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- Find the rectangular coordinates of the point P with cylindrical coordinates (r, θ, z) = (5, 5π/4, 6).Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<= x<= 2, 0<= y <= 2 in the first quadrant.In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10 where a is a parameter. Find all the values of a for which this quadric is (1) an elliptical cone...
- Use a scalar projection (NOT A FORMULA- unless you derive that formula as part of your solution) to find the shortest distance from the point (1,−2,5) to the plane given by −2x+6y−z=18 . Please give a detailed solutionThe planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose origin is at the center of the planet, the magnetic field strength is given by I(x,y,z)=4xz+4yz+7. What is the strength of the magnetic field where the radio telescope will be positioned? will be positioned in the place where the planet's magnetic field is as weak as possibleYou are in charge of erecting a radio telescope on a newly discovered planet. To minimize interference, you want to place it where the magnetic field of the planet is weakest. The planet is spherical, with a radius of 6 units. Based on a coordinate system whose origin is at the center of the planet, the strength of the magnetic field is given by M(x, y, z) = 6x - y2 + xz + 60. Where should you locate the radio telescope?
- find an equation in cylindrical coordinates for the equation given in rectangular coordinates z= 49x^2 + 49y^2 - 6In a right spherical triangle ABC, B=90°. Using Napier’s first rule, what is the simplified form of the equation for side AB?Find equations for all the planes that intersect the y-axis at y =1 and the z-axis at z =2, and are tangent to the sphere (x−2)^2 + y^2 +z^2 =4. Do not use calculus.