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liberstina [14]

2 years ago

10

Find all the cube roots of cube roots

le="2 {e}^{2i\pi} " alt="2 {e}^{2i\pi} " align="absmiddle" class="latex-formula">

1 answer:

DochEvi [55]2 years ago

7 0

Answer:

It is

$1.26{e}^{ \frac{2i\pi}{3}}$

Step-by-step explanation:

$2 {e}^{2i\pi}$

cube root:

$= \sqrt[3]{2 {e}^{2i\pi}} \\ = ( {2 {e}^{2i\pi})}^{ \frac{1}{3} } \\ = {2}^{ \frac{1}{3} } ( {e}^{ \frac{2i\pi}{3} } ) \\ = 1.26{e}^{ \frac{2i\pi}{3}}$

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Correlation coefficient helps us to know how strong is the relation between two variables. The strength of the model is a strong positive correlation.

<h3>What is the correlation coefficient?</h3>

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

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3 years ago

A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let <em>x</em> be the width and <em>y </em>the length of the rectangular field.

Let <em>C </em>the total cost of the rectangular field.

The side made of heavy duty material of length of <em>x </em>costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are <em>x, y, y</em>. Thus

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We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

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2 years ago

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Phoenix [80]

Answer:

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Step-by-step explanation:

Quadratic function is function of the form $P(x)=ax^2+bx+c$ where a, b and c are real numbers and $a\neq 0$

A number is said to be a rational number if it can be written in the form $\frac{u}{v}$ where u and v are integers and $v\neq 0$ .

A number is said to be a complex number if it can be written in the form u+iv where u and v are real numbers.

A number 'a' is said to be a zero of a function P(x) if $P(a)=0$

We know that if zero of a fraction is of form u+iv then its other zero is u-iv.

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So, given equation is $\left ( x-(3-7i) \right )\left ( x-(3+7i) \right )$

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3 years ago