Given that p varies directly as q and √(q) varies inversely with t², show how p varies with t. ​

Question

Given that p varies directly as q and


`√(q)`
varies inversely with t², show how p varies with t.
​

Answer 1

Above is the step-by-step solution

Answer 2

`\\ \sf\longmapsto p\propto q`

`\\ \sf\longmapsto p=kq`

• Divide both sides by q

`\\ \sf\longmapsto (p)/(q)=k`

`\\ \sf\longmapsto q=(p)/(k)`

Now

`\\ \sf\longmapsto p\propto √(q)`

`\\ \sf\longmapsto p\propto (1)/(t^2)`

`\\ \sf\longmapsto p=(k)/(t^2)`

• Substitute√q

`\\ \sf\longmapsto √(q)=(k)/(t^2)`

`\\ \sf\longmapsto q=(k^2)/(t^4)`

• Substitute q=p/k

`\\ \sf\longmapsto (p)/(k)=(k^2)/(t^4)`

`\\ \sf\longmapsto p=(k)/(t^4)`

`\\ \sf\longmapsto p\propto (1)/(t^4)`

Done