The area bounded by the 2 parabolas is A(θ) = 1/2∫(r₂²- r₁²).dθ between limits θ = a,b...
<span>the limits are solution to 3cosθ = 1+cosθ the points of intersection of curves. </span>
<span>2cosθ = 1 => θ = ±π/3 </span>
<span>A(θ) = 1/2∫(r₂²- r₁²).dθ = 1/2∫(3cosθ)² - (1+cosθ)².dθ </span>
<span>= 1/2∫(3cosθ)².dθ - 1/2∫(1+cosθ)².dθ </span>
<span>= 9/8[2θ + sin(2θ)] - 1/8[6θ + 8sinθ +sin(2θ)] .. </span>
<span>.............where I have used ∫(cosθ)².dθ=1/4[2θ + sin(2θ)] </span>
<span>= 3θ/2 +sin(2θ) - sin(θ) </span>
<span>Area = A(π/3) - A(-π/3) </span>
<span>= 3π/6 + sin(2π/3) -sin(π/3) - (-3π/6) - sin(-2π/3) + sin(-π/3) </span>
<span>= π.</span>
Step-by-step explanation:
This is a right triangle with two congruent angles. so this is a isoceles right triangle or called a
45-45-90 triangle. This means that the legs are equal to each other so
Answer:
You will get 500g of sugar syrup.
I already answered this question.
You can get the answer by taking mass/mass% = 350/x
75/100 = 350/x
Therefore x = 500g of sugar syrup
Answer:
4:7
Edit: I just saw the multiple choice options, in this case the right answer is:
<h2>
8:14</h2>
but they're both equal
Step-by-step explanation:
The ratio you are looking for is
freestyle laps : (freestyle + butterfly) laps
so:
8 : (6+8)
8:14
Divide by 2 to simplify
4:7
