CPhill

Pizza Pie Problem: You and your two friends have purchased a pizza of radius "r" and you wish to divide it into three equal pieces by making vertial cuts similar to the ones shown below - obvously one of the cuts  is in the center.....when you find one more, you'll have the problem solved!!! (Note: The illustration indicates a radius of 3 , but the actual radius doesn't matter, since all circles are similar.)  The question is: Where should the cuts be made??

Your answer could be in terms of "r," or in terms of some angle "theta."  You might also consider letting the exact center of the pizza be (0,0).  Hint: The problem CAN  be solved with calculus, but trig will work, too - I've done it both ways - if I remember correctly. Also.......I believe you'll need a "solver" to "finish" your answer out......you will know when you have reached that point!!

Good luck!!

.....Hungry.......

OK, seriously....we have

$50(1.18) =   $59.00

OK...so basically...one angle is 2.5 times as large as the other. Let's call the smaller angle "x" and the larger angle "2.5x."  And since they're complementary, they sum to 90 degrees.

So we have

x + 2.5x = 90

3.5x = 90   So x ≈ 25.7°   and 2.5x ≈ 64.3°

And

25.7° + 64.3° = 90°

Let's divide these first, before we take any roots...so we have

(24x^5y^2) / (3x^2y) =

8*x^3*y  and taking the cubed root, we get

(8*x^3*y)^(1/3)  =   2x(y)^(1/3) .......... so, only "y" remains under the cubed root.

[Note that we are implying that neither x nor y = 0 in the division !!]

OK...let's call the number of boxes he bought holding 7 cards, x. And let's call the number of boxes he bought holding 9 cards, y.

So we have

x + y = 17    (A)

And , the number of cards in each box type, times the number it holds added together = 135 

So we have

7x + 9y = 135   and

x +  y   =   17      By multiplying the bottom equation on both sides by -7, we can "eliminate" x. So we have

7x + 9y =    135 

-7x - 7y =  -119    And we get

2y = 16   So

y  = 8      And substituting this into (A), we have

x + 8 = 17   

So x  = 9

So he bought 9 boxes of 7 cards and 8 boxes of 9 cards = 135 cards

Nice graph, Melody......do you use a website app to produce it??

Assuming we have a "2D" vector in some form like ..... ai + bj.....  or......<a, b>

We have

√(a² + b²) = Magnitude

For a "3D" vector .....ai + bj + ck, we have

√(a² + b² + c²) = Magnitude

Only the Shadow knows.............

I think we should call it :

Imperial

Minims

Mutual

Admiration

Day

Otherwise known as   "I'M  MAD"