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>
68>6t+4 when ever the number is per something(the 6) you put the variable with it and 4 is the constant
t>16
Step-by-step explanation:
3x(x2 + 2x – 6) + 4(x2
– 6x + 2)
Hey there!
The word sum usually means addition in mathematics!
27 + (-28) / 2
= 27 - 28 / 2
= -1 / 2
= -0.5
Answer: -1/2 OR -0.5 (either those should work because they are both equivalent)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Reason a) Alternate interior angles of parallel lines are congruent.
Statement b) Line RQ is congruent to line RQ.
Statement c) Angle PRQ is congruent to angle SQR.
Reason d) ASA Postulate
