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q=9r^(2)+16s^(2)r^(2) Which of the following equations correctly expresses r in terms of q and s ? Choose 1 answer: (A) r=+-(sqrtq)/(3+4s) (B) r=+-sqrt((q)/(9+16s^(2))) (c) r=+-sqrt((q)/(25s^(2))) (D) r=+-(sqrt(q-16s^(2)))/(3)

q=9r2+16s2r2 q=9 r^{2}+16 s^{2} r^{2} \newlineWhich of the following equations correctly expresses r r in terms of q q and s s ?\newlineChoose 11 answer:\newline(A) r=±q3+4s r= \pm \frac{\sqrt{q}}{3+4 s} \newline(B) r=±q9+16s2 r= \pm \sqrt{\frac{q}{9+16 s^{2}}} \newline(C) r=±q25s2 r= \pm \sqrt{\frac{q}{25 s^{2}}} \newline(D) r=±q−16s23 r= \pm \frac{\sqrt{q-16 s^{2}}}{3}

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Full solution

Q. q=9r2+16s2r2 q=9 r^{2}+16 s^{2} r^{2} \newlineWhich of the following equations correctly expresses r r in terms of q q and s s ?\newlineChoose 11 answer:\newline(A) r=±q3+4s r= \pm \frac{\sqrt{q}}{3+4 s} \newline(B) r=±q9+16s2 r= \pm \sqrt{\frac{q}{9+16 s^{2}}} \newline(C) r=±q25s2 r= \pm \sqrt{\frac{q}{25 s^{2}}} \newline(D) r=±q−16s23 r= \pm \frac{\sqrt{q-16 s^{2}}}{3}
  1. Given Equation: We start with the given equation:\newlineq=9r2+16s2r2q = 9r^2 + 16s^2r^2\newlineOur goal is to solve for rr in terms of qq and ss.
  2. Combine Like Terms: Combine like terms by factoring out r2r^2: q=r2(9+16s2)q = r^2(9 + 16s^2)
  3. Isolate r2r^2: Divide both sides by (9+16s2)(9 + 16s^2) to isolate r2r^2:\newliner2=q(9+16s2)r^2 = \frac{q}{(9 + 16s^2)}
  4. Solve for rr: Take the square root of both sides to solve for rr. Remember that taking the square root gives us both the positive and negative solutions:\newliner=±q(9+16s2)r = \pm\sqrt{\frac{q}{(9 + 16s^2)}}
  5. Compare with Options: Now we compare the result with the given options to find the correct one. The correct expression that matches our result is:\newliner=±q(9+16s2)r = \pm\sqrt{\frac{q}{(9 + 16s^2)}}

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