Find the coordinates of the point (x, y, z) on the plane z = 4 x...

Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 4 which is closest to the origin.

Expert Solution

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Colby Messinger answered 2 years ago

find the point lying on the intersection of the plane, x + (1/4)y + (1/3)z =...

find the point lying on the intersection of the plane, x + (1/4)y + (1/3)z = 0 and the sphere x 2 + y 2 + z 2 = 25 with the largest z-coordinate. (x,y,z)=(_)

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar...

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar coordinates (r, θ) of the point so that r > 0 and 0 ≤ θ ≤ 2π. (b). The polar coordinates (r, θ) = (−3, 5π/6) of a point are given. Find the Cartesian coordinates (x, y) of this point.

The coordinates of a point P in the x-y plane are (2;3) meters. q1 = 10...

The coordinates of a point P in the x-y plane are (2;3) meters. q1 = 10 C load (1;0) , q2 = 20 C load (-1;0) is placed in the metre position. The electric flied formed by these charges at the P point, find your size and direction.

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z):...

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}. (b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}. (c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}. *(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive. (a) For what value of...

Find the tangent plane to Z= xsin(x+y) at (1,1,0)

Find an equation of the tangent plane to the graph of f(x, y)=sin(x3y2) at point (4,...

Find an equation of the tangent plane to the graph of f(x, y)=sin(x3y2) at point (4, 2).

The following charges exist (given coordinates are (x, y) coordinates in the plane of the page):

The following charges exist (given coordinates are (x, y) coordinates in the plane of the page): • a −3.0 µC point charge located at (0, 0) • a −2.0 µC uniform spherical shell of charge of radius 3.0 cm centered at (+4.0 cm, 0) • a +2.0 µC uniform spherical shell of charge of radius 2.0 cm centered at (0, −4.0 cm) • a +4.0 µC uniform spherical shell of charge of radius 4.0 cm centered at (−1.0 cm,...

a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find...

a. consider the plane with equation -x+y-z=2, and let p be the point (3,2,1)in R^3. find the distance from P to the plane. b. let P be the plane with normal vector n (1,-3,2) which passes through the point(1,1,1). find the point in the plane which is closest to (2,2,3)

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z =...

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z = 5 and 2x+y−2z = 7 b). Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5). ( I ) Find an equation for the plane that passes through these three points. ( II ) Find the area of the triangle determined by these three points.

Find the equation of the tangent plane to the surface x + y^2 + z^3 +...

Find the equation of the tangent plane to the surface x + y^2 + z^3 + sin(x − yz) = 7 at the point (2, 2, 1).

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