The correct answer is 317
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.

The speed upstream is the difference between the boat speed and the current speed. It is (12 mi)/(4 h) = 3 mph.
The speed downstream is the sum of the boat speed and the current speed. It is (32 mph)/(4 h) = 8 mph.
The speed of the boat is the average of these: (3 + 8)/2 = 5.5 mph.
The speed of the current is that less the difference: 5.5 - 3 = 2.5 mph.
_____
<u>Check</u>
Boat + Current = 5.5 + 2.5 = 8 mph
Boat - Current = 5.5 - 2.5 = 3 mph
Answer:
50
Step-by-step explanation:
The angle is on the right side therefore the arrow is pointed at 180 and the other is pointed at 130. So to get the difference you need to subtract the greater number from the smaller (180-130)=50
As a rule the product of an ODD number of NEGATIVE SIGNS is always NEGATIVE
An the product of an EVEN number of NEGATIVE SIGNS is always POSITIVE
Then the following statement is the right one:
Negative, because the product (-7)(-2) is positive, and the product (-5)(1) is negative and the product of a positive and a negative number is negative