Question 1189653: Hi, any chance someone could help me out with this problem?
https://drive.google.com/file/d/1VjNtgtaZvxc99w-Ig2_eRBl6guaa_qrw/view?usp=sharing
Found 3 solutions by Theo, math_tutor2020, MathLover1:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is e(m) = (10^1.5)^m.
e(m) is the energy in kilowatt hours.
m is the magnitude.
(8a)
formula is e(9) = (10^1.5)^9 = 10^(1.5*9) = 3.16227766 * 10^13.
round to 3.2 * 10^13.
(8b)
formula is e(6.9) = (10^1.5)^6.9 = 10^(1.5*6.9) = 2.238721139 * 10^10.
round to 2.2 * 10^10.
(8c)
(3.16227766 * 10^13) / (2.238721139 * 10^10) = 1412.537545.
round to 1413.
(8d)
earthquake released 3,981,000 kilowatts of energy.
formula of e(m) = (10^1.5)^m becomes:
3,981,000 = (10^1.5)^m = 10^(1.5*m)
take the log of both sides of the equation to get:
log(3,981,000) = log(10^(1.5*m))
this becomes:
log(3,981,000) = 1.5 * m * log(10) which becomes:
log(3,981,000) = 1.5 * m
solve for m to get:
m = log(3,981,000) / 1.5 = 4.399994785.
round to 4.4.
let me know if you have any questions.
theo
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
Part A
Plug in M = 9.0 into the formula given
E(M) = (10^1.5)^M
E(9) = (10^1.5)^9
E(9) = (31.6227766016838)^9
E(9) = 31,622,776,601,683.9
E(9) = 32,000,000,000,000
E(9) = 3.2 * 10^13
Roughly 32 trillion kWh of energy was released.
Answer: 3.2 * 10^13 kWh
==============================================
Part B
This time we'll plug in M = 6.9
E(M) = (10^1.5)^M
E(6.9) = (10^1.5)^6.9
E(6.9) = (31.6227766016838)^6.9
E(6.9) = 22,387,211,385.6834
E(6.9) = 22,000,000,000
E(6.9) = 2.2 * 10^10
Roughly 22 billion kWh of energy was released.
Answer: 2.2 * 10^10 kWh
==============================================
Part C
Divide the results of parts A and B
A/B = (3.2 * 10^13)/(2.2 * 10^10)
A/B = 1,454.54545454546
A/B = 1455
Answer: Roughly 1455 times greater
==============================================
Part D
Unlike parts A and B, we don't know what M is.
But we do know that E(M) = 3,981,000 kWh.
We'll plug this in to find M.
You'll need to use logarithms.
E(M) = (10^1.5)^M
3,981,000 = (10^1.5)^M
3,981,000 = (31.6227766016838)^M
log(3,981,000) = log( (31.6227766016838)^M )
log(3,981,000) = M*log( 31.6227766016838 )
M = log(3,981,000)/log( 31.6227766016838 )
M = 4.39999478505607
M = 4.4
The magnitude on the Richter Scale is roughly a 4.4
If you were to plug M = 4.4 into the formula given, then,
E(M) = (10^1.5)^M
E(M) = (31.6227766016838)^M
E(4.4) = (31.6227766016838)^4.4
E(4.4) = 3,981,071.70553498
E(4.4) = 3,981,072
which isn't too far off the mark of the figure 3,981,000
Answer: Magnitude 4.4
Answer by MathLover1(20849)  (Show Source):
|
|
|
