Someone answer all of this clearly, I don't get it at all.
Suppose a ship is sailing at a rate of 35km/h parellel to a straight shoreline. The ship is 10km from shore when it passes a lighthouse at 11am.
Question 6 options:
a)
Let k be the distance between the lighthouse and the ship. Let d be the distance from the ship has travelled since 11am. Express k as a function of d. Please include a diagram.
b)
Express d as a function of t, the time elapsed since 11am.
c)
Find k∘d . What does this function represent?
Sure, let's break down each part of the question and explain how to approach it:
a) In order to express k as a function of d, we need to understand the relationship between the ship's distance from the lighthouse, which is k, and the distance it has traveled since 11am, which is d. To visualize this, we can create a right-angled triangle where the lighthouse is the starting point (vertex), the shoreline is the hypotenuse, and the ship's path is the adjacent side. The angle between the shoreline and the ship's path should be 90 degrees since they are parallel. Now, let's label the dimensions of the triangle: the distance between the ship and the shoreline is d, the distance between the lighthouse and the shoreline is k, and the distance between the ship and the lighthouse is the hypotenuse (which we don't know yet, so we'll leave it as h for now). Using the Pythagorean theorem, we can write the equation: h^2 = d^2 + k^2. Now, solve this equation for h (distance between the ship and the lighthouse) to get k as a function of d: h = √(d^2 + k^2) ⇒ k = √(h^2 - d^2).
b) To express d as a function of t, we need to understand the relationship between the distance the ship has traveled (d) and the time elapsed since 11am (t). We know that the ship is sailing at a constant rate of 35 km/h. Therefore, we can use the formula distance = rate x time, where distance is d, rate is 35 km/h, and time is t. So, d = 35t.
c) Now, let's find k∘d. This function represents the product of k and d. Since we expressed k as a function of d in part a, we can substitute the expression for k into the function: k∘d = (√(h^2 - d^2))∘d. This function represents the distance between the lighthouse and the ship (k) multiplied by the distance the ship has traveled (d).
I hope this explanation helps clarify each part of the question! Let me know if you have any further questions or need additional clarification.