Find the distance between (2,0) and (8, -3) The distance d between the points (x, y) and (x2, y2) is d = V(x, - x,)? + (Y2 - . O v3 O 3/5 O V89 O 15

Q: X =. Vy, x = -y,y = 2 about the x-axis

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Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

Q: Qz Find of the lines the point of inter section Linei X = 2 ti +1g y=3t,+29Z=4tı73 Line 2 x = t2 +2,…

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Q: The length of the curve y = 3 - 4Vx for 0 < x < 3 is calculated by the integral: %3D Select one: 3 O…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z2 22, P = (2,…

A:

Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…

Q: Q1 Frad Pavametric equations for the line through the Point (o,t, 2) that is Perfandicutar to U…

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

Q: Integrate counterclockwise dz by Cauchy's formula z2 – 16 counterclockwise around the circle C : |z…

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Q: 2. XY has an endpoint X at (2,– 4). If the midpoint of XY is (– 3,– 1), what are the coordinates of…

A: The midpoint of two points and is given by: where are coordinates of the midpoint.

Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: TEANUCOGl b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz = 0. he

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: The curve intersects the plane (in a three dimensional space) y+z = 2 at the point ( (Hint: First,…

A: Topic- intersection point of curve with Plane

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

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Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: a) Lollowng use Euler ncthoel tsoule The d = yx2-Y for メ=2 at h=o.Ś , h=0.25 y= x +zy h=ol y (2)= }

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Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0).…

A: Given problem:- Find the coordinates of the point(s) on the curve y = √(x + 3) that are closest to…

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: y = VT, y = 2 - x and r O about the x-axis?

A:

Q: Find a harmonic function ¢(x, y) in the right-half plane x>-1 such that on the boundary (-1, y) = 0,…

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

A:

Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

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Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: (a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between…

A: The number of vehicles coming and leaving the signal is same in all the signals. That is, Total…

Q: 4) Verify that Green's theorem is true for f,xy?dx – x²ydy ,where C consists of y = x² from (-1,1)…

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Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

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Q: A/Find the distance between the line 2x + 3y = 5 and the point(-1,0). ( B/Find by integrating along…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: Find the equation for the tangent plane and the normal line at the point Po(2,3,1) on the surface 3x…

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Q: az and ди az Given that z = exy, x = 2u + v, y = , find (using chain dv rule).

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Q: 1+iz if w= Find the image |z|<1 1-iz

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Q: y = x', y = 4x, x > 0 about the line y = 0 using the method of disks or washers. 2 Volume…

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Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo.Zo) (5,2 on the surface…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.