Answer:
The domain of this function is first restricted to all non negative integers because the theater can sell only a whole number of tickets.
The domain is restricted to numbers less than or equal to 125 because the theater cannot sell more tickets than capacity.
Step-by-step explanation:
In order to find out what the value is when x=π, we have to model the function. It says it is a cosine wave, and a amplitude of 1/3 so we start as
1/3(cos(x))
It says a period of π/3. So the period of a cosine function is
2π/n
Where n is cos(nx)
So to find n, we set the period and that equal to each other
Finding n we get 6. So now we have
1/3(cos(6x))
The shift is -2π. When we have a shift of something, we put the opposite sign with the x. So now it's
1/3(cos(6x+2π))
Factor out a 6 and we get
1/3(cos(6(x+π/3))
If we add the period to x, nothing happens so it remains
1/3(cos(6x))
The vertical shift is -3 so we just add that to everything so it becomes
1/3(cos(6x))-3
Plugging in x=π we get
1/3(cos(6π))-3
Cos(6π) is 1 so it is 1/3 - 3, or -8/3
Answer:
$36.75
Step-by-step explanation:
If you take the original cost 35.00 and add 5% to it, you would get 36.75. If you think about it, it has to be above $35 since the sales tax would be more.
Complementary angles are angles which add to 90 degrees, and supplementary angles are angles which add the 180 degrees.
So A and D are complementary, and B and C are supplementary.
To determine these answers, you can make note of which angles are acute (less than 90 degrees) and which angles are obtuse (more than 90 degrees). Because complementary angles add to 90, they both must be acute. Angles A and D work because 59+31 = 90.
Similarly, supplementary angles add to 180, therefore one of the angles must be obtuse. B is the only obtuse angle.. 119 + 61 = 180.
Answer:
Distance = 8
Step-by-step explanation: