Question 1:
Starting with the equation e=mc^2, we can solve for the speed of light "C" by isolating it on one side of the equation.
First, we can divide both sides of the equation by "m":
e/m = c^2
Then, we can take the square root of both sides of the equation:
√(e/m) = c
So the equation solved for the speed of light "C" is:
c = √(e/m)
Note that we can also use rational exponents to write the equation, as follows:
c = (e/m)^(1/2)
Question 2:
Using the equation we found in Question 1 using rational exponents, we can apply the properties of exponents to simplify the expression:
c = (e/m)^(1/2)
c = [(e^(1/2))/(m^(1/2))]
To rationalize the denominator, we can multiply both the numerator and the denominator by the conjugate of the denominator:
c = [(e^(1/2))/(m^(1/2))] * [(m^(1/2))/(m^(1/2))]
c = (e^(1/2) * m^(1/2)) / m
c = (em)^(1/2) / m
Question 3:
To rewrite the equation without writing it as a fraction, we can start from the original equation e=mc^2 and solve for "c" by dividing both sides by "m" and then taking the square root of both sides:
e/m = c^2
√(e/m) = c
So the equation without writing it as a fraction is:
c = √(e/m)
Question 4:
We can use the equation c = √(e/m) to find the speed of light in meters per second if a 3 kilogram mass of matter converts to 2.7·10^17 J of energy:
c = √(e/m)
c = √((2.7·10^17 J) / (3 kg))
c = √(9·10^16 m^2/s^2)
c = 3·10^8 m/s
Therefore, the speed of light is approximately 3·10^8 meters per second.