of the path. Then, the value of k can be

Q: 2:- find the line of interSection o f the plane -2x + 73 - 2324 given by 3x t6y-52=-3 f the plane

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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Q: 3. Consider in R? the straight line l of equation y = 2.x +1 and the point P = (1, -1). (a) Use the…

A: Lagranges Multipliers Method

Q: A car leaves Smogtown at noon, heading west at a speed of 60 km/h. Another car heads south at a…

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: Find all points on the curve 5x² + 8y² = 64 %3D

A: Given: The curve 5x2+8y2=64 where tangent line passes through the point (11, 0). To find: All the…

Q: A loan buyer in a secondary market believes that x% of the loans are high quality, and the rest are…

A: Solution: The inquiry says the worth of merchant selling high-quality bonds is equivalent to the…

Q: Q5. Use Lagrange Multiplier to find the minimum distance between the origin and the line (x=51 +3, y…

A: Solution :

Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: (b) The revenue R(x, y) that Scoot Airline collects from selling its normal seats and premium seats…

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Q: Find the minimum value of f(x,Y)=34x2+25y2 subject to the constraint x2+y2=196 %3D

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Find maximum and minumum values of f(x, y, z) = 9x – 18y +45z subject to the constraint x? + y² + z²…

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Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: Find the length of the curve. x = 413. y = 612. 0 sts v8 %3D The length of the curve x = 4t°, y = 6t…

A: Given curve x=4t3,   y=6t2    0≤t≤8

Q: Q1 Minimise f(x) = X;² + x;? + 2x3? – x1x2 %3D a) Determine the stationary point and check the…

A: Given, f(x)=x12+x22+2x32-x1x2 a) Stationary point:…

Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint x² + y? +…

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Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: B. Find the extremum of f(x, y) = -x - y subject to the constraint y + 4.x = 1. Use a graph of the…

A: We will answer the first question since we answer only one question at a time. Please resubmit the…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: 29. Find the extremum of x² + y? + z? subject to the constraint x + y + z = 3a. State whether it is…

A: Let us assume  fx,y,z=x2+y2+z2 and gx,y,z≡x+y+z−3a=0Using lagrange multiplier…

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? + y? +…

A: The given function is; f(x,y,z) = 8x-16y+40z

Q: 1. What is point-slope form? А) Ах + Вy %3D С y2 - Yı В) т%3 X2 - X, С) у - У1 %3 т(х - х) D) у %3D…

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Q: Find the maximum of 2x + 3y on the feasible set given by x2 0, y 20, 2x + y 22, 3x + 4y s 12. a) 6…

A: We sketch 2x+y≥2 , 3x+4y≤12 , x≥0, y≥0 using a graphing calculator.

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Q3) Find the local maximum and minimum points of the following curve: y = 3x + 2x? - 4x + 2

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Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: Q5:- Find the maximum value of the function f (x, y) = xy, subject to the constraint x + y = 16.…

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Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x² + y? +…

A: Hair we use langraj multi plier method to solve the the given problem.

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5", where the value ab is as…

A: We need to find the minimum value of ab So, let fx,y=xy We need to minimize this function and find…

Q: Use the simplex method to solve the following z = 3x1 + 3x2 - 9x3 4x1 + 4x2 - 12x3 s 60 5x1 + 5x2 +…

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Q: Q Use Lagrange multipliers to tind the maximum an Ċ minimnm valnes and Points (x ) at which they…

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Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e9, where the value ab is as…

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Q: Q:- find the line of interseetion o f the given by 3X +6y -SZ=-3 S the plane plane -2x + 7y -Z=24 1)…

A: We know that a straight line is the intersection of two planes. So a pair of equations of first…

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

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Q: Use Lagrange multipliers to find the point (a,b) on the graph of y = e^(5x) where the value ab is as…

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Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The graph of 3x – 2y + z = 12 is a with x-intercept at A. Plane, x = 3 O B. Line, x = 3 O C. Line, x…

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Q: Find the minimum value of f (x,y,z) = 2x2 + y? + 3z? subject to the constraint 2x - 3y - 4z = 49

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Q: C. Find the extrema of f(x, y) = x2 +y subject to x2 – y? = 1. Use a graph of the contours and…

A: Given:f(x,y)=x2+y   subject to x2-y2=1

Q: a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and…

A: Given Data The equation is w=xyz. The first equation of plane is x + y + z = 40. The second equation…

Q: Find the shortest Distance d faumthe point to the plane X+y+Z=8.

A: Let's find.

Q: Find a point with z = 2 on the intersection line of the planes x + y + 3z = 6 and x - y + z= 4 .…

A: Given, equation of planes x+y+3z=6x-y+z=4

Q: III Locate the possible y = x³ + 6x² + 9x max and min points and pt/s of inflection

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Q: Use the simplex method to solve the following. z = 4x1 + 4x2 - 8x3 10x3 s 95 12x3 s 128 X1 20, x2 2…

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Q: Use Lagrange multipliers to find the maximum and minimum of f(r, y) = 3r+y subject to a+y? = 10. %3D…

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.