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Taya2010 [7]
3 years ago
12

Which simplifications of the powers of i are correct? There may be more than one correct answer.

Mathematics
1 answer:
fredd [130]3 years ago
6 0

\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^{22}\implies i^{(4\cdot 5)+2}\implies i^{4\cdot 5}i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^{11}\implies i^{(2\cdot 5)+1}\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark

\bf i^{21}\implies i^{(4\cdot 5)+1}\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^{12}\implies i^{3\cdot 4}\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^{20}\implies i^{4\cdot 5}\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^{26}\implies i^{(4\cdot 6)+2}\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^{27}\implies i^{(4\cdot 6)+3}\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes

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The distributive property means to distribute the number being multiplied by the numbers in the parentheses.
In this case, (v+12) is being multiplied by 10.
To solve this, you simply have to multiply 10 by each term inside the parentheses.
That means it would be (v•10)+(12•10).
(v•10) is equal to 10v, since v is the variable and we don't know its value.
(12•10) is equal to 120.
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3 years ago
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Step-by-step explanation:

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2 years ago
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In 1 1/2 hours, Sebastian can walk 4 1/2 miles.<br> What is his average speed in hours per mile?
jeka94

Answer:

The average speed of Sebastian is 3 miles per hour.

<u>Solution:</u>

Given, In 1 \frac{1}{2} hours, Sebastian can walk 4 1/2 miles.  

we have to find What is his average speed in hours per mile

We know that, average speed =\frac{\text {total distance walked}}{\text {total time taken}}

In our problem, total distance travelled = 4 \frac{1}{2} \text { miles }=\frac{4 \times 2+1}{2} \text { miles }=\frac{9}{2} \text { miles. }

\text { And, total time taken }=1 \frac{1}{2} \text { hours }=\frac{1 \times 2+1}{2} \text { hours }=\frac{3}{2} \text { miles. }

Now, average speed of Sebastian =\frac{\frac{9}{2}}{\frac{3}{2}}=\frac{9}{2} \times \frac{2}{3}=\frac{9}{3}=3

Hence, the average speed of Sebastian is 3 miles per hour.

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= 8 / 6 = 1.3333333334

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3 years ago
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