CPhill

I think you forgot about the "front-end" deposits made in years 2 and 3....

At the end of the first year, the account is worth ... (10,000)(1.1) = $11, 000

At the start of the second year....he deposits $10,000 more dollars.....so the account is worth (11000 + 10000)(1.1) = $23,100 at the end of the second year.

At the start of the 3rd year $10,000 is added to this, so the account balance at the end of the third year is just(23,100 + 10000)(1.1) = $36,410

We need to get a common denominator between 25, 30 and 40

25 = 5^2

30 = 2  x 3 x 5

40 = 2^3 x 5

So....the common denomimator = 2^3 x 3 x 5^2  = 8 x 3 x 5 = 24 x 25 =  600

To make the same amount of money from each he would have sold

600/25 apples  = 24 apples

600/30 pears = 20  pears  and

600/40 oranges = 15 oranges

So....20 pears is the fewest that he could have sold if the money he made from selling each type of fruit was equal.......and 20 pears would have cost $6.00

4cot(4x)= 2cot(2x)-2tan(2x) 

4cos(4x)/sin(4x) =

4[cos²(2x) - sin²(2x) ] / [(2cos(2x)sin(2x)] =

2 [( cos²(2x)/cos(2x)sin(2x) ) - sin²(2x)/cos(2x)sin(2x) ] =

2[ cos(2x)/sin(2x) - sin(2x)/cos(2x)]

2 [cot(2x) - tan(2x) ] =

2cot(2x) - 2tan(2x)

And the left side = the right side

(66 - 2^x) / ( 2^x + 3)  = (4 - 2^x) / (2^(x+1) + 6)

The easiest way to solve this is to graph both sides and see if there are any points of intersection

-12=f/0.2   multiply both sides by 0.2

(0.2)(-12) = f = -2.4

Y=1/2x+3 does x=3 and y=4

If x = 3  then y = (1/2)(3) + 3  =  3/2 + 3  = ( 1 + 1/2) + 3  = 4 + 1/2  = 4.5

The largest cube we can use would be 7

And we can pair this with the integers (1 trough 5 cubed)...."6' is too large!!!

So that's 5 numbers right there

And 6 cubed can be paired with integers (1 through 5 cubed) = 5 numbers

And 5 cubed can be paired with (1 through 4 cubed) = 4 numbers, etc.

So we have....

5 +  [ 5(6)/ 2 ] =   5 + 15  = 20 numbers

That was very nice, saseflower......!!!!

Seems easy, doesn't it....????

We would "plug" in a value for x, first, square this, and then multiply this result by - 5.....

Hope that helps