# 2.3E: Exercises

- Page ID
- 30820

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## More Practice

**Solve a Formula for a Specific Variable**

Solve each of the following equations for the indicated variable.

\(x − f = g\) for \(x\)

**Answer**-
\(x=f+g\)

\(a + c = b\) for \(c\)

\(S = L + 2B\) for \(L\)

**Answer**-
\(L=S-2B\)

\(x + 5y = 3\) for \(x\)

\(ab = c\) for \(b\)

**Answer**-
\(b=\dfrac{c}{a}\)

\(rt = d\) for \(r\)

\(DS = ds\) for \(D\)

**Answer**-
\(D=\dfrac{ds}{S}\)

\(E = mc^2\) for \(m\)

\(3x = \dfrac{a}{b}\) for \(x\)

**Answer**-
\(x=\dfrac{a}{3b}\)

\(lwh = V\) for \(w\)

\(at − bw = s\) for \(w\)

**Answer**-
\(w=\dfrac{at-s}{b}\)

\(R = aT + b\) for \(T\)

\(S = πrh + πr^2\) for \(h\)

**Answer**-
\(h=\dfrac{s-\pi r^2}{\pi r}\)

\(h = vt − 16t^2\) for \(v\)

\(V = \dfrac{4}{3} πr^3\) for \(π\)

**Answer**-
\(\pi =\dfrac{3V}{4r^3}\)

\(V = \dfrac{πDn}{12}\) for \(D\)

\(V = \dfrac{πr^2h}{3}\) for \(h\)

**Answer**-
\(h=\dfrac{3v}{\pi r^2}\)

\(E = \dfrac{mv^2}{2}\) for \(m\)

\(p = \dfrac{3y}{q}\) for \(y\)

**Answer**-
\(y=\dfrac{pq}{3}\)

\(\dfrac{ym}{b} = \dfrac{c}{d}\) for \(y\)

\(g = \dfrac{h}{i}\) for \(h\)

**Answer**-
\(h=gi\)

\(\dfrac{f}{g}x = b\) for \(x\)

\(c = \dfrac{4y}{m + n}\) for \(y\)

**Answer**-
\(y=\dfrac{cm+cn}{4}\)

\(\dfrac{rs}{a − 3} = k\) for \(r\)

\(\dfrac{k − m}{r} = q\) for \(k\)

**Answer**-
\(k=qr+m\)

\(T = \dfrac{D − d}{L}\) for \(D\)

\(I = \dfrac{E_a − E_q}{R}\) for \(E_a\)

**Answer**-
\(E_a=IR+E_q\)

\(C = \dfrac{5}{9} (F − 32)\) for \(F\)

\(P = n(p − c)\) for \(n\)

**Answer**-
\(n=\dfrac{P}{p-c}\)

\(L = L_0(1 + at)\) for \(L_0\)

\(q = 6(L − p)\) for \(L\)

**Answer**-
\(L=\dfrac{q+6p}{6}\)

\(F = k(R − L)\) for \(k\)

\(Q_1 = P(Q_2 − Q_1)\) for \(Q_2\)

**Answer**-
\(Q_2=\dfrac{Q_1+PQ_1}{P}\)

\(L = π(r_1 + r_2) + 2d\) for \(r_1\)

\(P = \dfrac{V_1(V_2 − V_1)}{g}\) for \(V_2\)

**Answer**-
\(V_2=\dfrac{Pg+V_1^2}{V_1}\)

\(R = \dfrac{kA(T_1 + T_2)}{d}\) for \(T_1\)