A point moves along the intersection of the elliptic paraboloid z = 4x + 11y and the plane y = 4. At what rate is z changing with respect to x when the point is at (4, 4, 240)? Rate =

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: find the point in which the line with symmtric equation2-x =y-1/3 =z/4 intersect the plane 2x-y+z=2

A: we are given the line with symmetric equation:  2-x =y-13=z4 and equation of the plane is:  2x-y+z=2…

Q: Solve for the distance between the point P(0,0,0,0) and the plane w + x + y + z = 3 in R^4.

A:

Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

A:

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ < t < ∞, at the point…

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Q: Find the distance between the skew lines with parametric equations x=3+t, y=2+6t, z = 2t, and…

A: Given :x=3+ty=2+6tz=2tx=2+2sy=4+14sz=-2+5s

Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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