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)
5 girls, 5 boys...total of 10 students
P(1st pick is a girl) = 5/10 which reduces to 1/2
P(2nd pick is a boy) = 5/9
P (both) = 1/2 * 5/9 = 5/18 <=
Answer:

Step-by-step explanation:

This is written in the standard form of a quadratic function:

where:
- ax² → quadratic term
- bx → linear term
- c → constant
You need to convert this to vertex form:

where:
To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

Using your original equation, identify the a, b, and c terms:

Insert the known values into the equation:

Simplify. Two negatives make a positive:

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

Simplify using PEMDAS:

The value of y is -6 (3,-6). Insert these values into the vertex form:

Insert the value of a and simplify:

:Done
Check the picture below.
using a second for it, since it's a horizontal line, then say hmmm we'll use the y-intercept, or (0, 1), so the equation of a line that passes through (2,1) and (0,1)
Answer:
The answer is 41
Step-by-step explanation:
(35 + 7) (6 - 5)
(42) × (1) = 41
Thus, The answer is 41
<u>-TheUnknownScientist</u>