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That’s actually wrong sooooo.

2325341154

But f(9)=f(9) and f(5)=f(5)... not really understanding what you mean ://

Your question makes no sense. 

1 - M = 2/3 log_10((8×10^14)/(1×10^4.4)) =~7 - Magnitude on the Richter scale.

2 - solve 5.9 = 2/3 log_10(P/(1×10^4.4)) for P

P = 1.77828×10^13 - Joules - the amount of energy released in a 5.9 Magnitude earthquake.

Slope = rise/run =   100/-50 = -2

Distance = sqrt (100^2 + 50^2) = 111.8 units

Oh ok lol

That is a nice alternate explanation Chris.  

It is more technical than mine which is a good thing, maybe it will help people understand the notation.   

Oh I'm in fifth grade so lol

No that is not correct.

Average rate of change from x=5 to x=9 is

\(\frac{f(9)-f(5)}{9-5}   \)

What is f(9) ?      What is f(5) ?    Look at the table. 

No one answer over the top of me please.  I'm trying to teach.

OK.....!!!

What do you want???

The slope between the points??

The equation of a line through the points???

Thanks, CPhill!!!

Second one

Don't get intimidated, here   !!!

f(64) = -∛ 64  =  -4

f(8) =  - ∛ 8   =   -2

So

Avg rate of change from x = 8 to x = 64   is given by :

[ f(64) - f(8)]           -4 - (-2)             -2               -1

_________  =        ______   =       ___    =      ___

      64 - 8                   56                56               28

I will give you a very big hint:

the denominator is of the from    x^2+x+1 where   x=cube root of 3

AND

(x-1)( x^2+x+1) = x^3-1

You need to rationalize the denominator.

Please no one answer over the top of me - I am trying to help guest learn!

First one

f(2)  = Ln (3*2) + 2.5   =   Ln (6) + 2.5

f(7) = Ln (3*7) + + 2.5  =  Ln ( 21) + 2.5

Avg rate of change  from   2 to 7 =

[ f(7) - f (2)]          [  (Ln(21 + 2.5) - (Ln(6) + 2.5) ]             Ln(21) - Ln(6)

__________  =   _________________________   =       ___________   ≈  0.25

    7 - 2                                 5                                                   5

We can write this as

[ b(a + c) + ca ] ¹²

We have .....

C( 12, 1) * [ b ( a + c)]¹¹ * (ca)¹   =

(12)b¹¹ * (a + c)¹¹ * a¹ c¹  =

(12)acb¹¹ * (a + c)¹¹  =

(12)acb¹¹ *  C(11,3) (a)⁸ * c³  =

(12) acb¹¹ * (165)a⁸ c³  =

1980  a⁹ b¹¹  c⁴

I'm asking because I am, and I've seen this problem or a binomial theorem problem similar to this before since Im in Honors Alg 2 :) So I'm just wondering if you are.

wdym?

(f / g) (x)   =   f(x) / g(x)  =

 2x^2 -5x - 3             (2x + 1) (x - 3)                 x - 3

____________  =    ____________   =        ______           { x not equal to 0 or -1/2 }

 2x^2  +  x                 x (2x + 1)                          x

   {{

Thanks !!!!

Hey, forgive me for asking but are you a K¹² student?

(fg)(x)  =  f(x) * g(x) =

(2x^2 - 3) ( x + 4) =

2x^3  + 8x^2 - 3x - 12  

Yah....you are correct...that was a typo

uW = micro watt

i. Since the amount of energy, E in this instance, is 8* 10^14, just plug 8*10^14 into (E/E_0). Then 8*10^14 / 10^4.4 would get you the right side of the equation. After that, calculating the magnitude would mean 2/3 log 31848573644.3(according to google calculator, but don't trust me on this one, I'd recommend you find some way to calculate it). solving 2/3 log 31848573644.3 you get 7.00205999133(I'd really recommend a calculator for this one).

ii. lol I can't solve it rn, since I'm on a car, but I'd imagine that you would do the reverse of #1, as you know that M is 5.9, and you already have E_0, so you can write the equation 2/3 log (E * 10^4.4) = 5.9, and from then on, you'd need some knowledge of logs and probably a calculator with u to solve it