So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
<h3>
Which ones are the first three possible values?</h3>
The set of the whole numbers is {0, 1, 2, 3...}
Then the first possible value is when g = 0.
0^2 + 3 = 3
The second possible value is when g = 1
1^2 + 3 = 4
The third possible value is when g = 2.
2^2 + 3 = 7
So the first three possible values of g^2 + 3 are:
3, 4, 7
The first option is the correct one.
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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)
Oliver withdraws an amount of $285.10 from his saving account
His saving account earns 1.8% annually
The interest Oliver could have earned in five months:
Monthly interest = Annual interest ÷ 12
Monthly interest = 1.8% ÷ 12
Monthly interest = 0.018 ÷ 12 = 3/2000
After five months = Principle × (1 + interest)ⁿ
After five months = 285.10 × (1 + 0.018)⁵
After five months = 311.70
Interest earned = 311.70 - 285.10 = $26.60