Answer:
The polar coordinates are as follow:
a. (6,2π)
b. (18, π/3)
c. (2√2 , 3π/4)
d. (2, 5π /6)
Step-by-step explanation:
To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .
To calculate r, we use Pythagorean theorem:
r =
---- (1)
To calculate the θ, first we will find out the θ
' using the inverse of cosine as it is easy to calculate.
So, θ
' =
cos
⁻¹ (x/r)
If y ≥ 0 then θ = ∅
If y < 0 then θ = 2
π − ∅
For a. (6,0)
Sol:
Using the formula in equation (1). we get the value of r as:
r = 
r = 6
And ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (6/6)
∅ =cos
⁻¹ (1) = 2π
As If y ≥ 0 then θ = ∅
So ∅ = 2π
The polar coordinates are (6,2π)
For a. (9,9/
)
Sol:
r = 9 + 3(3) = 18
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (9/18)
∅ = cos
⁻¹ (1/2) = π/3
As If y ≥ 0 then θ = ∅
then θ = π/3
The polar coordinates are (18, π/3)
For (-2,2)
Sol:
r =√( (-2)²+(2)² )
r = 2 √2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ (-2/ 2 √2)
∅ = 3π/4
As If y ≥ 0 then θ = ∅
then
θ = 3π/4
The polar coordinates are (2√2 , 3π/4)
For (-√3, 1)
Sol:
r = √ ((-√3)² + 1²)
r = 2
and ∅ =
cos
⁻¹ (x/r)
∅ =
cos
⁻¹ ( -√3/2)
∅ = 5π /6
As If y ≥ 0 then θ = ∅
So θ = 5π /6
The polar coordinates are (2, 5π /6)
Answer: 2000
Step-by-step explanation:
Simple interest is calculated as:
(Principal × Rate × Time) / 100
We then slot the value into the formula. This would be:
720 = (P × 6 × 6)/100
720 × 100 = 36P
72000 = 36P
Principal = 72000/36
Principal = 2000
Answer:
A and F
Step-by-step explanation:
first figure out the slope.
4-(-5)/2-(-3)= 9/5
slope: 9/5
y-y1=m(x-x1)
you substitute either coordinate for the second variables. we automatically take out any slopes that have a negative because the slope is positive.
C, D, E all have negative slopes so it is wrong.
B does not work because a negative times a negative is a positive. the equation shows it to be negative so it is wrong.
A & F fit the solution.
Answer:
let me tell you firstly i am juat writing this
Step-by-step explanation:
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Answer:
Here's a possible example:
Step-by-step explanation:

Each piece is linear, so the pieces are continuous by themselves.
We need consider only the point at which the pieces meet (x = 3).

The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.