Answer:
Step-by-step explanation:
As you can see from the graph I attached you, the possible solutions in the interval from 0 to 2π are approximately:
So, it's useful to solve the equation too, in order to verify the result:
Taking the inverse sine of both sides:
Using this result we can conclude the solutions in the interval from 0 to 2π are approximately:
A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.
There are going to be two solutions because the "biggest" x is x^2 but you can factor to find what they actually are.
The <em>correct answer</em> is:
A) A tangent is never a secant.
Explanation:
A tangent is a line that touches a circle in exactly one point. A secant is a line that touches a circle in two different points.
Since a tangent only touches once and a secant touches twice, there is no way a tangent can be a secant.