\[\sum_{n=1}^{7} 2(-2)^{n-1}\]
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
Answer:
d = 8t
Step-by-step explanation:
A lot of math is about matching patterns. Here, the pattern you can match is given in the problem statement:
d = 6t . . . . . equation for distance traveled at 6 miles per hour
You are asked to write an equation for distance traveled at 8 miles per hour. You can see the number 6 in the above equation matches the "miles per hour" of the traveler. This should give you a clue that when the "miles per hour" changes from 6 to 8, the number in the equation will do likewise.
The equation you want is ...
d = 8t . . . . . equation for distance traveled at 8 miles per hour
Answer:
f(3) = g(3)
General Formulas and Concepts:
<u>Algebra I</u>
- Reading a Coordinate Graph
- Coordinates (x, y)
- Solving systems of equations by graphing
- Functions
- Function Notation
Step-by-step explanation:
According to the graph, we see that both lines intersect at <em>x</em> = 3. Therefore, that means both lines at that <em>x</em> point will have the same <em>y</em> value. Both f(3) and g(3) would equal 6, leading us to the answer of f(3) = g(3).
