Let L represent lower level tickets and U upper level.
Starter equations:
L + U = 2368
78L + 59U = 157800
Solve simultaneous equations:
59L + 59U = 139712
so 19L = 18088
L = 952
U = 2368 - 952 = 1416
952 lower level tickets and 1416 upper level tickets were sold.
Answer: the service charge per hour for premium services is $5.5
the service charge per hour for regular services is $3
Step-by-step explanation:
Let x represent the service charge per hour for premium services.
Let y represent the service charge per hour for regular services.
One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that
2x + 9y = 38- - - - - - - - - - - 1
Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that
3x + 6y = 34.5- - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes
6x + 27y = 114
6x + 12y = 69
Subtracting, it becomes
15y = 45
y = 45/15
y = 3
Substituting y = 3 into equation 1, it becomes
2x + 9 × 3 = 38
2x + 27 = 38
2x = 38 - 27 = 11
x = 11/2 = 5.5
1. cot(x)sec⁴(x) = cot(x) + 2tan(x) + tan(3x)
cot(x)sec⁴(x) cot(x)sec⁴(x)
0 = cos⁴(x) + 2cos⁴(x)tan²(x) - cos⁴(x)tan⁴(x)
0 = cos⁴(x)[1] + cos⁴(x)[2tan²(x)] + cos⁴(x)[tan⁴(x)]
0 = cos⁴(x)[1 + 2tan²(x) + tan⁴(x)]
0 = cos⁴(x)[1 + tan²(x) + tan²(x) + tan⁴(4)]
0 = cos⁴(x)[1(1) + 1(tan²(x)) + tan²(x)(1) + tan²(x)(tan²(x)]
0 = cos⁴(x)[1(1 + tan²(x)) + tan²(x)(1 + tan²(x))]
0 = cos⁴(x)(1 + tan²(x))(1 + tan²(x))
0 = cos⁴(x)(1 + tan²(x))²
0 = cos⁴(x) or 0 = (1 + tan²(x))²
⁴√0 = ⁴√cos⁴(x) or √0 = (√1 + tan²(x))²
0 = cos(x) or 0 = 1 + tan²(x)
cos⁻¹(0) = cos⁻¹(cos(x)) or -1 = tan²(x)
90 = x or √-1 = √tan²(x)
i = tan(x)
(No Solution)
2. sin(x)[tan(x)cos(x) - cot(x)cos(x)] = 1 - 2cos²(x)
sin(x)[sin(x) - cos(x)cot(x)] = 1 - cos²(x) - cos²(x)
sin(x)[sin(x)] - sin(x)[cos(x)cot(x)] = sin²(x) - cos²(x)
sin²(x) - cos²(x) = sin²(x) - cos²(x)
+ cos²(x) + cos²(x)
sin²(x) = sin²(x)
- sin²(x) - sin²(x)
0 = 0
3. 1 + sec²(x)sin²(x) = sec²(x)
sec²(x) sec²(x)
cos²(x) + sin²(x) = 1
cos²(x) = 1 - sin²(x)
√cos²(x) = √(1 - sin²(x))
cos(x) = √(1 - sin²(x))
cos⁻¹(cos(x)) = cos⁻¹(√1 - sin²(x))
x = 0
4. -tan²(x) + sec²(x) = 1
-1 -1
tan²(x) - sec²(x) = -1
tan²(x) = -1 + sec²
√tan²(x) = √(-1 + sec²(x))
tan(x) = √(-1 + sec²(x))
tan⁻¹(tan(x)) = tan⁻¹(√(-1 + sec²(x))
x = 0
Answer:
i = -7/12
Step-by-step explanation:
(-3/4 + 4/3) + i = 0
(-9/12 + 16/12) + i = 0
7/12 + i = 0
i = -7/12
