![\bf \begin{array}{clclll} -6&+&6\sqrt{3}\ i\\ \uparrow &&\uparrow \\ a&&b \end{array}\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\ -------------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bclclll%7D%0A-6%26%2B%266%5Csqrt%7B3%7D%5C%20i%5C%5C%0A%5Cuparrow%20%26%26%5Cuparrow%20%5C%5C%0Aa%26%26b%0A%5Cend%7Barray%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%0A%5Ctheta%20%3Dtan%5E%7B-1%7D%5Cleft%28%20%5Cfrac%7Bb%7D%7Ba%7D%20%5Cright%29%0A%5Cend%7Bcases%7D%5Cqquad%20r%5Bcos%28%5Ctheta%20%29%2Bi%5C%20sin%28%5Ctheta%20%29%5D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C)
now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.
thus
![\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]](https://tex.z-dn.net/?f=%5Cbf%2012%5Cleft%5Bcos%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%2Bi%5C%20sin%5Cleft%28%20%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%20%5Cright%29%20%5Cright%5D)
What needs to be done first is to add up females and males that have passed.
42 + 14 = 56
so out of 56 students who passed 42 females passed 42/56 = 3/4 = 0.75
out of 56 students who passed, 14 males passed which turns into 14/56 = 1/4 = 0.25
check work; 0.75 + 0.25 = 1.00
NOW WE ARE DOING FAILS.
15 + 5 = 20
so out of 20 students who failed, 15 females failed so it turns into 15/20 = 3/4 = 0.75
out of 20 students who failed, 5 males failed. 5/20 = 1/4 = 0.25
check work; 0.75 + 0.25 = 1.00
i hope this helped! :)
Answer:
103/28
Step-by-step explanation:
Let the number be 'x'
Equation:-
7x - 3/4 = 25
7x = 25 + 3/4
7x = 100/4 + 3/4
7x = 103/4
x = 103/(4 x 7)
x = 103/28
Answer:
-200 | -500 | -500-(-200) | -300
-200 | -0 | 0 -(-200) | 200
Step-by-step explanation:
-vp+40<95
subtract 40 from each side
-vp < 55
divide by -p (which flips the inequality) assuming p>0
v > -55/p
