Quiz: Random Problems Set 2

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Quiz: Random Problems Set 3

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Quiz: Random Problems Set 4

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Quiz: Random Problems Set 1

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03 Area Enclosed by Cardioids: r = a(1 + sin θ); r = a(1 - sin θ), r = a(1 + cos θ), r = a(1 - cos θ)

Problem
Find the area individually enclosed by the following Cardioids:
(A)   $r = a(1 - \cos \theta)$
(B)   $r = a(1 + \cos \theta)$
(C)   $r = a(1 - \sin \theta)$
(D)   $r = a(1 + \sin \theta)$
 

003-cardioid-neg-pos-sine-cosine.gif

 

Two Gamblers Play Until One is Bankrupt: Chance That the Better Player Wins

Problem
Player M has Php1, and Player N has Php2. Each play gives one the players Php1 from the other. Player M is enough better than player N that he wins 2/3 of the plays. They play until one is bankrupt. What is the chance that Player M wins?

A.   3/4 C.   4/7
B.   5/7 D.   2/3

 

08 Area Enclosed by r = a sin 3θ and r = a cos 3θ

Problem
Find the area bounded by $r = a \sin 3\theta$ and $r = a \cos 3\theta$.
 

008-polar-area-three-leaf_rose_sine_cosine.gif

 

05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

Problem
Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.
 

008-polar-area-four-leaf_sine_cosine.gif

 

01 Area Enclosed by r = 2a cos^2 θ

Problem
Find the area enclosed by r = 2a cos2 θ.
 

004-polar-area-two-leaf-rose-integration.gif

 

07 Area Enclosed by r = 2a cos θ and r = 2a sin θ

Problem
Find the area enclosed by the following:

(a)   $r = 2a \cos \theta$
(b)   $r = 2a \sin \theta$

 

001-polar-area-circle_01.gif

 

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