Question

Christy earned $41.25 for selling 3 birdhouses at a craft market. The equation y=13.75x can be used to represent this situation.



What is the constant of proportionality? Express your answer in decimal form.

Answer 1

Step-by-step explanation:

Theorem 1: For any real numbers x and y, sin x = sin y implies x = nπ + (–1)n y, where n ∈ Z

Proof: Consider the equation, sin x = sin y. Let us try to find the general solution for this trigonometric equation.

sin x = sin y

⇒ sin x – sin y = 0

⇒2cos (x + y)/2 sin (x – y)/2 = 0

⇒cos (x + y)/2 = 0 or sin (x – y)/2 = 0

Upon taking the common solution from both the conditions, we get:

x = nπ + (-1)ny, where n ∈ Z