The domain of the function given are:
y=cot x
{x∈R: πn<x<π(n+1)} where n any integer
y=csc x
{x∈R: πn<x<π(n+1)} where n any integer
y=cos x
R (all real numbers)
y=sec x
{x∈R:π(n+1/2)<x<π(n+3/2)} where n is all integers.
from above we see that the the function that has a domain of all real numbers except npi is y=cot x and y=csc x
Add 3 to both sides so that the equation becomes -2x^2 + 5x + 5 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -5 ± √(5^2 - 4(-2)(5)) ] / ( 2(-2) )
x = [-5 ± √(25 - (-40) ) ] / ( -4 )
x = [-5 ± √(65) ] / ( -4)
x = [-5 ± sqrt(65) ] / ( -4 )
x = 5/4 ± -sqrt(65)/4
The answers are 5/4 + sqrt(65)/4 and 5/4 - sqrt(65)/4..
His profit =$71.00
Profit % = 52.6 % (to 1 decimal place)
The GCF is actually 1. Just 1.
