Answer:
C, 11.62 units
Step-by-step explanation:
tan 54° = 
x tan 54° = 16
x = 
x≈11.62468045
x= 11.62
Do you want a general solution or from 0 <= x < 2pi?
tan^2(2x) - 1 = 0
tan^2(2x) = 1
Take the square root of both sides,
tan(2x) = +/- 1
Two equations:
tan(2x) = 1
tan(2x) = -1
Solve each equation.
tan(2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},
x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }
tan(2x) = -1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },
x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}
So for solutions within [0, 2pi),
x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }
Answer:
A: The solution to this system is no viable because it results in fractional values of tickets
Step-by-step explanation:
Let number of adult, child, and senior tickets be x, y and z respectively.
Thus;
x + y + z = 12 - - - (eq 1)
she purchases 4 more child tickets than senior tickets.
Thus, y = z + 4
Thus:
x + (z + 4) + z = 12
x + 2z + 4 = 12
x + 2z = 8 - - - (eq 2)
Also, We are told that Adult tickets are $5 each, child tickets are $2 each, and senior tickets are $4 each. She spends a total of $38,
Thus;
5x + 2(z + 4) + 4z = 38
5x + 2z + 8 + 4z = 38
5x + 6z + 8 = 38
5x + 6z = 38 - 8
5x + 6z = 30
Divide through by 5 to get;
x + (6/5)z = 6 - - - (eq 3)
Subtract eq 2 from eq 1 to get;
2z - (6/5)z = 8 - 6
2z - (6/5)z = 2
Multiply through by 5 to get;
10z - 6z = 10
4z = 10
z = 2½
It's not possible to have a fractional value of a ticket and thus we can say that the solution is not viable.
I’d say 5cm 7cm 5cm because it all multiples to 175cm.
