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3 years ago

14

What is the simplified version of 3\sqrt{135}

2 answers:

Aleonysh [2.5K]3 years ago

7 0

Answer:

The simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$ .

Step-by-step explanation:

The given expression is

$\sqrt[3]{135}$

According to the property of radical expression.

$\sqrt[n]{x}=(x)^{\frac{1}{n}}$

Using this property we get

$\sqrt[3]{135}=(135)^{\frac{1}{3}}$

$\sqrt[3]{135}=(27\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3\times 5)^{\frac{1}{3}}$

$\sqrt[3]{135}=(3^3)^{\frac{1}{3}}\times (5)^{\frac{1}{3}}$ $[\because (ab)^x=a^xb^x]$

$\sqrt[3]{135}=3\times \sqrt[3]{5}$ $[\because \sqrt[n]{x}=(x)^{\frac{1}{n}}]$

$\sqrt[3]{135}=3\sqrt[3]{5}$

Therefore the simplified version of $\sqrt[3]{135}$ is $3\sqrt[3]{5}$ .

ohaa [14]3 years ago

4 0

$9 \sqrt{15}$

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The load balance $(x_1,x_2,x_3)=(545.5,272.7,181.8)$ Mw minimizes the total cost

Step-by-step explanation:

<u>Optimizing With Lagrange Multipliers</u>

When a multivariable function f is to be maximized or minimized, the Lagrange multipliers method is a pretty common and easy tool to apply when the restrictions are in the form of equalities.

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It means the cost for each generator is expanded as

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$\displaystyle C_3=3x_3+\frac{3}{40}x_3^2$

The total cost of production is

$\displaystyle C(x_1,x_2,x_3)=3x_1+\frac{1}{40}x_1^2+3x_2+\frac{2}{40}x_2^2+3x_3+\frac{3}{40}x_3^2$

Simplifying and rearranging, we have the objective function to minimize:

$\displaystyle C(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)$

The restriction can be modeled as a function g(x)=0:

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$x_1=545.5\ MW$

$x_2=272.7\ MW$

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