the seismic waves of a magnitude 6 earthquake are 10 squared times as great as a magnitude 4 earthquake. The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake. How many times as great are the seismic waves of a magnitude 6 earthquake as those of a magnitude 3 earthquake? Write as a monomial
let magnitude 3 be represented by c
then maginitude 4 would be 10c
and magnitude 6 would be 10^2 x 10c = 1000c
it would be 1000 times as great.
To find the ratio of the seismic waves of a magnitude 6 earthquake to a magnitude 3 earthquake, we can follow these steps:
1. The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake.
2. The seismic waves of a magnitude 6 earthquake are 10 squared times as great as a magnitude 4 earthquake.
Let's calculate the ratio:
Magnitude 6 earthquake / Magnitude 4 earthquake = (10^2) / 10 = 100 / 10 = 10
Magnitude 4 earthquake / Magnitude 3 earthquake = 10 / 1 = 10
Magnitude 6 earthquake / Magnitude 3 earthquake = (Magnitude 6 earthquake / Magnitude 4 earthquake) * (Magnitude 4 earthquake / Magnitude 3 earthquake) = 10 * 10 = 100
Therefore, the seismic waves of a magnitude 6 earthquake are 100 times as great as a magnitude 3 earthquake.
The ratio can be written as a monomial: 100
To find out how many times greater the seismic waves of a magnitude 6 earthquake are compared to those of a magnitude 3 earthquake, we need to multiply the ratios of each step.
Given information:
- The seismic waves of a magnitude 6 earthquake are 10² (or 100) times as great as a magnitude 4 earthquake.
- The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake.
To determine the overall ratio, we multiply these ratios together:
100 * 10 = 1000
Therefore, the seismic waves of a magnitude 6 earthquake are 1000 times greater than those of a magnitude 3 earthquake.
In monomial form, this can be written as:
1000x
where "x" represents the seismic waves magnitude 3 earthquake.