--&& Daily Math/Physics Questions Thread &&--

[Mannish]

The three men didn't each pay $9, they collectively paid $25 ($30 minus the $5 the bellhop brings back), or $8.33 each. Splitting the $2 tip between the 3 of them accounts for $0.67. This adds up to $9, and they have $1 remaining of the $10 each they originally contributed.

 

[Mannish]

Softball one

Difficulty: Easy
Category: Calculus

lim {x -> 1} ( x^2 + x - 2 ) / ( x - 1 )

Note: It reads 'limit as x approaches one'.
'^' this symbol signifies exponent. So 'x^2' reads 'x to the 2nd power'.
'/' signifies division. So '3 / 2' reads '3 divided by 2'

L'hopital's Rule states that lim {x -> a} f(x) / g(x) = lim {x -> a} f ' (x) / g ' (x), so differentiating the numerator and denominator we get

lim {x -> 1} (2x + 1) / (1) -> (2*1 + 1) / 1 = 3

 

[TheAnointedOne]

The three men didn't each pay $9, they collectively paid $25 ($30 minus the $5 the bellhop brings back), or $8.33 each. Splitting the $2 tip between the 3 of them accounts for $0.67. This adds up to $9, and they have $1 remaining of the $10 each they originally contributed.

Spoiler

There are many ways of explaining/thinking about this truly brain bending riddle! It all boils down to the fact that the lawyers's math is incorrect.

They did NOT spend $9 • 3 + $2.

They spent exactly $27 dollars. $25 for the room and $2 for the tip. Remember they got exactly $3, in total back.

L'hopital's Rule states that lim {x -> a} f(x) / g(x) = lim {x -> a} f ' (x) / g ' (x), so differentiating the numerator and denominator we get

lim {x -> 1} (2x + 1) / (1) -> (2*1 + 1) / 1 = 3

Correct

 

[TheAnointedOne]

Difficulty: Medium
Category: Geometry

 

[Elle Seven]

Difficulty: Medium
Category: Geometry

Spoiler: Answer

108

 

[TheAnointedOne]

Spoiler: Answer

108

Unfortunately nope.

 

[Elle Seven]

Unfortunately nope.

Really? Ok...I've got to look at this again.

ETA:

Spoiler: Redo

126

 

[Ahadi]

Great thread. Especially if you have kids.

 

[TheAnointedOne]

Really? Ok...I've got to look at this again.

ETA:

Spoiler: Redo

126

Closer but still not correct I'm afraid.

 

[shopthatwrecks]

Closer but still not correct I'm afraid.

Spoiler

135

 

[TheAnointedOne]

Really? Ok...I've got to look at this again.

ETA:

Spoiler: Redo

126

Spoiler

135

 

[Gold]

 

[shopthatwrecks]

 

[Elle Seven]

Closer but still not correct I'm afraid.

 

[Cereal_Bowl_Assassin]

Dope thread