Question

10-4 exercises

solve each equation or formula for the variable specified.
assume that no variables are equal to zero.

1. (a = lw) for (l)
2. (c = pi d) for (d)
3. (v = pi r^2 h) for (r)
4. (m = \frac{a + b}{2}) for (b)
5. (p = i \times e) for (i)
6. (p = \frac{e^2}{r}) for (e)
7. (x = ay + t) for (y)
8. (e = mc^2) for (m)
9. (c = \frac{q}{v}) for (v)
10. (s = 6s^2) for (s)
11. (p = i^2 r) for (i)
12. (x_c = \frac{1}{2pi fc}) for (c)
13. (f = \frac{1}{2pisqrt{lc}}) for (l)
14. (z = sqrt{x^2 + r^2}) for (x)

Explanation:

Isolate variables in linear formulas

Using the Literal Equations and Formula Rearrangement knowledge points

$$
LATEXBLOCK0
$$

Isolate variables with square roots and squares

Using the Literal Equations and Formula Rearrangement knowledge points

$$
LATEXBLOCK1
$$

Isolate variables in denominators

Using the Literal Equations and Formula Rearrangement knowledge points

$$
LATEXBLOCK2
$$

Isolate variables under radical signs

Using the Literal Equations and Formula Rearrangement knowledge points

$$
LATEXBLOCK3
$$

Answer:

No.	Problem	Answer
2	\(C = \pi d\) for \(d\)	\(d = \frac{C}{\pi}\)
3	\(V = \pi r^2 h\) for \(r\)	\(r = \sqrt{\frac{V}{\pi h}}\)
4	\(m = \frac{a+b}{2}\) for \(b\)	\(b = 2m - a\)
5	\(P = I \times E\) for \(I\)	\(I = \frac{P}{E}\)
6	\(P = \frac{E^2}{R}\) for \(E\)	\(E = \sqrt{PR}\)
7	\(x = ay + t\) for \(y\)	\(y = \frac{x-t}{a}\)
8	\(E = mc^2\) for \(m\)	\(m = \frac{E}{c^2}\)
9	\(C = \frac{q}{V}\) for \(V\)	\(V = \frac{q}{C}\)
10	\(S = 6s^2\) for \(s\)	\(s = \sqrt{\frac{S}{6}}\)
11	\(P = I^2 R\) for \(I\)	\(I = \sqrt{\frac{P}{R}}\)
12	\(X_C = \frac{1}{2\pi f C}\) for \(C\)	\(C = \frac{1}{2\pi f X_C}\)
13	\(f = \frac{1}{2\pi\sqrt{LC}}\) for \(L\)	\(L = \frac{1}{4\pi^2 f^2 C}\)
14	\(Z = \sqrt{X^2 + R^2}\) for \(X\)	\(X = \sqrt{Z^2 - R^2}\)