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3 years ago

Please help. thank you

Mathematics

2 answers:

Strike441 [17]3 years ago

7 0

The first answer is correct

Ne4ueva [31]3 years ago

3 0

Answer:6 units^2

Cut the shape in two to make a square and triangle.

Square:(2)(2)=4

Triangle:(1/2)(2)(2)=2

add both together 4+2=6

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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

4 years ago

Suppose the professor decides to grade on a curve. If the professor wants 16% of the students to get an A, what is the minimum s

vladimir1956 [14]

There isn't enough info to determine that, I believe. You would need an equation that would allow me to determine the minimum output for an A.

3 0

3 years ago

Are the points U, H, and L collinear? U E S H

butalik [34]

Answer:

Yes

Step-by-step explanation:

Collinear means points are lying on the same straight line. U, H, and L are all lying on the line l.

4 0

3 years ago

Make s, u subject of the formula <img src="https://tex.z-dn.net/?f=v%5E%7B2%7D%20%3D%20u%20%7B%7D%5E%7B2%7D%20%2B%202as" id="

Romashka [77]

Answer:

s = $\frac{v^2-u^2}{2a}$

Step-by-step explanation:

Given

v² = u² + 2as ( subtract u² from both sides )

v² - u² = 2as ( divide both sides by 2a )

$\frac{v^2-u^2}{2a}$ = s

Given

v² = u² + 2as ( subtract 2as from both sides )

v² - 2as = u² ( take the square root of both sides )

± $\sqrt{v^2-2as}$ = u

6 0

4 years ago

Read 2 more answers

Please help with this

Arturiano [62]

The missing side of the triangles are 5, 16.92, 7 and 5 respectively.

Step-by-step explanation:

Step 1: Use the Pythagoras Theorem to find the missing sides.

a² + b² = c²

In the first triangle, a = 3, b = 4.

c² = 3² + 4² = 9 + 16 = 25

⇒ c = 5

∴ Missing side is 5

In the second triangle, a = 15, b = 8

c² = 15² + 8² = 225 + 64 = 289

⇒ c = 16.92

Missing side is 16.92

In the third triangle, b = 24, c = 25

a² = c² - b²

a² = 25² - 24² = 625 - 576 = 49

⇒ a = 7

Missing side is 7

In the fourth triangle, a = 12, c = 13

b² = c² - a²

b² = 13² - 12² = 169 - 144 = 25

⇒ b = 5

Missing side is 5

7 0

3 years ago