Given that p=2q and 2r=3q. Express 2pr2 interms of p only
2pr^2 = 2(2q)(3q/2)^2 = 9q^3 = 9(p/2)^3 = 9/8 p^3
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To express 2pr² in terms of p only, we first need to eliminate the variables q and r.
Given that p = 2q, we can rewrite the equation 2r = 3q in terms of p:
2r = 3q
2r = 3(2p) (substituting p = 2q)
2r = 6p
Now, we have two equations:
p = 2q
2r = 6p
We can solve these two equations simultaneously to eliminate q and r in terms of p.
From p = 2q, we can rearrange it to get q = p/2.
We can substitute q = p/2 into the equation 2r = 6p:
2r = 6p
2r = 6(p/2) (substituting q = p/2)
2r = 3p
Now, we have eliminated q from the equations.
To express 2pr² in terms of p only, we substitute the values we found for q and r into the expression:
2pr² = 2(p/2)(3p²)
2pr² = 2(p/2)(3p²)
2pr² = p(3p²)
2pr² = 3p³
Therefore, 2pr² expressed in terms of p only is 3p³.