SOLUTION: Hi, any chance someone could help me out with this problem?
https://drive.google.com/file/d/1VjNtgtaZvxc99w-Ig2_eRBl6guaa_qrw/view?usp=sharing
Algebra.Com
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): You can put this solution on YOUR website!
given: the magnitude earthquake
in scientific notation
b.
an earthquake of magnitude
in scientific notation
c. how many times greater was the energy that was released in British Columbia than the Northwest Territories?
times
d.
given:
Find the magnitude
.......take log of both sides
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