120 is good engough if you dont kn o
Answer:
No. of hours already volunteered + total volunteer hours dedicated in w weeks > = Least volunteer hours required to graduate
=> 52 + 3w >= 90
Step-by-step explanation:
Given that Antonina needs to have worked at least 90 volunteer hours to graduate means that she needs to volunteer either for 90 hours or more than that . Mathematically this can be written as
Total volunteer hours required to graduate greater than or equal to 90
Total volunteer hours required to graduate>= 90
No. of hours already volunteered = 52
no. of hours left for volunteering = Total volunteer hours required to graduate - No. of hours already volunteered = 90 - 52 = 38
No. of hours in one week she can dedicate for volunteering= 3
if w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours
then total volunteer hours dedicated in w weeks will be = w*No. of hours in one week she can dedicate for volunteering = w*3 = 3w
Thus,
No. of hours already volunteered + total volunteer hours dedicated in w weeks > = Least volunteer hours required to graduate
=> 52 + 3w >= 90
Givens
y = 2
x = 1
z(the hypotenuse) = √(2^2 + 1^2) = √5
Cos(u) = x value / hypotenuse = 1/√5
Sin(u) = y value / hypotenuse = 2/√5
Solve for sin2u
Sin(2u) = 2*sin(u)*cos(u)
Sin(2u) = 2(
) = 4/5
Solve for cos(2u)
cos(2u) = - sqrt(1 - sin^2(2u))
Cos(2u) = - sqrt(1 - (4/5)^2 )
Cos(2u) = -sqrt(1 - 16/25)
cos(2u) = -sqrt(9/25)
cos(2u) = -3/5
Solve for Tan(2u)
tan(2u) = sin(2u) / cos(2u) = 4/5// - 3/5 = - 0.8/0.6 = - 1.3333 = - 4/3
Notes
One: Notice that you would normally rationalize the denominator, but you don't have to in this case. The formulas are such that they perform the rationalizations themselves.
Two: Notice the sign on the cos(2u). The sin is plus even though the angle (2u) is in the second quadrant. The cos is different. It is about 126 degrees which would make it a negative root (9/25)
Three: If you are uncomfortable with the tan, you could do fractions.
28/100 then simplify
14/50
