Show that the equation represent a sphere, and find its center and radius. x2+y2+z2+8x-6y-2z+17=0

(x-(-4))² + (y-3)² + (z-1)² = 3²

that is the equation for a sphere with radius 3 and center in (-4,3,1)

Step-by-step explanation:

from the equation

x²+y²+z²+8x-6y-2z+17=0

x²+y²+z²+8x-6y-2z+17+(16-16+9-9+1-1) =0

(x²+8x+16) + (y²-6y+9)+ (z²-2z+1) +(17-16-9-1) =0

(x+4)² + (y-3)² + (z-1)² - 9 =0

(x+4)² + (y-3)² + (z-1)² = 9

(x-(-4))² + (y-3)² + (z-1)² = 3²

that is the equation for a sphere with radius 3 and center in (-4,3,1)

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).