Given:
The revenue function is

The cost function is

To find:
The profit function.
Solution:
We know that, the total profit P is defined as total revenue R minus total cost C.
So, the profit function is




Therefore, the profit function is
.
9514 1404 393
Answer:
- sin(Ф) = (4/41)√41; csc(Ф) = (√41)/4
- cos(Ф) = (5/41)√41; sec(Ф) = (√41)/5
- tan(Ф) = 4/5; cot(Ф) = 5/4
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you with three of the functions. Then you need to remember the relations between those and the other three.
Tan = Opposite/Adjacent
tan(Ф) = 4/5
This suggests you can draw a triangle like the one attached that has adjacent side 5 and opposite side 4. Then hypotenuse can be found from the Pythagorean theorem:
AC² = AB² +BC² = 5² +4² = 41
AC = √41 . . . . . hypotenuse
Then the other trig functions are ...
Sin = Opposite/Hypotenuse
sin(Ф) = 4/√41 = (4/41)√41
Cos = Adjacent/Hypotenuse
cos(Ф) = 5/√41 = (5/41)√41
And the reciprocal functions are ...
csc(Ф) = 1/sin(Ф) = (√41)/4
sec(Ф) = 1/cos(Ф) = (√41)/5
cot(Ф) = 1/tan(Ф) = 5/4
1. 3 & 7 and 2 & 6
2. 5
3. Alternate exterior angles
4. Consecutive interior angles
5. 2
6. 4
7. 146
8. 128
9. 13x + 63 = 180
13x = 117
x = 9
8x + 63 = y
8(9) + 63 = y
72 + 63 = y
m
10. 5x = m5(9) = 45
m
11. 2 & 7 and 1 & 8
12. 8
13. Alternate interior angles