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Assoli18 [71]
3 years ago
7

Which answer is equal to i^58? A) -i B) -1 C) i D) 1

Mathematics
2 answers:
rjkz [21]3 years ago
6 0
Since it is positive power, the answer is -1 so it is B.
bearhunter [10]3 years ago
5 0

Answer:

B) - 1.

Step-by-step explanation:

Given  : i^{58}.

To find : Solve it.

Solution : We have given   i^{58}.

We know that even power of imaginary number is -1 .

i^{2} = -1.

So, (i^{2})^{2}= 1.

(i^{4})= 1.

We can write  i^{58} as  (i^{4})^{14}.

Then  i^{58}= (i^{4})^{14} *  i^{2}.

Plug  (i^{4})= 1 and  i^{2} = -1.

i^{58}=  (1^{14}) *  i^{2}

  i^{58} = 1 *-1.

i^{58} = -1.

Therefore, B) - 1.

 

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2 years ago
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+
tekilochka [14]

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

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How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

h(t) = -16t^{2} + 72t + 100

-16t^{2} + 72t + 100 = 0

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16t^{2} - 72t - 100 = 0

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

16t^{2} - 72t - 100 = 0

So

a = 16, b = -72, c = -100

\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584

t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61

t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.

3 0
3 years ago
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Dmitry_Shevchenko [17]

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3 0
3 years ago
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