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Just divide 500,000 by 365. You should get around 1369.86 days Wait sorry I submitted twice

Just divide 500,000 by 365. You should get around 1369.86 days

Thanks. I realized I put the question in the wrong place.

We can write

y = [ 2x + 3 ] / [ kx - 2]        isolate x

y [ kx - 2 ] =  2x + 3

(ky)x - 2y = 2x + 3

(ky)x - 2x =  2y + 3

(ky - 2) x =  2y + 3    

x =  (2y + 3) / ( ky - 2)    "swap" x and y

y = (2x + 3) / (kx - 2)  =  the inverse

The inverse is the same as f(x)

So.....k can take on any real value

To find the inverse of f(x), set f(x) = y. Then solve for x in terms of y. 

By doing this I got \(x=\frac{2y+3}{ky-2}\), so \(f^{-1}(x)=\frac{2x+3}{kx-2}\).

This means that \(k\) can be any real number for \(f(x) = f^{-1}(x)\) (as long as \(x\ne\frac{2}{k}\)).

Sorry, how do you do that?

1. You set up a proportion to solve. If you divide 1 tablespoon of cocoa by 0.25 of water, the answer should be the same if you divide x cocoa by 1.5 cups of water.

So you set up the equation.

\(\frac{1}{\frac{1}{4}}=\frac{x}{\frac{3}{2}}\)

2. Then you solve by cross multiplying,

Try it yourself!

1.5 cups of water is just 6 1/4 cups of water. So you will need 6 tablespoons of cocoa. 

The common difference is    -9 - 6 =    - 15

So...the third term would need to be - 24

The common ratio between the second and third terms  is    (-24) /(-9) =  8/ 3

So....the fourth term is    - 24 ( 8/3)  = -64

So....the series is

6 , -9, -24, -64

Eh......a slight mis-statement by me....we have a single root with a multiplicity of 2

So....we actually  have a "double root"....but....it's the same repeated root....

See the graph here :

You can also use infinite series to sum them up:

Sum =F / [1 - R], where F =First term = 1.5, R =Common ratio = 1/6

Sum =1.5/ [1 - 1/6]

Sum =1.5 / (5/6)

Sum =1.5 x 6/5

Sum = 9 / 5.

QS: according to my math book, it says that if the discriminent=0, it has a double root. sooo

21b^x

_____   = 7b^9

n b^3

This implies that 

21 / n = 7    ⇒        n   = 3

And

b^x / b^3 = b^9      means that

b^x = b^9 * b^3

b^x = b^12

x = 12

If we only have a single solution, then the discriminant = 0

So

(-5)^2 - 4(2)(k) = 0

25 - 8k  =  0

25 = 8k     

25 / 8 = k

The polynomial  is  2x^2 - 5x + 25/8

And the  single  root  (solution) to this is   x = 5/4

It depends on how big the chair is. How do you know that the chair seat is the same width as the sofa seats? You need more information.

Thanks CPhill!

Not as tough as it seems, CU

(n + 1) ! + ( n + 2) !   = n! * 440         divide both sides by  n !

(n + 1) !          (n + 2) !

______     +   _______    =     440

   n !                  n !

Note that   the first term simplifies to  ( n + 1)

And the second term simplifies to  ( n + 2) ( n + 1)

So....we really have

(n + 1) + ( n + 2)(n + 1) =  440      factor

(n + 1)  ( 1 + n + 2) = 440

(n + 1) ( n + 3) = 440

We could solve this with the quad formula....but......a little logic might lead to the answer much more quickly

Note that 

20 * 22 =   440

This would imply that n = 19

And the sum of its digits =  10

******

You're not kidding....!!!

If I had to use that Difference Quotient everytime i had to take a derivative....I'd have never made it through Calc I

LOL!!!!