Width = 9cm
Length = 18cm
<u>Explanation:</u>
Let width = b,
So, length = 2b
Perimeter of rectangle = 2x(length + width)
According to the question,
Hence,
Width = 9cm
Length = 18cm
What is the simplified form of the following expression? (n5)(n2)
1 answer:
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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)
Answer:
So, the arc length is
Step-by-step explanation:
We are given
diameter =36m
so, we can find radius
and angle as
Since, it is in degree
so, we can change it in radian
now, we can find arc length
now, we can plug values