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3 years ago

6

A marathon is 131/5 miles long. If 4 people divide up the distance equally, how many miles does each person need to run?

1 answer:

disa [49]3 years ago

8 0

Answer:

$6\frac{11}{20}\ mi$

Step-by-step explanation:

we know that

A marathon is 131/5 miles long

If 4 people divide up the distance equally,

then

Divide the total distance by 4

$\frac{(131/5)}{4}=\frac{131}{20}\ mi$

Convert to mixed number

$\frac{131}{20}\ mi=\frac{120}{20}+\frac{11}{20}=6\frac{11}{20}\ mi$

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Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer t

11Alexandr11 [23.1K]

Answer:

The solution is $z = -2.853 - i 0.927$ .

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

$z^{n} = r^{n} \cdot (\cos n\theta + i \sin n\theta)$

Where $r$ is the norm of the complex number. In this case, expression can be written as:

$-i 243 = 3^{5} \cdot (\cos 5\theta + i \sin 5\theta)$

The real component must be equal to zero and complex component must be equal to -1. That is to say:

$\cos 5\theta = 0$

$\sin 5\theta = -1$

Possible solutions for each component are, respectively:

Real component

$5\theta = \cos^{-1}0$

$5\theta = \frac{\pi}{2} \pm \pi\cdot j$ , $\forall j \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{10} \pm \frac{\pi}{5} \cdot j$ , $\forall j \in \mathbb{N}_{O}$

Possible solutions: $\frac{11\pi}{10}$ , $\frac{13\pi}{10}$ , $\frac{3\pi}{2}$

Complex component

$5\theta = \sin^{-1}(-1)$

$5\theta = \frac{3\pi}{2} \pm 2\pi \cdot j$ , $\forall j \in \mathbb{N}_{O}$

$\theta = \frac{3\pi}{10} \pm \frac{2\pi}{5} \cdot j$ , $\forall j \in \mathbb{N}_{O}$

Possible solutions: $\frac{11\pi}{10}$ , $\frac{3\pi}{2}$

There is one solution whose argument is strictly between 180 degrees ( $\pi$ ) and 270 degrees ( $1.5\pi$ ).

$z = 3 \cdot \left( \cos \frac{11\pi}{10} + i \sin \frac{11\pi}{10} \right)$

$z = -2.853 - i 0.927$

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alexandr402 [8]

try calculating the two numbers together

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anygoal [31]

I think the answer is (3,3) I’m sorry if it’s wrong

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vaieri [72.5K]

Answer:

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Step-by-step explanation:

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zloy xaker [14]

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