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An oceanographer uses the equation $s=\frac{3}{2}P$ to model the speed $s$, in knots, of an ocean wave, where $p$ represents the period of the wave, in seconds. Which of the following represents the period of the wave in terms of the speed of the wave?
Difficulty: Medium
A:
$p=\frac{2}{3}s$
B:
$p=\frac{3}{2}s$
C:
$p=\frac{2}{3}+s$
D:
$p=\frac{3}{2}+s$
The function $f$ is defined by $f(x)=\frac{1}{6x}$. What is the value of $f(x)$ when $x=3$?
Difficulty: Easy
A:
$\frac{1}{3}$
B:
$\frac{1}{6}$
C:
$\frac{1}{9}$
D:
$\frac{1}{18}$
If $x^{2}=a+b$ and $y^{2}=a+c$ which of the following is equal to $(x^{2}-y^{2})^{2}$?
Difficulty: Medium
A:
$a^{2}-2ac+c^{2}$
B:
$b^{2}-2bc+c^{2}$
C:
$4a^{2}-4abc+c^{2}$
D:
$4a^{2}-2abc+b^{2}c^{2}$
Which of the following is a solution to the equation $2x^{2}-4=x^{2}$?
Difficulty: Easy
A:
1
B:
2
C:
3
D:
4
\[q-29r=s\]
The given equation relates the positive numbers \(q\), \(r\), and \(s\). Which equation correctly expresses \(q\) in terms of \(r\) and \(s\)?
Difficulty: Easy
A:
\(q=s-29r\)
B:
\(q=s+29r\)
C:
\(q=29rs\)
D:
\(q=-\frac{s}{29r}\)
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