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adoni [48]
3 years ago
8

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:

<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.

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

Or

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?<br><br> A- 0.1575<br> B- 157.25<br> C-15.25<br> 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
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