### Video Transcript

𝑣 is inversely proportional to
𝑡. When 𝑡 equals four, 𝑣 equals
7.5. Find the value of 𝑣 when 𝑡 is
equal to 10.

As 𝑣 is inversely proportional to
𝑡, as 𝑡 gets bigger, 𝑣 gets smaller and vice versa. We can write this as 𝑣 is
proportional to one over 𝑡 or one divided by 𝑡. The inverse of 𝑡 is one over
𝑡. This can be rewritten as 𝑣 is
equal to 𝑘 divided by 𝑡, where 𝑘 is the constant of proportionality that we can
calculate.

Substituting 𝑡 equals four and 𝑣
equals 7.5 into this equation gives us 7.5 is equal to 𝑘 divided by four. Multiplying both sides of this
equation by four gives us a value of 𝑘 equal to 30 as 7.5 multiplied by four equals
30. Substituting this value of 𝑘 back
into the equation gives us 𝑣 is equal to 30 divided by 𝑡.

We can now use this equation to
work out the value of 𝑣 for any corresponding value of 𝑡. In this case, we are asked to find
the value of 𝑣 when 𝑡 is equal to 10. 30 divided by 10 is equal to
three. Therefore, the value of 𝑣 when 𝑡
equals 10 is 𝑣 equals three.

We can see that when the value of
𝑡 increases, the value of 𝑣 decreases as they are inversely proportional to each
other.