Find the point at which the line F (t) = < 2, – 7,7 > +t < - 5, – 6, 6 > intersects the yz plane.

Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

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Q: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: (b) Compute the slope of the line that is parallel to the xz-plane and tangent to the surface z = x…

A: Given: Let's calculate the slope of the line tangent to the surface z=x(x+y) at the point that is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

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: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

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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: Sketch the plane curve r(t) = t2i − 4tj and find its length over the given interval [0, 5] .

A:

Q: Find the point(s) on the surface z = x2 − xy + y2 − 2x − 2y, at which the tangent plane is…

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Q: 2. Find the equation of the plane tangent to the elliptic paraboloid z = point (1, 1,3). 2.a2 +y, at…

A: To find out the equation of the plane tangent to the elliptic paraboloid.

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Sketch the plane curve r(t) = t3i + t2j and find its length over the given interval [0, 1] .

A:

Q: Find an equation for the plane that is tangent to the surface z= Vy - I at the point (2, 3, 1).

A: We have to find partial derivatives first.

Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: 3. z = (c

A:

Q: Find the point on the surface f(x,y)=x²+y²+xy-17x+9y at which the tangent plane is horizontal.

A:

Q: Let z=f(x,y) = y² – x³ . Find the slope of the line tangent to this surface at the point (-1, -2)…

A: Given surface is z=f(x,y)=y2-x3.

Q: Find the point on the surface f(x,y)=x2+y2+xy-26x+29y at which the tangent plane is horizontal.

A: For Given surface f(x,y) The slope of horizontal tangent plane is equal to zero.

Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Find the coordinates of the point where the line F = (1+21)î + tĵ – 2tk intersects the plane 2x – y…

A: Let's find.

Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

Q: Find an equation of the tangent plane to the surface 2² + 2y? + z? = 175 at the point (5, -5, 10).

A:

Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

A:

Q: Find the equation of the plane tangent to the grapl UI z = f(x, y) = x² + 2y³. + 1 at the points in…

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Q: Find an equation for the tangent plane of z 3.xy? + y + 2 at the point (-1, 1, 0).

A:

Q: (b)Let f(x, y) = /3x +2y. %3D Find the slope of the surface z = f(x, y) in the x-direction at the…

A: (b) Slope of z= f(x,y) in the y- direction at the point (4,2) Slope ofz in the y - direction means…

Q: Find the equation of the tangent plane to the surface z = 6x4 + 5y + 3xy at the point (-3,0, 486). z…

A:

Q: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

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Q: Find an equation of the plane tangent to the following surface at the given point. z= 3- 3x -y:…

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Q: Find the point at which the line 7(t) = +t intersects the yz plane.

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Q: Please help solve this. If this can be solved without linear algebra I would prefer to see that…

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Q: find an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

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Q: Find the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

A:

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

Q: Let ƒ(x, y) = 2x + 3y - 4. Find the slope of the line tangent to this surface at the point (2, -1)…

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Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

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Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Find the equation of the tangent plane to z = e² + y+ y*+3 at the point (0, 5, 634).

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.