Quiz: Random Problems 01 (Easy)

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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

 

08 - Sound of Impact be Heard Before the Report of the Gun

Problem
A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.
 

05 - Sum and Difference of Two Numbers Multiplied to Sum and Difference of Their Squares

Problem
Find two numbers such that their sum multiplied by the sum of their squares is 5500, and their difference multiplied by the difference of their squares is 352.
 

07 - A Man Covers an Unknown Distance at Different Rates

Problem
A man covers the distance A to B in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from B to A, by traveling 1 km/hr faster than during the first half of his trip from A to B, he consumed 3-3/4 hours. Determine the distance AB.
 

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