1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
<em />
Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
Answer:
I think letter B is the answer
Explanation:
I provided this for who may ask later
Explanation:
I can do it, how many pages do you want
Answer:
X has travelled 4 times as far as Y
X is moving 2 times as fast as Y
Explanation:
Because x=1/2at²(get rid of the first portion of x=vt+1/2at² because initial v is 0 which multiplies to 0). If the acceleration is set to for example 10 (keep this constant for both X and Y) and we use t=1 and t=2 for time (as the time travelled of X is twice that of Y). Plugging this into the equation, at t=1, x=4. At t=2, x=20. 20 is four times greater than 5, so X has travelled 4 times as far as Y.
To find the difference in speed between the two objects, use the equation
. Since the initial velocity is 0, that part can just be removed from the equation. With v=at, it is easy to see that if the time plugged in is twice for one than the other (and the acceleration is the same for both), the final result will be twice of the other as well. For example: If the acceleration is 10 again for both, then v=10t. If t is 1, the velocity is 10. If t is 2, the velocity is 20.
Answer:
9/22 or 40.9%
Explanation:
Probability describes the likelihood of an event. To find simple probability, like in this question, use division.
To find the probability of the first question being a free response, you first need to find the total number of questions. This can be done by adding together all of the given information. There are 10 multiple choice, 3 essays, and 9 free responses.
This means that there are 22 total questions. Next, find how many of these questions are free-response. We know that there are 9 free responses and 22 questions in total. So, 9 out of 22 are free responses. This can be rewritten as 9/22.
If you want to find the percentage, simplify the fraction and convert it to a percentage.
Then, move the decimal 2 places to the right. This gives you 40.9%, which is the probability of the first question being a free-response.