3D Geometry Questions and Answers

A pyramid with three regularly side S.ABC know m<BSC-60 degree. Through BC make a perpendicular line H with AS. Height of the pyramid is 2root2. Find the slice of H with the pyramid

Use perturbation theory to find the real root of the polynomial equation: x^3+x-1=0

Describe the surface. cone xy = 6 O ellipsoid O hyperboloid O elliptic cylinder O hyperbolic cylinder O parabolic cylinder O elliptic paraboloid O hyperbolic paraboloid Sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (Write an equation for the cross section at z = -6 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 6 using x and y.)

Consider the equation below. x² + y² - 2x - 4y - z+ 5 = 0 Reduce the equation to one of the standard forms. Classify the surface. O ellipsoid O elliptic paraboloid O hyperbolic paraboloid O cone O hyperboloid of one sheet O hyperboloid of two sheets Sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (Write an equation for the cross section at z = -1 using x and y.) (Write an equation for the cross section at z = 1 using x and y.) (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 2 using x and z.) (Write an equation for the cross section at x = 0 using y and z.) (Write an equation for the cross section at x = 1 using y and z.)

Match the equation with its graph. y² = x² + 4z²

SITUATION. A frustum of a conical tank whose upper radius is 10 cm, lower radius of 8 cmand height of 12 cm is filled with water to aheight of 6 cm. Water in this tank istransferred to a hemispherical tank whoseradius is 20 cm. What is the Volume of water incm³? O 1233.45 O 1533.23 O 1433.67 O 1363.45