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3 years ago

What are the real and complex solutions of the polynomial equation? x^3-64=0

Mathematics

1 answer:

Marrrta [24]3 years ago

4 0

Answer:

Step-by-step explanation:

A difference of two perfect cubes, x^3 - y^3 can be factored into

(x-y) • (x^2 +xy +y^2) =0 equation 1

x ^3 - 64 = 0

(x)^3 - (4)^3 = 0 equation 2

Now substituting equation 2 into equation 1, we get

(x-4) (x^2+(x).(4) +(4)^2) = 0

(x-4) (x^2+4x+16) = 0

so the solutions are

1) x - 4 =0

x=4

x^2 + 4x + 16 = 0

By using the quadratic formula we get the followig solutions:

- B ± √ B2-4AC

x = ————————

x =(-4-√-48)/2=-2-2i√ 3 = -2.0000-3.4641i

x =(-4+√-48)/2=-2+2i√ 3 = -2.0000+3.4641i

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umka2103 [35]

16 balls.

Let's call x the total number of golf balls that Ricardo had before he lost the first 6 balls. (x - 6).
Then he bought 12 more and lost 4 so basically 12 - 4 = 8
Add that to the equation: (x-6) + 8
And now that he has 18 golf balls at end of the second day the total must add to 18.

Full equation: (x-6) + 8 = 18

(x-6) + 8 = 18
(x-6) = 18 - 8 <-- Transpose
(x-6) = 10
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16 is the number of golf balls the Ricardo began with.

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3 years ago

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3 years ago

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.3degrees°F and a standard deviation of 0.6

mylen [45]

<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n=106

Sample mean : $\overline{x}=98.3^{\circ}\ F$

Standard deviation : $\sigma= 0.69^{\circ}F$

Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Then , 99% confidence interval estimate of the mean body temperature of all healthy humans will be :-

$98.3\pm (2.576)\dfrac{0.69}{\sqrt{106}}\\\\\approx98.3\pm0.173=(98.3-0.173,\ 98.3+0.173)=(98.127,\ 98.473)$

Since 98.6 is higher than the upper limit of the confidence interval (98.473), then this suggest that the mean body temperature could be lower then 98.6 degrees.

The best estimate of population mean is always the sample mean. $\mu=\overline{x}=98.3^{\circ}\ F$

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3 years ago

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frez [133]

There were 200 students that attend the dance.

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4 years ago

What is <br> -65 x -2? <br> 5j + 10j?

dolphi86 [110]

They are both simple exercises in addition.
The solutions are:

(-65) x (-2) = <em>130</em>

(5j) + (10j) =<em> 15j</em>

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4 years ago