Find the points on the ellipse 2x + 4y = 1 where f(x.y) = xy has its extreme values.

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Two children weighing 18 and 20 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

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Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Q3 Find dyldx on the graph y secx + y = cos2x at point (1, 2).

A: We have to find the derivative of above function at (1,2) Please see the explanation below

Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

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Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: Find the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: Find the equation of the tangent to the hyperbola x² – 3y² = 1 at the point S(2,-1). A) 2x + 3y – 1…

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Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: 4. Find the orthogonal trajectories of the family of parabola described by the equation (y– 3) = Cx.…

A: The solution of the problem is given in the next step.

Q: 4. Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci…

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Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: Determine the coefficients a, b, c, and d, so that the curve y = ax' + bx² + cx + d have critical…

A: Since you have asked multiple questions, as per our policy we will answer first question. Please…

Q: What is the equation of the normal line to the ellipse 8x^2 + 32y^2 = 256 at the point (4,2)?

A: the equation of the normal line to the ellipse can be found by differentiating the given equation…

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: Use Lagrange multipliers to Önd the points on the ellipse 2x2+y2 = 1 where f (x, y) = xy has its…

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Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

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Q: Use Lagrange multipliers to find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme…

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

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Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

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Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

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Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

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Q: Find the maximum and minimum valves of f(xy)=5x+Y on the ellipse X+36y=!

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Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

A: We need to find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find the equation of tangent line to the parabola y² = 6x – 3 which is perpendicular to the line x +…

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Q: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

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Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.