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>
I can help you round 206834 and 194268 to its nearest thousands place. 207000 would be the estimate for the first number and 194000 would be the estimate for the second number.
Answer:
A=πr(r+h2+r2)
Step-by-step explanation:
literally just search it up
Answer:
48 questions.
Step-by-step explanation:
x is for the unknown variable, the number you are trying to figure out.
12= 25%x
if you convert to a fraction, 12 is 1/4 of x. if you then multiply your answer by 4, 12 is 25% of 48.
to figure this out you can also ask, 12 is 25% of what number?
