question 1(multiple choice worth 1 points) (sinusoidal function transformations mc) given functions f and g…

Explanation:

Step1: Recall period formula for cosine

The period of the cosine function $y = A\cos(Bx)$ is $T_f=\frac{2\pi}{B}$. For $f(x)=4\cos(2.4x)$, $B = 2.4$, so $T_f=\frac{2\pi}{2.4}=\frac{20\pi}{24}=\frac{5\pi}{6}$.

Step2: Find period of g(x)

The period of the sine function $y=\sin(bx)$ is $T_g=\frac{2\pi}{b}$. Given that $T_g=\frac{1}{6}T_f$.

Step3: Substitute and solve for b

Substitute $T_f=\frac{5\pi}{6}$ into $T_g=\frac{1}{6}T_f$, we get $T_g=\frac{1}{6}\times\frac{5\pi}{6}=\frac{5\pi}{36}$. Since $T_g = \frac{2\pi}{b}$, then $\frac{2\pi}{b}=\frac{5\pi}{36}$. Cross - multiply gives $5\pi b=2\pi\times36$. Divide both sides by $5\pi$: $b=\frac{2\times36}{5}=14.4$.

Answer:

$b = 14.400$ (corresponding to the last option)