# Quiz: Random Problems 01 (Easy)

# 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)

# 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

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

# 01 Area Enclosed by r = 2a cos^2 θ

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

# 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.