Answer:
Option (3)
Step-by-step explanation:
w = ![\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5B%5Ctext%7Bcos%7D%28225%29%20%2B%20i%5Ctext%7Bsin%7D%28225%29%5D)
Since, cos(225) = cos(180 + 45)
= -cos(45) [Since, cos(180 + θ) = -cosθ]
= -
sin(225) = sin(180 + 45)
= -sin(45)
= -
Therefore, w = ![\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})]](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5B-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2Bi%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%5D)
= 
= 
z = 1[cos(60) + i(sin(60)]
= 
= 
Now (w + z) = 
= 
= 
= 
Therefore, Option (3) will be the correct option.
The required number is 4
Step-by-step explanation:
We need to find the number from the given statement:
What number increased by two is equal to two less than twice the number?
Converting statement into mathematical form.
Let number=x
number increased by two: x+2
is equal: =
two less than twice the number: 2x-2
So, equation is:

Solving the equation to find value of x:




So, the required number is 4.
Keywords: Word Problems
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The last one because it touches the x axis twice to turn
Answer:
Multiply each expression by the same number.
Step-by-step explanation:
Answer: z(99) = (99-98.2)/0.62 = 1.2903
P(x < 99) = P(z < 1.2903) = 0.9015 = 90.15%ile