Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and radius of this sphere.

This is a sphere with a center    and radius

Step-by-step explanation:

Given that: (x,y,z)

where;

d₁ is the distance from the origin =

d₂ is the distance from (2,2,2) =

Also;

d₁ = 2d₂

By squaring both sides;

Collect the like terms:

Divide both sides by 3

Using the completing the square method;

∴

This is a sphere with a center    and ;

radius;

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m