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3 years ago

Simply each of the following powers I. i^15=

Mathematics

2 answers:

9966 [12]3 years ago

5 0

Answer:

-i

Step-by-step explanation:

i = √-1, i² = -1, i^4 = 1

i^15 = i^4 • i^4 • i^4 • i² • i

= 1 • 1 • 1 • -1 • i

= -i

vitfil [10]3 years ago

3 0

Answer:

-i

Step-by-step explanation:

i means Imaginary unit.

i to the zero power is 1

i to the first power is itself

i to the second power is -1

i to the third power is -i

Then, i to the fourth power is 1, so it all repeats again.

You might be interested in

the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 48 M. the length of the alley

Firdavs [7]

Answer:

Length is 20 m and width is 4 m.

Step-by-step explanation:

Given:

Perimeter of the rectangular alley, $P=48\textrm{ m}$

Length is 5 times the width.

Let width be $x$ .

So, as per question,

Length, $l = 5x$

Now, perimeter of rectangle is given as:

$P=2(l+b)$

Plug in 48 for $P$ , $5x$ for $l$ and $x$ for b.

$48=2(5x+x)\\48=2(6x)\\48=12x\\x=\frac{48}{12}=4$

Therefore, width is 4 m.

Length is $5x=5\times 4=20$ m.

8 0

3 years ago

Two perpendicular lines intersect at the origin. If the slope of the first line is .5, what is the equation of the second line?.

Sedaia [141]

The origin is at the point (0,0). Therefore, the y-intercept will be 0. For two points to be perpendicular, the slopes must be opposite reciprocals of each other. .5 can be seen as 1/2, so the reciprocal is 2, and it is positive, making that 2 negative. Your equation would be y = -2x.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csf%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Ccfrac%7B%5Csqrt%7Bx-1%7D-2x%20%7D%7Bx-7%7D" id=

BARSIC [14]

<h3>Answer: -2</h3>

======================================================

Work Shown:

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}\left(\sqrt{x-1}-2x\right) }{ \frac{1}{x}\left(x-7\right) }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \frac{1}{x}*\sqrt{x-1}-\frac{1}{x}*2x }{ \frac{1}{x}*x-\frac{1}{x}*7 }\\\\\\$

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}}*\sqrt{x-1}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x^2}*(x-1)}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{\frac{1}{x}-\frac{1}{x^2}}-2 }{ 1-\frac{7}{x} }\\\\\\\displaystyle L = \frac{ \sqrt{0-0}-2 }{ 1-0 }\\\\\\\displaystyle L = \frac{-2}{1}\\\\\\\displaystyle L = -2\\\\\\$

-------------------

Explanation:

In the second step, I multiplied top and bottom by 1/x. This divides every term by x. Doing this leaves us with various inner fractions that have the variable in the denominator. Those inner fractions approach 0 as x approaches infinity.

I'm using the rule that

$\displaystyle \lim_{x\to\infty} \frac{1}{x^k} = 0\\\\\\$

where k is some positive real number constant.

Using that rule will simplify the expression greatly to leave us with -2/1 or simply -2 as the answer.

In a sense, the leading terms of the numerator and denominator are -2x and x respectively. They are the largest terms for each, so to speak. As x gets larger, the influence that -2x and x have will greatly diminish the influence of the other terms.

This effectively means,

$\displaystyle L = \lim_{x\to\infty} \frac{ \sqrt{x-1}-2x }{ x-7 } = \lim_{x\to\infty} \frac{ -2x }{ x} = -2\\\\\\$

I recommend making a table of values to see what's going on. Or you can graph the given function to see that it slowly approaches y = -2. Keep in mind that it won't actually reach y = -2 itself.

5 0

2 years ago

If Zach has 4 times as many dimes as quarters and they have a combined value of 455 cents, how many of each coins does he have?

aliya0001 [1]

<u>ANSWER: </u>

Zach has 28 dimes and 7 quarters.

<u>SOLUTION: </u>

Given, Zach has 4 times as many dimes as quarters

And they have a combined value of 455 cents,

We need to find how many of each coins does he have?

Let, the number of dimes be x and number of quarters be y.

Then, x = 4y → (1)

Total combined value = 455 cents

x(value of one dime) + y(value of one quarter) = 455 cents

x(10 cents) + x(25 cents) = 455 cents

10x + 25y = 455 → (2)

Now, substitute (1) in (2)

10(4y) + 25y = 455

40x + 25y = 455

65y = 455

y = 7

substitute y value in (1)

x = 4(7) = 28

Hence, zach has 28 dimes and 7 quarters.

4 0

2 years ago

Select the situation that can be represented by 20x

ipn [44]

You work x hours. you get 20 dollars per hour. this is a random situation, because u didn't give us choices.

3 0

2 years ago