Question

question 1 of 10
the depth of water at a dock can be modeled as ( y = 3sinleft(\frac{pi}{6}x
ight)+7 ). at low tide, the water is 4 feet deep. what is the depth of water at high tide (its maximum point)?
a. 10 feet
b. 11 feet
c. 14 feet
d. 7 feet

Explanation:

Step1: Identify the sine function form

The model is \( y = A\sin(Bx) + C \), where \( A=3 \), \( C=7 \).

Step2: Find maximum value of sine term

The maximum value of \( \sin(\text{any angle}) \) is 1.

Step3: Calculate maximum depth

Substitute max sine value into the model: \( y = 3(1) + 7 = 10 \).

Answer:

A. 10 feet