Problem 16
<h3>Answer: i</h3>
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Work Shown:
The exponent 41 divided by 4 leads to
41/4 = 10 remainder 1
The "remainder 1" means that
i^(41) = i^1 = i
The reason why I divided by 4 is because the pattern shown below
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
repeats itself over and over. So this is a block of four items repeated forever.
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Problem 18
<h3>Answer: 1</h3>
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Work Shown:
Divide 3136 over 4 to get
3136/4 = 784 remainder 0
Therefore,
i^3136 = i^0 = 1
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Problem 20
<h3>Answer: i</h3>
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Work Shown:
Combine i^6*i^7 into i^13. We add the exponents here
Now divide by 4 to find the remainder
13/4 = 3 remainder 1
So, i^13 = i^1 = i
First consider (x+c)^2 where c is just a random constant. if we expand this by foil (which is distributive property twice), we get x^2 + 2cx+ c^2. we want to find c^2 and to do that, we can first find c. we can find c by looking at the 2cx term. this term should match with 12x, so therefore 2c = 12 so c = 6. this also implies that c^2 = 36.
note that for this problem i was working backwards which is a very powerful problem solving tool: start with what you want to attain, and then see how you can go from where you are now to get to your destination.
let me know if you have any questions!!!
The number of books which Mr. Hartzel has now is:
<h3>What is Algebra?</h3>
This refers to the use of calculations to solve mathematical problems. There are different ways in which algebra is used and this can include addition, subtraction, division, etc.
With this in mind, we can see that Mr Hartzel had 12 books in his library
Then he got 9 new books and then sold off 6 books.
Therefore, the total number of books which he has now is:
12+9-6= 15 books
Read more about algebra here:
brainly.com/question/6143254
Answer:
56 people are late, 6 people that are late buy shirts, 644 people are on time
Step-by-step explanation:
