I'll walk you through the first one, and then you should be able to do the rest.
The first step is to right out your numbers from least to greatest
Problem #1: 2,4,5,6,8,10,13,17,19,20
To find the MEDIAN, you're simply crossing out a number from each end until you meet in the middle. In this case, you have an even number of data, which means once you get to the middle, you're have to find the average.
In this problem, your two middle numbers are 8 & 10. Since only one number can be the median, you add them together, and divide by 2:
8+10=18 18/2=9 < this is your middle, or MEDIAN
Next, your first and third quartiles-- they're the median of the lower half and data, and upper half.
For the lower quartile, find the mean of 2,4,5,6, and 8. again, cross out one from each side until you get to the middle. FIRST QUARTILE = 5
Do the same process for the upper half of data (10,13,17,19 & 20).
THIRD QUARTILE = 17
The MIN is the lowest number of data = 2
The MAX is the highest number of data = 20
Best of luck!
We let y equal to the elevation above sea level so that the elevation of the rock climber after x minutes of climbing would be:
y = 2x + 50
His initial height can be calculated when x is equal to zero it is when the climber is not yet climbing. Therefore, the rock climber'sinitial height above sea level would be 50 meters.
Notice that
cos(θ) + 2 cos²(θ) + 2 cos³(θ) + cos⁴(θ)
= cos(θ) (1 + 2 cos(θ) + 2 cos²(θ) + cos³(θ))
= cos(θ) ([1 + cos(θ)] + [cos(θ) + cos²(θ)] + [cos²(θ) + cos³(θ)])
= cos(θ) ([1 + cos(θ)] + [cos(θ) (1 + cos(θ))] + [cos²(θ) (1 + cos(θ))])
= cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))
Given that sin(θ) = cot(θ), by definition of cotangent this tells us that
sin(θ) = cos(θ)/sin(θ) ⇒ cos(θ) = sin²(θ)
and by the Pythagorean identity
cos²(θ) + sin²(θ) = 1
it follows that
cos(θ) = sin²(θ) = 1 - cos²(θ)
Substituting these results into the factorization above gives
cos(θ) (1 + cos(θ)) (1 + cos(θ) + cos²(θ))
= cos(θ) (1 + cos(θ)) (1 + [1 - cos²(θ)] + cos²(θ))
= 2 cos(θ) (1 + cos(θ))
= 2 sin²(θ) (1 + cos(θ))
= 2 (1 - cos²(θ)) (1 + cos(θ))
= 2 (1 + cos(θ) - cos²(θ) - cos³(θ))
= 2 (cos(θ) + cos(θ) - cos³(θ))
= 2 (2 cos(θ) - cos³(θ))
= 2 cos(θ) (2 - cos²(θ))
= 2 cos(θ) (1 + cos(θ))
= 2 (cos(θ) + cos²(θ))
= 2 (1 - cos²(θ) + cos²(θ))
= 2
Answer:
0.875
Step-by-step explanation:
they're proportional.
