By 4sing Logrange Multipliers; find the Minimug ond maxingum values of ferist)-4t or the ellipse which is the Inler section of the 4 the plora rt3+t e1 ond the ylin ser res?-8. jpr

Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: ine the orthogonal trajectories of the family of ellipses 16x² + 121y² = C. Sketch some of the…

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Q: .Find the orthogonal trajectories for the family of curves x² + y² +3cx = 0.

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Q: Find the length of the arc of the parabola x2 = 4y from x = -2 to x = 2. А. 4.3 В. 4.6 С. 4.9 D. 5.2

A: we have to find the length of the arc of the parabola x2=4y from x=-2 to x=2

Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

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

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Q: 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the…

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

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Q: Which way does the parabola open? (x+ 3 =4 y + 5). h drwn e laft d ninht aun

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Q: Which point or points on the ellipse x?+4y² = 4 are furthest away from the point (0, 1)? [Hint 1:…

A: Given equation of the ellipse is x2+4y2=4 Let the point be x1,y1 lies on the given ellipse.…

Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: 4.The parabola opens O A. upward O B. forward O C. backward O D. downward

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Q: Find a parabola with equation y = ax? + bx + cthat has slope 4 at x-1, slope -8 at x=-1, and passes…

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Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: Given the 1-parameter family of parabolas y = trajectories of the family if the angle of…

A: We are given: y=ax2 Now, we will find the tangential slope, dyTdx=a×2x⇒dyTdx=2ax…

Q: Use the Lagrange multiplier method to find the maxima and minima of the function f(x, y) = xy on the…

A: Consider the given function fx,y=xy and let gx,y=3x2+y2-6. Using Lagrange multipliers,…

Q: The vate of groow th fa fish population was modeles by -0.6t G(t) = 60000e %3D timeasurd in G: Kg…

A: The rate of growth of a fish population is Gt=60000e-0.6t1+5e-0.6t2. The biomass in the year 2000 is…

Q: The 2011 Tōhoku, Japan earthquake is the newest deadliest earthquake. The power was equal as about…

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Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: Find the shortest distance from the point (1, 0) to the parabola y? by: (a) Eliminating the variable…

A: We have to find the shortest distance  from the point (1,0) to the parabola y2=4x.

Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: Wrat is the equation in standard form of ahyperbola whose asymptotes are y=- うオー and y= -x- and a…

A: Given: y=32x-92         asymptote 1 to hyperbola                                         1y=-32x -32…

Q: Find the shortest distance +rom the point (0,5)to the ellipse 3 y? = x'

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Q: /A: Given; y? = 6kx %3D Find orthogonal Trajector.

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Q: Consider the hyperbolic PDE shown below = 4- at? For a value of At=0.1, what are the values of Ax…

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Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

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Q: (a) Find the first order DE corresponding to the family of parabolas y = Cx² . (b) Find the equation…

A: a)The family of the curve of the parabola is y=Cx2 To find the first order differential equation…

Q: Maximize xy? on the ellipse 9 x² + 4 y? = 36 . a) O The maximum is 6. b) O The maximum is 12V3. c) O…

A: Given ellipse 9x2+4y2=36 and xy2

Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: Find the smallest outputs of the function x^2+2y^2 on the slanted ellipse x^2+y^2+xy=3

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Q: Find two values of d such that the line 2x + y = d is tangent to the ellipse 4x2 + y? = 36. Find the…

A: follow next step

Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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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: Q9: Show that in an ellipse b2 = a² (1 – e? ).

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Q: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

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Q: A certain bridge arch is in the shape of the top half pf an ellipse 122 feet wide and 25.6 feet…

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Q: A Ferris wheel has a radius of 30 m, makes a full rotation in 3 minutes, and the axle stands 35 m…

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Q: The graph of the acceleration a(t) of a car measured in ft/s is shown. Use the Trapezoidal Rule with…

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Q: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…

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: stimate the population will grow to P(t) (408)4, where t represents the number of %3D rding to this…

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Q: A parabola having its x axis parallel to the y-axis has its focus at (5,6) and vertex at (5,4).…

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Q: A string is in the shape of an ellipse described by 4x2+y2=8. The temperature at every point (x, y)…

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: A vehicle travels in a straight line for t minutes witha velocity ofh hod ne VHY=102t-6t feet…

A: Given:- A Vehicle travels in a straight line for t minutes  with a velocity of V(t) = 102 t - 6t2…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.