Question

The wake of a boat which is moving at constant speed keeps gettingwider after the boat passes. The wake is the same width as the boatwhen it first forms, and then it gets wider in proportion to the square root of the distance from the boat. If a 2-meter wide boat passes yourposition at 5 m/sec, which domain is appropriate for a function thatmodels the width of the wake, f(x), and the distance from the boat, x?a) all numbers greater than 2b) all rational numbers c) all positive numbers d) all numbers greater than 5

Answer 1

The appropriate domain for the function modeling the width of a boat's wake as a function of the distance from the boat is all positive numbers.

Step-by-step explanation:

The student is asking about the appropriate domain for a function that models the width of a boat's wake as a function of the distance from the boat. The wake begins as wide as the boat, which is 2 meters, and increases in width proportional to the square root of the distance from the boat. Given that the boat moves at a constant speed, the domain in question is the set of all distances where the wake's width is defined, which would be all positive numbers. The boat's speed and initial width only provide context and do not influence the domain of the function directly.

Answer 2

Since x it is the distance from the boat not from you, and the boat is a 2-meter wide, the distance must be greater than 0, because if any value of x is less than 0 the root could not be used for representing a real function, it would be a complex function due to the negative result. The answer is all positive numbers.