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
Answer:
There are 4 quarts in one gallon. 36 divided by 4 is 9 gallons.
Step-by-step explanation:
9 gallons.
I think it is 20 because you have to multiply and then divide them add 11 then subtract 9 idk what I am saying
9514 1404 393
Answer:
-361
Step-by-step explanation:
Your calculator can tell you the result. It is -361.
Start with the inner parentheses and work outward. Do multiplication and division in the order shown, left to right, before addition or subtraction.
-3[2/6+8{-9/3(8-5*3)-6}]
= -3[2/6+8{-9/3(8-15)-6}]
= -3[2/6+8{-9/3(-7)-6}]
= -3[2/6+8{-3(-7)-6}]
= -3[2/6+8{21-6}]
= -3[2/6+8{15}]
= -3[1/3+8{15}]
= -3[1/3+120]
= -3[361/3]
= -361
Answer:
Step-by-step explanation:
Let x represent the number of hours that that he spent washing cars.
Let y represent the number of hours that that he spent landscaping.
In a week, he can work no more than 19 total hours. This means that
x + y ≤ 19- - - - - - - - - - - -1
Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. He must earn at least $170. This means that
10x + 8y ≥ 170 - - - - - - - - - -2
If Jacob worked 4 hours landscaping, it means that
x + 4 ≤ 19
x ≤ 19 - 4
x ≤ 15
Also,
10x + 8 × 4 ≥ 170
10x + 32 ≥ 170
10x ≥ 170 - 32
10x ≥ 138
10x ≥ 138/10
x ≥ 13.8
The minimum number of hours is 14
