Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:


For angle θ:
- If x > 0 and y > 0:
;
- If x < 0:
; - If x > 0 and y < 0:
;
Calculating:
a) (4,2,-4)
= 6
For θ, choose 1st option:
b) (0,8,15)
= 17


The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = 
c) (√2,1,1)
= 2

= 

d) (−2√3,−2,3)
= 5

Since x < 0, use 2nd option:



Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
= 

z = -4
b) (0, 8, 15)
= 8

z = 15
c) (√2,1,1)
= 

z = 1
d) (−2√3,−2,3)
= 4

z = 3
We want to get x by itself
First we will multiply both sides by 6 to cancel out the 6 on the left
5x = 120
We then divide by 5 on both sides to get x by itself
x = 24
Answer:
Answer in file:
Step-by-step explanation:
Answer:
r=8 ft
Step-by-step explanation:
V/6π=r2
r=√v/6π
r=√1206 cubic feet/6π
r=8 ft
Answer:
x-intercept= (5,0)
y-intercept= (0,-2)
Slope= 2/5
Step-by-step explanation: