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juin [17]
4 years ago
9

What is (3 -i) + (1 - 2i)

Mathematics
1 answer:
Viefleur [7K]4 years ago
8 0

Answer:

4-3i

Step-by-step explanation:

Add the real components

3+1 =4

Add the imaginary components

-i+-2i = -3i

The solution is 4-3i

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Some people think it is unlucky if the 13th day of a month falls on a Friday. Show that in every calendar year (non leap or leap
MakcuM [25]
We will set a variable, d,  to represent the day of the week that January starts on.  For instance, if it started on Monday, d + 1 would be Tuesday, d + 2 would be Wednesday, etc. up to d + 6 to represent the last day of the week (in our example, Sunday).  The next week would start over at d, and the month would continue. For non-leap years:
If January starts on <u>d</u>, February will start 31 days later.  Following our pattern above, this will put it at <u>d</u><u> + 3</u> (28 days would be back at d; 29 would be d+1, 30 would be d+2, and 31 is at d+3).  In a non-leap year, February has 28 days, so March will start at <u>d</u><u>+3</u> also.  April will start 31 days after that, so that puts us at d+3+3=<u>d</u><u>+6</u>.  May starts 30 days after that, so d+6+2=d+8.  However, since we only have 7 days in the week, this is actually back to <u>d</u><u>+1</u>.  June starts 31 days after that, so d+1+3=<u>d</u><u>+4</u>.  July starts 30 days after that, so d+4+2=<u>d</u><u>+6</u>.  August starts 31 days after that, so d+6+3=d+9, but again, we only have 7 days in our week, so this is <u>d</u><u>+2</u>.  September starts 31 days after that, so d+2+3=<u>d</u><u>+5</u>.  October starts 30 days after that, so d+5+2=d+7, which is just <u>d</u><u />.  November starts 31 days after that, so <u>d</u><u>+3</u>.  December starts 30 days after that, so <u>d</u><u>+5</u>.  Remember that each one of these expressions represents a day of the week.  Going back through the list (in numerical order, and listing duplicates), we have <u>d</u><u>,</u> <u>d,</u><u /> <u>d</u><u>+1</u>, <u>d</u><u>+2</u>, <u>d+3</u><u>,</u> <u>d</u><u>+3</u>, <u>d</u><u>+3</u>, <u>d</u><u>+4</u>, <u>d</u><u>+5</u>, <u>d</u><u>+5</u>, <u /><u /><u>d</u><u>+6</u><u /><u /> and <u>d</u><u>+6</u>.  This means we have every day of the week covered, therefore there is a Friday the 13th at least once a year (if every day of the week can begin a month, then every day of the week can happy for any number in the month).  
For leap years, every month after February would change, so we have (in the order of the months) <u></u><u>d</u>, <u>d</u><u>+3</u>, <u>d</u><u>+4</u>, <u>d</u><u />, <u>d</u><u>+2</u>, <u>d</u><u /><u>+5</u>, <u>d</u><u />, <u>d</u><u>+3</u>, <u>d</u><u /><u>+6</u>, <u>d</u><u>+1</u>, <u>d</u><u>+4</u>, a<u />nd <u>d</u><u>+</u><u /><u /><u>6</u>.  We still have every day of the week represented, so there is a Friday the 13th at least once.  Additionally, none of the days of the week appear more than 3 times, so there is never a year with more than 3 Friday the 13ths.<u />
5 0
3 years ago
What is the product of 1.38 and 2.5
Salsk061 [2.6K]

Answer:

3.45

Step-by-step explanation:

Product, meaning multiplication would just mean that you multiply these two numbers together

7 0
3 years ago
Read 2 more answers
Sandy made 8 friendship bracelets she gave 1 bracelet to her best friend and 5 to to her friends in the tennis team
Oduvanchick [21]

Answer:

2

Step-by-step explanation:

1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

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8 0
4 years ago
Evaluate the integral. (remember to use absolute values where appropriate. Use c for the constant of integration.) 5 cot5(θ) sin
ozzi

I=5\int \frac{cos^{4}\theta }{sin\theta }\times cos\theta d\theta \\\\I=5\int \left ( 1-sin^{2}\theta  \right )^{2}\times \frac{cos\theta }{sin\theta }d\theta \\put\ \sin\theta =t\\\\dt=cos\theta d\theta \\\\I=5\int\frac{t^{4}+1-2t^{2}}{t}dt\ \ \ \ \ \ \ \ \ \ \because (a-b)^2=a^2+b^2-2ab\\\\I=5\left ( \int t^{3}dt + \int \frac{1}{t} -2\int t \right )dt

by using the integration formula

we get,

\\I=5\left ( \frac{t^{4}}{4} +logt -t^{2}\right )\\\\I=\frac{5}{4}t^{4}+5\log t-5t^{2}+c

now put the value of t=\sin\theta in the above equation

we get,

\int 5\cot^5\theta \sin^4\theta d\theta=\frac{5}{4}sin^{4}\theta+5\log \sin\theta - 5sin^{2} \theta+c

hence proved

7 0
3 years ago
A container can hold five orange slices.If a company has 737 orange slices to put in containers how many more slices would they
Phantasy [73]
Answer:2
You need 2 more orange slices to fill up the last container.
5 0
3 years ago
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