Consider the LP problem below: Max P= 12x + 10y Subject to: 4x+3y <= 480 2x+3y <=360 x,y >=0 Which point is the intersection point of the line 4x+3y=480 and 2x+3y=360? Select your answer. (180,0) (80,160) (120,0) (60,80)

Q: Show that the equations x+ y +z = 4, 2x + 5y - 2z = 3, x + 7y - 7z = 5 are not consistent.

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Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

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Q: For what values of the constants k and c does the line x- 3 ** =- lie in the plane x - y + 2z = c? O…

A: Given equation of   line  ;   x-32=y-2k=z+14plane;  x-y+2z=c key points 1)  given line lies in the…

Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

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Q: 14. If f(z) = 2 + z² – zª, then the equation S(x) = 0has a solution on the interval A [1,2] B (0,1]…

A: We will make use of the fact that for f to have a solution in an interval it must be that f has…

Q: Solve graphically the dual of the LLP Minimise: z=4w, +6w, +5w,-wĄ Sub. to w; +w, 23 W;,W,W,Wq 20

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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: Find the null space associated with the equations: 2x+z+w = 0 7x-6y-z-w-v= 0 -5x+4y+w = 0 (Needless…

A: NOTE: Refresh your page if you can't see any equations. . system Ax=0 is the matrix A is

Q: 21 Calculate the coordinates of the point of intersection I of the two lines : 1° (D) : x + 3 = 0 2°…

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Q: Use variation of parameters to find the particular solution to y'' - 7y' +12y = 3e³t Y(t)= Preview

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Q: 4) Isosceles trapezoid ABCD has diagonals AC and BD. If AC= 5x+ 13 and BD= 11x-5, what is the value…

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Q: For what values of the constants k and c does the line x- 3 _ y-2 z+1 * = = 2 lie in the plane x - y…

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Q: 3. Find the maximum and minimum values of f(x, y) = x² + y² - 2x - 2y + subject to the constraint…

A: We use langrange multiplier method

Q: Q1: if AB = i + 4j – 2k and B is the point (5,1,3), find point A.

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: The solution of the IVP t(t + 4)y + (t + 4) y= t, y(2) =2 exists in the interval

A: In the question it is asked to solve the initial value problem as shown below. t(t+4)y'+(t+4)y=t2…

Q: 45 14 B. 56 C. 68 D. 90 Which line is paraliel to y = x-2? Ay=x+5 By = 6x+5 C. y = -6x + 8 D. y…

A: We have to find the following conditions according to the given information

Q: 14. If f(z) = 2 + ² -r', then the equation S(z) = 0has a solution on the interval A [1,2] B (0,1] c…

A: Given equation, fx=2+x2-x3, To find the interval on which the equation fx=0 has a solution.

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: Determine the equation of the perpendicular bisector of KL if it's endpoints are at K O-7,5) and…

A: Given:    Points : K ( 7 , 5 )    ,   L ( 9 , 1 )

Q: and Lg:글3D%3D- z+3 Q4] Find distance between lines L1: =5

A: solution:-L1 : x-13 = y-22= z+32L2 : x-22 = y+2-1= z-34distance between two line is given by L1 :…

Q: 15. Let z and y be positive numbers such that 2r +3y = 5 and f(r, y) = (r-3)(y+2) is optimized.…

A: We need to optimize the function f(x, y) = (x-3)(y+2) subject to the constraint 2x+3y=5

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: Determine the maximum value of p=r-2y and where it occurs subject to: 5 + 4y 40 3r 120 Be sure to…

A: This is a Linear programming problem. Linear programming is a mathematical technique used to solve…

Q: Find the solution of y'(x) -ay(x) = 0

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: 5. Determine a solution of the following equation which satisfies the given condition: y-3y'+ 2y = 0…

A: Given that, The differential equation is following, y''' - 3y' + 2y = 0 y(0) = 0,  y'(0) = 2  and…

Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 7. How many points of intersection exist between y= x' +4x2- 2x - 5 and y = 3? %3D None B. One Two…

A: To find the number of intersection of the given curves  y = x3 + 4x2 - 2x -5  and y = 3

Q: 18. In the standard (x,y) coordinate plane, the line represented by which of the following equations…

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Q: what about a point? horizontally point vertically to the point If F(x, y, z) = 2x² + xyz – y²z What…

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Q: 3. Which equation passes through the point (1, -2) and is perpendicular to y = x O y = 3x - 1 O y =…

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Q: Find the real number ( B) such that the line of symmetric equations ( x – 3 == ) is parallel to the…

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Q: How many circles touch the x-axis and the y-axis and pass through the point (2,1)? Select one: a.…

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Q: The function f(x,y)=4x+4y has a max and min to the constraint 16x2-16xy+16y2=25. Use Lagrange…

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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: Q1: if AB = i+ 4j – 2k and B is the point (5,1,3), find point A.

A: AB vector is given. AB = i +4j -2k   Creat vector AB by taking variable point A and given point B…

Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint æ? + y² +…

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Q: Find the real number ( B ) such that the line of symmetric equations ( x - 3 = = ) is parallel to…

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Q: 7o. ther line (X=.3+2t.g y=2b.g Zot).intersects. the. planc 5X-2y+42=10 at paint p. Find the…

A: Solution

Q: There are three collinear points A, M and E. M is in between A and E. Segment AM equals 3x+1.…

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Q: Q7) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=5X+7Y…

A: Answer is given below.

Q: 2: Show that the line equation passing through two distinct points (a1, b1) and (a2, b2) can be…

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Q: Al Q2/ Choose the correct By using fixed point method, which of the following formulas can use to…

A: The given equation is 3xex=1 on [0,1]. To Find: which of the following is the fixed point iteration…

Q: ind an equation of the line of intersection of the following two plane x + y + z = 0 nd 2я — у + 32…

A: We have to find out

Q: 20. Determine B such that 3x + 2y - 7 = 0 is perpendicular to 2x - By + 2 = 0 A. 5 B. 4 C. 3 D. 2

A: Topic = Geometry

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

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Q: Use back-substitution to solve the triangular s 5x - 5y + z = 0 y + 5z = 21 Z = 5 (x, y, z) =

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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: 4. Determine the unknowns using [X] = [A]¯*[B] and [A] by the adjoint method. %3D 10x + 2y – z = 27…

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

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.