Answer:
Solution : ![-\frac{3}{4}-\frac{3}{4}i](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B4%7D-%5Cfrac%7B3%7D%7B4%7Di)
Step-by-step explanation:
![-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right]](https://tex.z-dn.net/?f=-3%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%7D%7B4%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%7D%7B4%7D%5Cright%29%5Cright%5D%5C%3A%5Cdiv%20%5C%3A2%5Csqrt%7B2%7D%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%2Bi%5Csin%20%5Cleft%28%5Cfrac%7B-%5Cpi%20%5C%3A%5C%3A%5C%3A%7D%7B2%7D%5Cright%29%5Cright%5D)
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
![\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7Di%5Cright%29%7D%7B2%5Csqrt%7B2%7D%5Cleft%280-1%5Cright%29i%7D)
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÷ ![2\sqrt{2}\left(0-1\right)i](https://tex.z-dn.net/?f=2%5Csqrt%7B2%7D%5Cleft%280-1%5Cright%29i)
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÷ ![-2\sqrt{2}i](https://tex.z-dn.net/?f=-2%5Csqrt%7B2%7Di)
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÷
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÷
= ![-\frac{3}{4}-\frac{3}{4}i](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B4%7D-%5Cfrac%7B3%7D%7B4%7Di)
As you can see your solution is the last option.
Step-by-step explanation:
Percentage change is 25%
Answer:
The answer would be B, or the second option.
Step-by-step explanation:
To find the volume, you must multiply the length, width, and height of the object. (Length x Width x Height)
<em>l × w × h</em>
Replace each of the following variables with the length of each side. In this case, they are all 3, but remember that it doesn't matter in which order you put them in.
3 × 3 × 3.
Now multiply!
3 × 3 × 3 = 27 cubic feet.
Meaning, the final answer would be B.
Answer:
y = 4x - 4
Step-by-step explanation:
first, find the slope:
y2 - y1/ x2 -x1
8 - 0/ 3 - 1 = 4
no plug in your slope and one of the points to find the b:
y = mx+b
0 = 4 (1) + b
b= -4
so
y = 4x - 4