Given,
Area = 225 yd²
Base = 30 yd
Height = [To be calculated]
To find:
The height of the given triangle.
We know that, area of a triangle is:
Therefore, the require height is 15 yd.
Proof:
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )
<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))
<em>z</em> = (-3 - 3<em>i </em>) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have
arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>
arg(<em>z</em>) = arctan(1) - <em>π</em>
arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>
arg(<em>z</em>) = -3<em>π</em>/4
where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.
Answer:
Basically, you have to think: more bricks : more time
more workers : less time
2,400 bricks 6 workers takes 18 hours
You now have to solve for 4,500 blocks and 10 workers
4,500 / 2,400 = 1.875 (times greater)
10 / 6 = 1.666666666 (times less)
So, we get 18 hours, multiply it by 1.875 and divide it by 1.666666666
which equals 20.25 hours
So, it seems you were correct on your third try.
Step-by-step explanation:
Answer:
2; 28.5 ; 34 ; 36 ; 38
Step-by-step explanation:
Given the data:
X = 25, 28, 29, 30, 34, 35, 35, 37, 38
n = 9
Values have been arranged in ascending order ;
The 5 number summary :
Maximum value : highest data value in the list = 38
Minimum value : Lowest data value in the list = 25
The lower quartile ; Q1 = 1/4(n+1)th term
Q1 = 1/4(10) th term = 2.5th term
Q1 = (2nd + 3rd) / 2 = (28+29)/2 = 28.5
Q2 = 1/2(n+1)th term
Q2 = 1/2(10) th term = 5th term
Q2 = 34
Q3 = 3/4(n+1)th term
Q3 = 3/4(10) th term = 7.5th term
Q3 = (7th + 8th) / 2 = (35+37)/2 = 36
Maximum value = 38 (highest data value in the list)
