find n and m
W=F^n d^m
find n
a=r^0v^n
verify if they are equal to each other
mgh=1/2mv^2
To find n and m in the given expressions, we need to apply algebraic techniques and solve for the variables.
1. W = F^n * d^m
To find n, we can take the logarithm of both sides of the equation and use the logarithmic rules to simplify:
log(W) = log(F^n * d^m)
log(W) = log(F^n) + log(d^m)
log(W) = n*log(F) + m*log(d)
n = (log(W) - m*log(d)) / log(F)
2. a = r^0 * v^n
To find n, we can rewrite the expression as follows:
a = 1 * v^n
n = log(a) / log(v)
To verify if the two expressions are equal to each other, we need to set them equal and solve for the variables.
For the given equation: mgh = 1/2mv^2
We can rewrite it as:
2mgh = mv^2
Dividing both sides by m, we get:
2gh = v^2
Taking the square root of both sides, we have:
v = sqrt(2gh)
Now we can substitute this value of v into the second equation and solve for n:
a = r^0 * sqrt(2gh)^n
a = 1 * (2gh)^n
Taking the logarithm of both sides:
log(a) = n * log(2gh)
n = log(a) / log(2gh)
To summarize:
1. n = (log(W) - m*log(d)) / log(F)
2. n = log(a) / log(v)
3. Calculate the value of v using v = sqrt(2gh)
4. n = log(a) / log(2gh)
Plug in the given values of W, F, d, a, r, g, and h into the respective equations to get the numerical values of n and m.