Melody08
Answered

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



Answer :

mhanifa

Answer:

  • p varies inversely with t⁴

Step-by-step explanation:

Direct variation:

  • y = kx, where k is constant

Inverse variation:

  • y = k/x, where k is constant

Given:

  • p = kq   (1)

and

  • √q = k/t²    (2)

From the first equation we can see:

  • kq = p ⇒ q = (1/k)p ⇒ q = np, where n is a constant

It means if p varies directly as q, then q directly varies as p.

Square the second equation:

  • q = k²/t⁴ = m / t⁴, where m is constant

Since p varies directly as q and q varies inversely with t⁴, we can state p varies inversely with t⁴.