Mean, in terms of math, is the total added values of all the data in a set divided by the number of data <em>in</em> the set. Make sense? If not, here' an example...
Let's say this is my data set:
1, 2, 5, 4, 3, 8, 7, 4, 6,10
To find the mean...
Step 1: Add all of them together.
1+2+5+4+3+8+7+4+6+10 is what? 50. Now that you have this number...
Step 2: Divide by the amount there are. Basically, count up all of the numbers. How many are there? There are 10. Finally...
Step 3: Divide. 50/10 is 5, so the mean of this data set would be 5. Get it? I sure hoped this helped :)
8 mins
1 mile
1 hr and 12 mins
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.
Answer:
Net power = 20kW
B.) $128
Step-by-step explanation:
Given that :
Coefficient of performance = 2.5
Rate = 20kW
The net power required to operate the heat pump :
Energy delivery rate / Coefficient of performance
= 20kW / 2.5
= 8kW
B.) Given that electricity cost equals $0.08 per kW
If pump operates for 200 hours
Total energy used in kWhr :
8kW * 200= 1600kW
Cost per kW = $0.08
1600 * 0.08 = $128