Melody08
contestada

Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.
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Respuesta :

m4rcus06

Answer:

Above is the step-by-step solution

Ver imagen m4rcus06

[tex]\\ \sf\longmapsto p\propto q [/tex]

[tex]\\ \sf\longmapsto p=kq[/tex]

  • Divide both sides by q

[tex]\\ \sf\longmapsto \dfrac{p}{q}=k[/tex]

[tex]\\ \sf\longmapsto q=\dfrac{p}{k}[/tex]

Now

[tex]\\ \sf\longmapsto p\propto \sqrt{q}[/tex]

[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^2}[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{k}{t^2}[/tex]

  • Substitute√q

[tex]\\ \sf\longmapsto \sqrt{q}=\dfrac{k}{t^2}[/tex]

[tex]\\ \sf\longmapsto q=\dfrac{k^2}{t^4}[/tex]

  • Substitute q=p/k

[tex]\\ \sf\longmapsto \dfrac{p}{k}=\dfrac{k^2}{t^4}[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{k}{t^4}[/tex]

[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^4}[/tex]

Done

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