9x - 6x - 36y + 37 = 0 (x, v) = (| center (x, V) = (| focus (smaller x-value or only focus) (x, Y) = ( focus (larger x-value) (x, y) = (| (smaller x-value or only vertex) vertex vertex (x, y) = (larger x-value) length of the major axis length of the minor axis asymptotes directrix

Q: A company manufactures running shoes and basketball shoes. The total revenue (in thousands of…

A: We use partial differentiation technique to maximize the revenue. The solution is explained below.

Q: Use Lagrange multipliers to find the point on the surface 2x+y-4 = 0 closest to the point (9, - 2, -…

A:

Q: 1. Mang Vicente has 1000m of fencing material and wishes to enclose a rectangular field. Two (2)…

A: Mang Vicente has 1000 m of fencing material and wishes to enclose a recangular field. Two adjacent…

Q: 5. Where does y = 2Vx-3 intersect with y =Vx-1? Support your answer with algebra. %3D %3D graph is…

A: The given equations of the curves are: y=2x-3 and y=12x-1 To find their intersection point, equate…

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

A:

Q: Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on…

A: please refer to the image below

Q: An architect is attempting to fit a rectangular closet of maximal volume into a chopped-off corner…

A: Given : x+2y+3z=24--(1) We have to find the maximum volume of the rectangular closet. Let x, y, z be…

Q: 10. Use Lagrange multiplier to find the point(s) on the circle x² +(y-1)´ = 9 closest to the point…

A: Given circle isx2+y-12=9  and point is (4,4) solve it by using Lagrange multiplier find the closest…

Q: A wire is shaped as an ellipse and is described by 4x2+y2=8. The temperature at every point (x, y)…

A:

Q: Find the maximum profit and number of units that must be produced and sold (in that order) in order…

A:

Q: Use Lagrange multiplier method to find both the maximum and minimum values of the function…

A: Given:  f(x,y)=2x2+y2+2g(x,y)=x2+4y2-4

Q: 5) Using Lagrange multipliers, find the maximum value of z =x + 2y subject to the constraint that x2…

A: For a function f(x) which is to be maximized subjected to the constrains g(x,y)=0, and taking λ as…

Q: 4. Graph the quadratics given by the equations y = x² and y = - --3(x – 5)° +8 Plot at least 5…

A: Calculate 5 value for each equation

Q: Answer the question below: A gift from an organization is wrapped in a box provided that the sum of…

A: This is the problem of maxima and minima of the function. By using lagrange multipliers we will…

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: We need to find length and width.

Q: struct the sides. If styrofoam costs 150 dollars per square meter, and carton costs 100 dollars per…

A: Please refer to the image below

Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

A: Centerville is located at (15,0) in the xy-plane, Springfield is at (0,3), and Shelbyville is at…

Q: A company manufactures running shoes and basketball shoes. The total revenue (in thousands of…

A: We have to maximize revenue.

Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)…

A:

Q: o projectiles are shot into the air from the same location. The paths of the projectiles are…

A: Given, Two projectiles are shot into the air from the same location. The paths of the projectiles…

Q: 7) A piece of sheet metal 20 cm x 12 cm is used to make an open box. To do this, squares of side x…

A:

Q: Find the asymptodes of Hx)= x²- 5x+6 the funchion given below X-2

A:

Q: 2. f(x) = 2 - 5x + 2x Sketch: Opens: Vertex: Equation for Axis of Symmetry:

A: The quadratic function is f(x)=2-5x+2x2 Let the function of the form f(x)=ax2+bx+c, if a > 0 then…

Q: A rectangular field is to be fenced off along the bank of a river, and no fence is required along…

A:

Q: You are building a right-angled triangular flower garden along a stream as shown in the figure. The…

A: Given:- You are building a right-angled triangular flower garden along a stream as shown in the…

Q: In an open-top drawer, the material cost of the two sides is $240 per m2. The material cost of the…

A:

Q: farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No…

A: Let length =x and width=y No fencing is needed along the barn, and the fencing along the west side…

Q: 2. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A:

Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

Q: Minimize z = 22x1 + 44x2 + 33x3 subject to x1 + 2x2 + x3 > 3, x1 + x3 3, 3x1 + 2x2 + 2x3 8 using two…

A: Given LPP is  Minimize z=22x1+44x2+33x3Subject tox1+2x2+x3≥3x1+x3≥33x1+2x2+2x3≥8x1,x2,x3≥0 In order…

Q: Cuboid warehouse will have volume V=216 m^3 For the builidng of walls they are using boards in the…

A: Given: Volume of warehouse = 216m3 cost of using boards: Walls = $30/m2 Flooring = $40/m2 Ceiling =…

Q: Farmer Brown wants to fence in a rectangular plot in a large field, using a straight rock wall that…

A:

Q: 2. f(x) = 2x² - 8x +3 Vertex; Opening/Direction: Maximum or Minimum Value? Min/Max Value: Equation…

A: We can Draw graph of the function given and we can get max results from the graph .

Q: Minimize -z=-8 X1 – 10 X2 -7X3 Subject to XI +3 X2+ 2X3 < 10 -XI -5 X2 - X32 -8 XI, X2, X3 20

A:

Q: Using Lagrange multipliers, find three positive numbers whose sum is 15 and such that the sum of…

A:

Q: Find the maximum profit and number of units that must be produced and sold (in that order) in order…

A: Profit P(x) =R(x) -C(x).

Q: Find the maximum profit and number of units that must be produced and sold (in that order) in order…

A: The given revenue and cost function is,R(x)=50x-0.5x2 , C(x)=4x+10

Q: 6x – 2x and the x-axis into two There is a line through the origin that divides the region bounded…

A:

Q: 3. A rectangular room has dimensions 12x12x24. That is, the floor and ceiling and both the side…

A:

Q: In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm…

A: (2) The table containing the x and y values is shown below. x 0 30 60 90 y 23.5 37.2 35.8 19.3…

Q: In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm…

A: As per the honor code, we are entitled to solve only 1 question at a time. Kindly repost the…

Q: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

Q: 3. Find the maximum/minimum value of y = 2x² + 7x - 10 and where it occurs using partial factoring.

A: Given function is y=2x2+7x-10 we can write it as y=x(2x+7)-10

Q: 4. The parabola y = 48 - x² and the x-axis form the boundaries of a region in the first and second…

A:

Q: A nursery school wants to build a fence around the playground outback of three equal sections. The…

A: Consider the fig. for the playground to find the length and width for the playground.

Q: Find the minimum distance from the parabola x-y2=0 to the point (0,3)(0,3).

A: Given data:   The given expression for the parabola is x-y2=0. The given point is (x1, y1)=(0,3).…

Q: An open–top box with a square base is to be constructed from two materials, one for the bottom and…

A:

Q: Find the closest and most distant points to the origin on the curve x^2+xy+y^2=1.   Use lagrange…

A: Given that the curve is x2+xy+y2=1. It is required to find the closest and most distant points to…

Q: Draw the parabolic path of the bird based on the given data. Blue Bird • Vertex: (7,25) • Maximum…

A:

Q: A rectangle has one side on the xx-axis and two vertices on the curve y=2/(4+x^2) Find the vertices…

A: Given information:A rectangle has one side on the x-axis and two vertices on the curvey=2/(4+x^2)

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.