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CPhill's Challenge - Sphere Packing Problem
Burning The Candle At Both Ends.....
+80983 +80983 +80983 #1 +80983 1. This is a "thinking" problem. For every fifth part of the tank that is filled, 1/12th of it is being drained away. In effect, the draining is retarding the filling.
So we have: (The portion of the tank being filled per hour) * (time it takes to fill) = (whole tank filled)
In math terms this equates to: (1/5 - 1/12) * X = 1
So we have: (7/60) * X = 1
I'll let you finish this one......just solve for X......your answer will be in hrs.
2. This is a trig problem. We have a triangle whose opposite side is 12 and whose hypotenuse is 24. To find the incline angle, take the sine inverse of 12/24.
3.If the wife gets 1/2 and the daughter gets 1/8, the son gets what's left = 3/8. Then, 3/8 of the estate is 30000.
Let X be the total amount of the estate.
In math terms, we have............. 3/8 * X = 30000
Again, I'll let you finish this one for yourself.
4. Since it rained 7 days out of 30, the probability it rained on any one day is just......... 7/30.
5. The letters don't matter. The first digit is a non-zero number and the other two digits can be any digit from 0-9 inclusive.
So, the possible numbers are from 100 - 999 inclusive. We have 900 of these......... (999-100+1)
So, the total numbers that are 400 or greater = (999-400+1) = 600
Therefore, the probability that a number is greater than 400 is just 600/900 = 2/3.
Hope that helps......good luck!!
#2 +80983 Mmmmm....we have a dilemma here. If I take the cos inverse of (-32/40), I get about 143 degrees. But, if I take the sin inverse of ( 35/40), I get about 61 degrees.- or an angle of about 119 degrees, since the angle is in the second quadrant.
The other problem is that the hypotenuse = 40. But, SQRT((-32)^2 + (35)^2) = about 47.72. So, one hypotenuse is greater than the other.
Check your problem, ara, and see if your numbers are correct. (The sin and cos inverses of your original problem produce different angles, too)
As Melody said before, someone else is free to check any flaws in my logic!!