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3 years ago

Find the volume 14.2 mm 12 mm 8.5 mm

Mathematics

2 answers:

irga5000 [103]3 years ago

8 0

Answer:

1,448.4 mm.

Step-by-step explanation:

Volume is the length, width, and height multiplied together.

14.2 mm x 12 mm x 8.5 mm = 1,448.4 mm^2.

Sidana [21]3 years ago

7 0

Answer:

1448.4mm

Step-by-step explanation:

multiply them all

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Lagrange multipliers have a definite meaning in load balancing for electric network problems. Consider the generators that can o

Ivahew [28]

Answer:

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

Step-by-step explanation:

Optimizing With Lagrange Multipliers

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.

Consider three generators that can output xi megawatts, with i ranging from 1 to 3. The set of unknown variables is x1, x2, x3.

The cost of each generator is given by the formula

$\displaystyle C_i=3x_i+\frac{i}{40}x_i^2$

It means the cost for each generator is expanded as

$\displaystyle C_1=3x_1+\frac{1}{40}x_1^2$

$\displaystyle C_2=3x_2+\frac{2}{40}x_2^2$

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

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:

$g: x_1+x_2+x_3=1000$

$g(x_1,x_2,x_3)= x_1+x_2+x_3-1000$

We now construct the auxiliary function

$f(x_1,x_2,x_3)=C(x_1,x_2,x_3)-\lambda g(x_1,x_2,x_3)$

$\displaystyle f(x_1,x_2,x_3)=3(x_1+x_2+x_3)+\frac{1}{40}(x_1^2+2x_2^2+3x_3^2)-\lambda (x_1+x_2+x_3-1000)$

We find all the partial derivatives of f and equate them to 0

$\displaystyle f_{x1}=3+\frac{2}{40}x_1-\lambda=0$

$\displaystyle f_{x2}=3+\frac{4}{40}x_2-\lambda=0$

$\displaystyle f_{x3}=3+\frac{6}{40}x_3-\lambda=0$

$f_\lambda=x_1+x_2+x_3-1000=0$

Solving for \lambda in the three first equations, we have

$\displaystyle \lambda=3+\frac{2}{40}x_1$

$\displaystyle \lambda=3+\frac{4}{40}x_2$

$\displaystyle \lambda=3+\frac{6}{40}x_3$

Equating them, we find:

$x_1=3x_3$

$\displaystyle x_2=\frac{3}{2}x_3$

Replacing into the restriction (or the fourth derivative)

$x_1+x_2+x_3-1000=0$

$\displaystyle 3x_3+\frac{3}{2}x_3+x_3-1000=0$

$\displaystyle \frac{11}{2}x_3=1000$

$x_3=181.8\ MW$

And also

$x_1=545.5\ MW$

$x_2=272.7\ MW$

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

5 0

3 years ago

15 3/4% is equal to which decimal? A- 0.1575 B- 157.25 C-15.25 D- 15.34

eimsori [14]

15 3/4% = 15.75%
15.75% = 0.1575
The answer is A.

6 0

3 years ago

Read 2 more answers

The city council is considering a law that would ban smoking in all public facilities. A sample has been selected from the commu

lisov135 [29]

Answer:

Reject Null Hypothesis given that P-value < ∝

Step-by-step explanation:

Applying the Five ( 5 ) step model and assuming ∝ = 0.05

First step : determine the Null hypothesis

H0 : Age and support for Anti-smoking = independent

Second step : Determine the alternate hypothesis

Ha : Age and support for Anti-smoking ≠ independent

Thirdly : Identify significance level ( ∝ ) = 0.05

4th step : Calculate the Test statistic and P-value

Chi-squared test = 36.1429 using excel function

P-value = 1 - CHISQ.DIST(36.1429, 1, TRUE) < 0.0001

finally : we can conclude that Age and support for Anti -smoking are not Independent hence we Reject The Null hypothesis. Given that

P-value < ∝

3 0

3 years ago

What’s 1/5 divided by 1/12?

Ksivusya [100]

When divided fractions you flip the second fraction

1/5 x 12/1

This then equals
12/5

That simplifies to 2 2/5

7 0

3 years ago

Read 2 more answers

What are the first three terms of the sequence represented by the recursive formula

AnnyKZ [126]

Explecit formula
hmm, seems to be a geometric sequence
so
an=a1+d(n-1)
d=common differnce
a1=first term

given
a1=firstterm=9.2

and the difference between each tierm is 1.8

an=9.1-1.8(n-1) is da equation

so 4th option

5 0

3 years ago