$t$ is inversely proportional to $w$.
$t=9$ when $w=8$
a) Use the information above to write an equation for $t$ in terms of $w$.
b) What is the value of $t$ when $w=5$ ?
Give any decimal answers to 1 d.p.
\(\boxed{\text{b) The value of } t \text{ when } w=5 \text{ is } 14.4\)}
Step 1 :Given that $t$ is inversely proportional to $w$, we can write the equation as $t = \frac{k}{w}$, where $k$ is a constant of proportionality.
Step 2 :We are given that $t=9$ when $w=8$. We can use this information to find the value of $k$.
Step 3 :\(9 = \frac{k}{8}\)
Step 4 :\(k = 9 \times 8 = 72\)
Step 5 :Now that we have the value of $k$, we can write the equation for $t$ in terms of $w$ as $t = \frac{72}{w}$.
Step 6 :Next, we need to find the value of $t$ when $w=5$.
Step 7 :\(t = \frac{72}{5} = 14.4\)
Step 8 :\(\boxed{\text{a) The equation for } t \text{ in terms of } w \text{ is } t = \frac{72}{w} \text{.}}\)
Step 9 :\(\boxed{\text{b) The value of } t \text{ when } w=5 \text{ is } 14.4\)}