CPhill

Very nice, rosala....!!!

e^xy  = x + y    

Using implicit differentiation, we have

ye^xy + xy'e^xy  = 1 + y'

y' ( xe^xy - 1) = 1 - ye^xy

y' = [ 1 - ye^xy  ] / [ xe^xy - 1]  

{The volume has to be in cubic, not square, inches }

So we have

45 pi = pi (5)(r^2)  divide both sides by pi

45 = 5 r^2     divide by 5

9= r^2       take the square root of both sides

3 = r

The volume of the bottom tier is

5in x 9in x 2 in  = 90 in^3

And the volume of the top tier is

5in x 5in x 2in  =  50 in^3

So the total volume is (90 + 50) in^3 = 140 in^3

The term "tonnage" doesn't make sense here.....I assume you want to know the "volume"

We just need to convert the inches to meters

We have

3in x 1m/39.37in = (3/39.37)m 

So the total volume is given by

330m x 3m x (3/39.37)m = 68.58m^3

The interest on this is given by

I = Prt     

Here  P = $4000  r = 5% = .05   and t = 2 years 3 months = 2.25 years

So we have

I = 4000(.05)(2.25) = $450

So the total value is  $4000 + $450 = $4450

4 lb 12 oz  + 7lb 11 oz

Adding the ounces we have 11 + 12 = 23 oz

And since there are 16 ounces in one pound, this equals 1 lb 7 oz

And adding back the rest, we have

4 lb + 7lb + 1 lb + 7 oz  =

12 lbs 7 oz

Melody actually didn't  quite carry her calculations far enough.

We have

(n-3)(n-2)(n-1)n ≥ 8760

n⁴ - 6n³ + 11n² - 6n  ≥ 8760

Using WolframAlpha  ...we get the following  (somewhat messy) solution....

n  ≥ (3/2)  + (1/2)* sqrt(5 + 4√8761) =

n  ≥  about 11.239

Which confirms that we need more than 11.... (which means 12)

Her way is actually superior to my "guess and check" approach....!!!

But.....as she always says..."All roads lead to Rome"

If he combined them all.....there would be 1....

{It's an old joke....}

The square has equal sides and all vertex angles are right angles.

The rhombus has equal sides, and pairs of consecutive vertex angles angles are supplementary, but not right angles. And each pair is equal to the other.