Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically. (2,4) (2,3) (4,8) O (-4,-11)

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A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

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Q: Suppose the point (4, -2) lies on y = g(x) and the point (4, 5) lies on y = f[g(x)]. Then a point on…

A: Given query is to find the indicated point.

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

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A: Given y'+ye^(3x+7)=-2y² We know that the dy/dx gives the direction field. Hence the given DE can be…

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Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (2, 2, 0).

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A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

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Q: Find the points on the graph of z = xy +8y where the tangent plane is parallel to 9x + 5y + 9z = 0.…

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Q: Straight lines with slope twice the x-intercept.

A: Let us assume x-intercept is a. That is, x = a when y  =0. So,  slope  =2a. Let us assume that the…

Q: 3. Using different colors draw secant lines from (1,2) to each of the points (x+Ax, F(x+Ax) ).

A: (1) graph the given equation  h(x)=x+12+2

Q: Find the points on the graph of z = xy + 8y where the tangent plane is parallel to 2x + 5y + 2z = 0.…

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Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

Q: Re Question 17 Find a parameterization for the line segment from (2,-1) to (-6, 4). a) O (t) = -1–…

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Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

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Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

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Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: Show that the curve In (2X-1) , n> i has no stationary point

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Q: -4 -8 Let y = 9 and u = -2 -8 7 Compute the distance d from y to the line through u and the origin.…

A: I have appended the formula used in the solution part of the question

Q: Find the point(s) of intersection of the curves r = 1 and r = 2 sin 0. ^(1.5)(1.플) 1, 27 3 В. 1, 1,…

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Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

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Q: Consider the linearizable functions as follows. Find new transformed variables (rª, yª, Bor B as you…

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Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

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Q: 1 ,3/2 y92 - y"2 between the points 3 ,1 and (6,9). 3 Find the length of the curve x=-y" 1/2

A: Given : The curve is : x=13y32-y12  We have to find the length of the given curve between the points…

Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: Find the equation of the sphere if one of its diameters has endpoints (8, -2, 8) and (11, 4, 17)…

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Given :                    z = x2 + 3y2      at the point (1,2,13)

Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}