Answer: Choice C) AA similarity
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We are given that angle ABE = angle ECD since they are both right angles (square marker)
Angle AEB = angle CED as they are vertical angles
we have two pairs of congruent angles, leading us to be able to use the AA (angle angle) similarity theorem
add the two equations together
5a+5b=25
-5a+5b=35
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0 + 10b =60
divide by 10
b=6
5a + 5b = 25
5a +5(6) = 25
5a +30 =25
subtract 30 from each side
5a =-5
divide by 5
a = -1
Answer (-1,6)
or a=-1 b=6
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>
<span>Let x=apples that Andre picks
Then x/3=apples that Maria picks
And 2x=apples that Jane picks
Soooo,
x +(x/3)+2x=840 multiply each term by 3
3x+x+6x=2520 collect like terms
10x=2520
x=252</span>
