Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X + 7)² – 3 32 O f(x): 32 - (x + 7)² – 3 %3D 1 O f(x) = (x – 7)2 – 3 32 1 (x – 7)² – 3 O f(x): 32

Q: 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane,…

A:

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

Q: 2) The speeds of oscillation, x, of a loaded beam is given by the equation: x³ 3.25 x² + x -0.063 =…

A: NOTE: As per the guidelines we are supposed to answer only one question because of this is not a…

Q: Is ƒ defined at x = 2? (Look at the definition of ƒ.)

A: From the given function we have the function for x<2 and x>2

Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: Q4: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t…

A:

Q: O 4x +4X - 24Y+ 37 =O 4x4 4x LATERA RECTA y=3 = 24y-37 4x°+x) = 24y-37 4(x?+x+$) =24y-37+1 DIRECTRIX…

A:

Q: g(x) = Vx is reflected over the y-axis and vertically compressed by a factor of ¼ %3|

A: Given function is gx=x We have to find the transformed function which is reflected over the y-axis…

Q: h 2, k -1 and r 5 %3D (x - h)2 + (y- k)2 = r2 %3D %3D wwww x2 + y2 +Dx +Ey + F 0

A: Given:- h=2, k=-1 and r = 5 To find:- Equations of circle in form (x-h)2+(y-k)2 = r2  x2 +y2…

Q: If f(x) = 0 is a cubic equation whose roots are a, B, y and a is the harmonic mean of the roois %3D…

A:

Q: 1- Find the minimum and maximum values of the function f(x,y) = 2x2 + 3xy + 2y2 + x - y inside and…

A:

Q: f (x) = 5.6 sin (2.6x – 4.2) – 9.1- What is the equation of the midline of the function %3D o y =…

A:

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: 4.7.4. Find the extreme values taken by f(x, y) = xy(4x² + y² – 16) on the quarter-ellipse E = {(x,…

A: The given problem is to find the extreme values of given function in the given region of 1st quarter…

Q: Write an example for the following; a) Non-Homogeneous equation with order =2, degree =2 b)…

A:

Q: 6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a…

A:

Q: Find the absolute maxima and minima of the function on the given domain. f(x, y) = 9x + 8y on the…

A: Option (C) is correct.

Q: (a) k : R³→ R defined by: k (x) = x" Ax + b, %3D where: 3 -1 1 A = –1 3 1 1 1 -3 and b = 2. Is k (x)…

A: (a) k:R3→R defined by  kx=xT Ax+b where A=3-11-13111-3 and b=2. is kx a quadratic form?

Q: The orthogonal trajectories of the family of curves y = cx2 is A x=ky? B x²=ky² © 2x2+y²=k D…

A: Solution

Q: The cables of the suspension bridge shown in the figure carry a uniform load of w-Newton per…

A: Detailed explanation mentioned below

Q: The orthogonal trajectories of the family of curves y= cx2 is A 2x²+y²=k B x²+2y²=k © x=ky? D x²=ky²

A: Given family of curves is y = cx2 We have to find the orthogonal trajectories.

Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

A:

Q: 2 b. y" + y' - 2y = %3D

A:

Q: 3. а) Find the local maxima, minima and saddle points of the function f (x, y) = x² + y³ + 2xy. %3D…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: 16. For the shown equations below, let f(x) = 2x + 1, g(x) = x², and h(x) = Vx. Assume that all…

A:

Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: x²y" – 3ry + y = x°, r>0.

A:

Q: g(x,y)=y-x2=0 depending on the condition f(x,y) = x2+y2-6x+9   can you find with the lagrange method…

A:

Q: Problem 3 f(r, y) = (3r2 + 5y)e--y (d) Find the maxima and the minima of z-f(x,y) under the…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: In the following predator-prey model æ represents the prey, and y rep- resents the predator. Which…

A: We are given a prey-predator model comparable to the standard model.

Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

A:

Q: Solve the given problem. Show that v = (x + 2y + 4z)i + (2x – 3y – z)j + (4x – y + 2z)k is…

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: 2. Find a particular solution of the nonhomogeneous equation a. y" - 2y' + 5y = 6e3x

A: As per our guideline we can solve maximum one question ,you can repost other in next turn

Q: 2.23. The difference equation 5y – byk + 2 6y - 8yk + 3 Yk+1 = has two fixed points at (,5) and (1,…

A:

Q: Q3: Find the points on the surfac x^2+z^2-4=D0, closest to the origin.

A: Solution:-

Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: a) Find the extreme values of f(x, y) = x' + y' - 3xy +1 by using the Second Derivatives Test. b)…

A:

Q: Q2. Reduce the state equation: * = 7*+C, y = [1 1]x. to a controllable one. Show the resulting…

A: This question is about application of differential equation

Q: 2. You are standing at the point (1,1,3) on the hill whose equation is given by z = 5y – x² – y?. !!…

A:

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

A:

Q: (b) Classify the equation t - 2ty +2y =t, t> 0. What order is it? Is it linear or nonlinear? Is it…

A:

Q: 15 The curve y=xr'+px² +qx+r passes through the point (0, 5) and has stationary points at x= 4 and…

A: The given curve is  f(x) = x3 + px2 +qx + r The stationary points are that points where the curve…

Q: A tree frog jumps along a parabolic path given by y =-0.15x +1.2x, where x is the frog's horizontal…

A:

Q: Maximise Z = 3 a + 2 b S.T. la - 1 b s 1 l a + lb 2 3 and both x and y are > 0

A:

Q: the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows:…

A: the critical point is find by comparing the derivative to zero.

Q: The orthogonal trajectories of the family of curves y= cx² is A x² = ky? x² +2y² =k В © x=ky? D 2x2+…

A: In this question we have to find the orthogonal trajectories of the family of the curves y=cx2

Q: 2 (х + 2y)dx + (у - х)dy %3D 0

A:

Q: -B-2-1 -2 -3- -8- 16+ hich equation best represents the linear functi Oy=-5x + % Dy= -5x+ 3 Dy= % x…

A: