So to find the answer you want to isolate the y. So the first thing you want to do is to move everything to the opposite side of the = sign. You start by adding 10 to both sides.
10+ 5y -10 = -25 +10
5y = -15.
the tens cancel out on the left side and on the right you get left with -15/
Since y is being multiplied by 5 you always want to do the opposite so you divide by 5.
5y/5 = -15/5
y = -3
It's hard to explain but you just have to remember that what you do to one side you must do to the other to keep the equation balanced.
LFX=AZQ
XLF=QAZ
FXL=ZQA
XFL=QZA
The answer is either a or d but we know she did all of this for more than 52 minutes.
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>
