Answer:
1.x = pi/3 or 4pi/3
2. x = -pi/6 +2pi*n or 5pi/6 + 2pi *n where n is an integer
Step-by-step explanation:
1. sqrt(3) tan x = 3
Divide each side by sqrt(3)
sqrt(3)/sqrt(3) tan x = 3/sqrt(3)
tan x = sqrt(3) * sqrt(3)/sqrt(3)
tan x = sqrt(3)
Take the inverse of each side
arctan (tanx) = arctan (sqrt(3))
x = arctan (sqrt(3))
x =pi/3 or - 2pi/3
Since the domain is between 0 and 2pi, add 2pi to - 2pi/3 since the trig functions are circular
x = pi/3 or -2pi/3 + 6pi/3
x = pi/3 or 4pi/3
2. 3 tan x = -sqrt(3)
Divide each side by 3
3/3 tan x = -sqrt(3)/3
tan x = -sqrt(3)/3
Take the arctan of each side
arctan (tan x) = arctan ( -sqrt(3)/3)
x = arctan ( -sqrt(3)/3)
x =-pi/6 or 5pi/6
We want all values for x so add 2pi*n to each value where n is an integer
x = -pi/6 +2pi*n or 5pi/6 + 2pi *n where n is an integer
It is 12:04 when she arrives at the library. Add 50 mins to equal 12:54. Then add 4 to equal 12:56. She leaves at 12:56.
Answer:
Can't answer this
Step-by-step explanation:
For this question, I think you need to read more informations, find out the function
After you find out the function,
Replace f(x) as 12 and replace x with n
After that, try to solve it.
Good luck.
Answer:
1. 2x + 30° = 180°
2x = 150°
x = 75°
2. (2x - 24)° + (x + 12)° + (x - 8)° = 180°
4x - 20 = 180°
4x = 200
x = 50°
Answer:
12, 13, 14
Step-by-step explanation:
Three consecutive numbers means three numbers in a row, so if n is the first number, the second number is one more than n (which is n+1) and the third number is one more than that (which is n+2)
So three times (3 x) the first number (n) is equal to (=) nine more than (9 +) the sum of the other two ( (n+1) + (n+2) )
3 times n can be written as 3n
So 3n = 9 + (n+1) + (n+2)
3n = 9 + n + 1 + n + 2
3n = 9 + 1 + 2 + n + n
3n = 12 + 2n
Subtract 2n from each side
3n - 2n = 12 + 2n - 2n
1n = 12
n = 12
So the first number is 12, the second number is 12 + 1 (13) and the third number is 12 + 2 (14)
The numbers are 12, 13, 14
Hope this helps :)
