CPhill

16000(1 +.008)^300 = about   174694.65   (dollars  ???)

Call x one side of the rectangle......then the adjacent side will be (Phi)x

And the diameter of this circle will  = 20cm    ......and by the Pythagorean Theorem, we have.......

x ^2  +  [(Phi)x]^2  = 400

x^2 [ 1 + (Phi)^2]  = 400      and we can note that Phi^2  =  1 + Phi.......so we have

x^2 ( 1 + 1 + Phi)  = 400

x^2 (2 + Phi )  = 400

x^2  =   400 / (2 + Phi)        take the  positive square root of both sides

x = 20 / √(2 + Phi) 

So....the area of this rectangle  = (20/√(2 + Phi))* (Phi * 20/ √(2 + Phi) ) = 400Phi / (2 + Phi)  = about

178.88 cm^2

The area of the triangle at the base = (1/2)(10)(24)  = 120 cm^2

And the remaining side of the triangle  = √[24^2 + 10^2] = √676  = 26 cm

So we have......

Sa  = 2(120) + h(24 + 10 + 26)  = 2640    simplify

240 + h(60) = 2640 

h(60) = 2400   

h = 40 cm

And the volume is just ......   area of the base * height   =  120 (40)   = 4800 cm^3

Yeah, Melody......I like yours better........we don't have to split the sums that way.......

    43₆                         

     x 51₆                         

   --------

       43

     343

    ------

   3513₆

We have two sums to consider.....

2*3^(-1) + 2*3^(-3) + 2*3^(-5)+ ....+2*3^-(2n-1)  =  (2/3) /(1 - 3^(-2)) = (2/3) / (1 - 1/9)  =

(2/3)/(8/9)  = (2/3)*(9/8)  = 18/24 = 3/4   ...... and...... 

3^(-2) + 3^(-4) + 3^(-6) + ....+ 3^-(2n)  =  (1/9) / (1 - 3^(-2))  = (1/9)/ ( 1 - 1/9)  = (1/9)/(8/9) =

(1/9) * (9/8)  =  9/72  = 1/8

So .......  3/4 + 1/8  =  6/8 + 1/8 =  7/8

Let's just divide, here......

5 / 1.5    = 10/3  batches of 15  =  50 cookies 

4 / 1.25  = 32/10 batches of 15  =  48 cookies

1.75 / .5 = 35/10  batches of 15  =  52.5 cookies

He could bake 48 cookies, at most........

Nice answer, Melody.....

BTW....I think Melody meant to write.......  3(81) + 5    =  243 + 5  = 248

That's a nice approach and nice thinking, Melody....