An airplane is flying at altitude H when itbegins its descent to an airport runway that is at horizontal grounddistance L from the airplane, as shown in the accompanying figure.Assume that the landing path of the airplane is the graph of a cubicpolynomial function y = ax3 + bx2 + cx + d, where y(-L) = Hand y(0) = 0. What is dy/ dx at x = -L?

Q: The cubic y = ax3 + bx? + cx + d tangent to the line y = 12x + 13 at (-1, 1) and have a horizontal…

A: Solution...

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: The diagram shows a sketch of the curve with equation y = -r +7x 12 1 3. -2- 8 CMA Q3 Find the…

A: For the solution follow the next step.

Q: The horizontal asymptotes of the curve 3x y = (x4 + 1)'/4 are given by %3D Y1 = and Y2 = where y1 >…

A:

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: Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several…

A:

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

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Q: Find a cubic function d cx bx ax x f + + + = 2 3 ) ( whose graph has a relative minimum at (0, 1)…

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: Find the length of the graph of ; a. f(x)=⅓x2 -⅔ between x=2 and x=3.  b. x=cost, y=sint from t=0…

A: See the detailed solution below.

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: Q2) A- Find asymptotes for the following functions : x²-1 (1) (2) x²+2 B- Find dy dx x³+x²-x-3 x²-1…

A:

Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: (ii) Find the length of the curve y = E* from x = 0 to x = 2. %3D

A:

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: tiny, no bug lands on a piece of graph paper and walks along a path so that t minutes after it…

A: Increasing function

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

A:

Q: Show that the equation of the tangent ine to 'the graph of the parabola at the point Pt'=(t,t²) 1s…

A: Consider the given function whose equation of tangent is required to calculate.

Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

A:

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

A: The given family of curve y=cx2

Q: (ii) Find the extremum of Z= x2 +y2 subject to x + 4y 2 and examine whether the %3D %3D stationary…

A:

Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

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

A:

Q: Rotate the graph of g(x)=e^(−6x) on the interval [0,8] about the x-axis to generate a surface with…

A: Given that g(x)=e-6x To find the surface area by rotating the graph of g(x) on the interval [0,8]:

Q: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y)…

A: Given query is to find the point of horizontal tangent.

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A:

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

A:

Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

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…

A: Ggg

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

A:

Q: Q11 Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of…

A: Given y4-2y''+y=0 To do Write the general solution in terms of hyperbolic functions.

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

A:

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

A:

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

A:

Q: The curve x = t - 3t, y = Vt intersects the y-axis when x = 0, which occurs when t = 0 and t = y 3-…

A:

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

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: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A:

Q: EX Find the point the curve y=x3+x²-l where the tamjent on is parallel to the X-oaxis

A:

Q: Find the absolute maxima and minima of the function on the given domain. 6) f(x, y) = 6x + 5y on the…

A: f(x,y) = 6x+5yfx(x,y) = 6     fy(x,y) = 5  (Hence No critical points of the function itself)Lets…

Q: find the under the curve y=7-t^2 and above the t-axis

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.