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)

Given Equation: We are given the equation q = 9r^2 + 16s^2r^2. To express r in terms of q and s, we need to solve for r.Combine Like Terms: Combine like terms by factoring out r^2 from the terms on the right side of the equation. q = r^2(9 + 16s^2)Isolate r^2: Divide both sides of the equation by (9 + 16s^2) to isolate r^2. r^2 = q / (9 + 16s^2)Take Square Root: Take the square root of both sides to solve for r. Remember that taking the square root gives us both the positive and negative solutions. r = ±√(q / (9 + 16s^2))Compare with Answer Choices: We can now compare the expression we found with the answer choices given in the problem. r = ±√(q / (9 + 16s^2)) matches with option (B).

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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)

$q=9 r^{2}+16 s^{2} r^{2}$ $\newline$ Which of the following equations correctly expresses $r$ in terms of $q$ and $s$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $r= \pm \frac{\sqrt{q}}{3+4 s}$ $\newline$ (B) $r= \pm \sqrt{\frac{q}{9+16 s^{2}}}$ $\newline$ (C) $r= \pm \sqrt{\frac{q}{25 s^{2}}}$ $\newline$ (D) $r= \pm \frac{\sqrt{q-16 s^{2}}}{3}$

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Calculus

Find derivatives of using multiple formulae

Full solution

q=9 r^{2}+16 s^{2} r^{2}

\newline

Which of the following equations correctly expresses

r

in terms of

q

and

s

\newline

Choose

1

answer:

\newline

(A)

r= \pm \frac{\sqrt{q}}{3+4 s}

\newline

(B)

r= \pm \sqrt{\frac{q}{9+16 s^{2}}}

\newline

(C)

r= \pm \sqrt{\frac{q}{25 s^{2}}}

\newline

(D)

r= \pm \frac{\sqrt{q-16 s^{2}}}{3}

Given Equation: We are given the equation $q = 9r^2 + 16s^2r^2$ . To express $r$ in terms of $q$ and $s$ , we need to solve for $r$ .
Combine Like Terms: Combine like terms by factoring out $r^2$ from the terms on the right side of the equation. $\newline$ $q = r^2(9 + 16s^2)$
Isolate $r^2$ : Divide both sides of the equation by $(9 + 16s^2)$ to isolate $r^2$ . $\newline$ $r^2 = \frac{q}{(9 + 16s^2)}$
Take Square Root: Take the square root of both sides to solve for $r$ . Remember that taking the square root gives us both the positive and negative solutions. $r = \pm\sqrt{\frac{q}{(9 + 16s^2)}}$
Compare with Answer Choices: We can now compare the expression we found with the answer choices given in the problem. $\newline$ $r = \pm\sqrt{\frac{q}{(9 + 16s^2)}}$ matches with option (B).