Question

Help with Answer to question 4 part a & b

Answer 1

Given,

a) The value of g is 18 when t is 3.

It is given that g is directly proportional to t.

According to the question,

`\begin{gathered} g\propto t \\ g=kt \end{gathered}`

Here, k is proportionality constant.

Substitutitng the value of t and g in the above expression then,

`\begin{gathered} 18=k(3) \\ k=(18)/(3) \\ k=6 \end{gathered}`

The value of g when t is 5,

`\begin{gathered} g=kt \\ g=6*5 \\ g=30 \end{gathered}`

Hence, the value of g is 30 when t = 5.

b)The value of z is 5 when the value of r is 4.

It is given that z is inversely proportional to r+3.

According to the question,

`\begin{gathered} z\propto(1)/(r+3) \\ z=(k)/(r+3) \end{gathered}`

Here, k is proportionality constant.

Substitutitng the value of t and g in the above expression then,

`\begin{gathered} 5=(k)/(4+3) \\ 5=(k)/(7) \\ k=5*7 \\ k=35 \end{gathered}`

The value of r when z is 9,

`\begin{gathered} z=(k)/(r+3) \\ 9=(35)/(r+3) \\ r+3=(35)/(9) \\ r=(35)/(9)-3 \\ r=(35-27)/(3) \\ r=(8)/(3) \end{gathered}`

Hence, the value of r is 8/3 when z=9.