Given that 0≤β<2π, which of the following gives all solutions to the equation 2sin2β=9sinβ−4?

We know the following equation:

So we can write this equation as two function that are equalized, that is:

So let's solve this equation graphically. We know that:

And this interval is indicated with the two vertical lines drawn in red below. For this graph the x-axis represents β.

So the β-values of the graph of f(β) that makes this function to be zero are:

And those two values lies on the given interval.

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315

your answer would be 12