Certainly! Let's go through the given problem step-by-step to find [tex]\( m \)[/tex] given the variables [tex]\( h \)[/tex], [tex]\( t \)[/tex], [tex]\( c \)[/tex], and [tex]\( k \)[/tex].
We’re given the following variables:
- [tex]\( h = 1 \)[/tex]
- [tex]\( t = 6 \)[/tex]
- [tex]\( c = 3 \)[/tex]
- [tex]\( k = 2 \)[/tex]
We need to make [tex]\( m \)[/tex] the subject of the formula given:
[tex]\[
t = \frac{k m^2 L}{t^2}
\][/tex]
Given that [tex]\( L = c \)[/tex], we can substitute [tex]\( L \)[/tex] with [tex]\( c \)[/tex]:
[tex]\[
t = \frac{k m^2 c}{t^2}
\][/tex]
First, let's isolate [tex]\( m^2 \)[/tex] on one side of the equation. Multiply both sides by [tex]\( t^2 \)[/tex] to get rid of the fraction:
[tex]\[
t^3 = k m^2 c
\][/tex]
Next, solve for [tex]\( m^2 \)[/tex] by dividing both sides by [tex]\( k c \)[/tex]:
[tex]\[
m^2 = \frac{t^3}{k c}
\][/tex]
Finally, solve for [tex]\( m \)[/tex] by taking the square root of both sides:
[tex]\[
m = \sqrt{\frac{t^3}{k c}}
\][/tex]
Now, substitute the given values into the equation:
[tex]\[
m = \sqrt{\frac{6^3}{2 \cdot 3}}
\][/tex]
[tex]\[
m = \sqrt{\frac{216}{6}}
\][/tex]
[tex]\[
m = \sqrt{36}
\][/tex]
[tex]\[
m = 6
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] is [tex]\( 6 \)[/tex].
Thus, the result is:
- [tex]\( h = 1 \)[/tex]
- [tex]\( t = 6 \)[/tex]
- [tex]\( c = 3 \)[/tex]
- [tex]\( k = 2 \)[/tex]
- [tex]\( m = 6 \)[/tex]
