Find the center and radius of each of the following spheres: a) x^2 + y^2 + 8y + z^2 + 8y - 2z + 1 = 0 b) x^2 + y^2 + z^2 - 4x + 8y + 6z + 4 = 0
Find the intercepts and sketch the graph of each of the following planes.
a) 2x + 3y + 2z = 6
b) 3x + y = 6

75

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4