Determine the center and radlus of the fto floWing equation : x2+y²-bx-82 = 0

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: nissile is propelled from the origin of a coordinate system with the x units

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Q: A particle follows the trajectory x(t) = t3 + 2t, y(t) = 20t – t2 with t measured in seconds and…

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Q: Find an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and…

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z)…

Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: Two children weighing 18 and 20 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: f(x, y) = 2x – x² – y? %3D -

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the equation: (x² + x – 2) y" + (x + 1) y' + 2y = 0, - find the singular points and determine…

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Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

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Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

Q: Find the length of the curve x = 1+ 312, y = 4 + 213, 0 <t < 1. Length =

A: Given,

Q: Differentiate. y = Y =_et %3D 3x2 y' = %3D

A: The detailed solution is as follows below:

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x +y +5 = 0. YI…

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Q: Solve: y''' – 3y'" – 6y' + 8y = 0 %3D y(0) = – 6, y'(0) = - 12, y'"(0) : - 54 %3D y(t) =

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Q: gives axis. y = 0.35 0.3 0.25 0.2 y 0.15 0.1 0 05

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Q: Find and determine type of stationary point for ƒ(x,y)=x' – 3x² + 2xy – y

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Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: dbout specified axis. y = 8x - x2, y = 12; about x = 2 %3D V =

A: The method of cylindrical shell to find the volume of the region bounded is solved using the…

Q: Find an equation of the conic described.Graph the equation.

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Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Classify the equation yʻuxx + 2xyuxy + 2x-uyy + xux = 0, and reduce it to canonical form.

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Q: draw vertical and horizontal traces to identify the surface y = x^2 + 9z^2

A: The graph of the given surface is

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: A particle travels along the parabola y = ax^2 + x + b. At what point do its abscissa and ordinate…

A: Given: y=ax2+x+b

Q: Define properties of Solutions of y' = y?

A: Solution: Consider the given equation is y' = y First, find the solution to this equation. dydx  =…

Q: Solve for the x-component (in cm) of the centroid if that a=98.7cm, b=78.9cm, and r-58.5cm. Round…

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Q: Calculate || xVy² + x²dA, Where R = {(x, y) /0 < y <land 0 < x < y}

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Q: (c) y" – y' = t², y(0) = y'(0) = 0.

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Explain Axisymmetric flow in detail.

A: I have explained axisymmetric flow  Axisymmetric means symmetric about an axis

Q: y = mx + b is called the v ---Select--- rm of the equation of a line. standard Additional Materials

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Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Consider the equation d'y da² +y = 3x², with the boundary conditions (0,0) and (2.31145, 4.62291).

A: To Solve: The given differential equation d2ydx2+y=3x2, with boundary conditions (0,0) and…

Q: An airplane is flying in the direction 25° west of north at 800 km&gt; h. Find the component form of…

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Q: y = 1+(t- y), 2<153, y(2) = 1, with h = 0.5 %3D %3D

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Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

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Q: An airplane is flying in the direction 25° west of north at 800 km/h. Find the component form of the…

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Q: y² = 8x,x=2, AOR = Y AXIS

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Q: d²y dy +y=1²-2t +3 4- dt? dt

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Q: Find the total differential. 6x + y w = 4z - 8y

A: The given function is: w=6x+y4z-8yw=f(x, y, z)

Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: draw the slope field for y' = x² – y², then use it to sketch three solution curves. %|

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Q: A researcher is nunning a simulation of an upward rocket to study the upward velocity of the rocket…

A: v = ulnmomo-qt -gtv=upward velocity 680ms                                u=fuel expelling velocity…

Q: 3.) y = Vr, y = 3, x = 0 around the x axis.

A: To find: The volume of the solid that is generated by the revolving the given function y=x around…

Q: A drone, flying at a constant altitude, is designed to monitor an industrial area for signs of…

A: (a) The given function has fine details which is complex to be traced manually. We are, therefore,…