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eimsori [14]
3 years ago
8

Which value is NOT a solution of 8x3 – 1 = 0?

Mathematics
1 answer:
Tpy6a [65]3 years ago
7 0

<u><em>Note: As you may have unintentionally missed to add the value choices. But, I would make sure to explain the concept so that you may improve your understanding in terms of solving these type of questions.</em></u>

Answer:

Any value other than the values x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4} will not be a solution of 8x^3\:-\:1\:=\:0.

Step-by-step explanation:

Considering the equation

8x^3\:-\:1\:=\:0

Steps to solve the equation

8x^3-1=0

\mathrm{Add\:}1\mathrm{\:to\:both\:sides}

8x^3-1+1=0+1

\mathrm{Simplify}

x^3=\frac{1}{8}

\mathrm{Divide\:both\:sides\:by\:}8

\frac{8x^3}{8}=\frac{1}{8}

\mathrm{Simplify}

x^3=\frac{1}{8}

As

\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}

x=\sqrt[3]{\frac{1}{8}},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1-\sqrt{3}i}{2}

So,

x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}

Therefore,

Any value other than the values x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4} will not be a solution of 8x^3\:-\:1\:=\:0.

Keywords: solution, value

Learn more about equation solution from  brainly.com/question/1679491

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27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 47 college students are randomly sele
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Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

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P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

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Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

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0.82226 - 0.084102

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