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jek_recluse [69]
3 years ago
14

Here is the third problem:)

Mathematics
2 answers:
lesya [120]3 years ago
6 0

Answer:

15.0

Step-by-step explanation:

we are finidng the adjacent angle, they have given us the opposite and the missing adjacent side so we use tan

tan25=7/x

since x is at the bottom then switch

x= 7/tan25

x= 15. 012

Debora [2.8K]3 years ago
5 0

Answer:

x = 15.01

Step-by-step explanation:

Given degrees 25

Since x is between the right angle and 25, x is adjacent

7 being the other shortest side would be the opposite

Given adjacent and opposite, you can use tangent

Tangent = opposite/adjacent

Tan(25) = 7/x

0.4663076582 = 7/x

x = 7/0.4663076582 (use calculator)

Solution: x = 15.0115484421

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32.9% i think

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What number would be ten times greater than 0.05?
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Answer:

0.5?

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3 years ago
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
Which of the following represents the factorization of the binomial below ? x^2 - 144
Dima020 [189]

It factors to (x+12)(x-12)

This is the same as (x-12)(x+12) as we can multiply two expressions in any order we want. This is like saying 7*5 is the same as 5*7

I used the difference of squares rule to factor x^2 - 144. It might help to write x^2 - 144 as x^2 - 12^2, then compare it to a^2 - b^2 = (a-b)(a+b)

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3 years ago
Find the mean of the following<br> data set.<br> 1,1,2,4,6,7,7,8,9,10,12,13,17,17,18
lisabon 2012 [21]

Answer:

8.8

Step-by-step explanation:

Add all numbers together to get 132

All number of numbers together to get 15

Divide the sum of all numbers by the number of numbers:

132/15

8.8

pls mark brainliest!

6 0
2 years ago
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