CPhill

3, 10, 50, 25     575

(10 x 50 ) +  (3 x 25 ) =

500 + 75  =

575

Volume of the storage room  = 8 x 5 x 2 = 80 cu ft

Volume of each box  = 2.25 x 1.5 x 1 = 3.375  cu ft

So  

80 / 3.375 = about 23 whole boxes

We need to find "r"......this is given by

√[ 8^2 + (-3)^2 ] =  √[64 + 9] = √73

So, the exact value for the sine is :

y / r = -3 / √73

{You could rationalize the denominator if you wanted to.......doesn't really matter }

Yep....I cheated....your method was far more impressive.....!!!!

 This is a GOOD ONE to learn from....!!!!

For every 7  gallons of water in the original mixture, the orange juice concentrate comprises 2 gallons.

So, if this 7 gallons  is mixed with lemonade in a ratio of 3 : 4....there must be  7 x (4/3)  = 28/3  gallons of

lemonade in this mixture.

Then the ratio of orange juice concentrate to lemonade in this mixture is   2  : 28/3    =  6 : 28 =  3 : 14

cos(13 pi/4)  = cos (5 pi / 4)   =  -1 /√2

Amended answer...sorry, Mellie....I realized the answer I gave before was incorrect....

(a) It appears that a constant term will occur when n is a multiple of 3

For instance  

When n = 3, the constant term is 3  =  C(n, [2/3]n) = C(3,2)

When n = 6,  the constant term is 15  = C(6,4)  

When n = 9, the constant term is 84  = C(9,6)

(b) So  ...it appears that the constant term is produced by C(n,[2/3]n)    

This happens because at C(n, [2/3]n ).......x^1  is being raised to the [n - (2/3)n]  = (1/3)n power...and...

x^-1 is being raised to the (2/3)n power....

So   (x^2)^[(1/3)n]  * (x^-1)^[(2/3)n]   =   (x)^(2/3)n  * (x)^(-2/3)n  = 1

And  C(n, [2/3]n) * (1)   =  C(n, [2/3]n )   = a constant

I'm not sure how to do it with unit multipliers, but here's the answer

mm^2   =  mm x mm

And there are 10 mm in each cm

So

cm^2  = cm x cm    =   mm/ 10 x mm/10   =  mm^2 / 100

So   1000mm^2   =  1000/ 100  =  10cm^2