Ask question

Ask question

All categories

3 years ago

5

Find the value of c and AB if B is between A and C,AB=2r,AC=-5and BC=7

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

AB=2r

BC=7

AC=AB+BC

-5=2r+7

-12=2r

-6=r

AB=-12

You might be interested in

Please help me with this!

stich3 [128]

Answer:

y = x^2 - 4x - 6.

Step-by-step explanation:

The roots are 2 + √10 and 2 - √10, so in factor form we have:

(x - (2 + √10))(x - (2 - √10))

= ( x - 2 - √10)(x - 2 + √10)

= x^2 - 2x + √10x - 2x + 4 - 2√10 - √10x + 2√10 - √100

= x^2 -4x + 4 - 10

= x^2 - 4x - 6.

7 0

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

Solve 4x-2y=12 for y <br> Ayo help

Leni [432]

Answer:

y = - 6 + 2x

Step-by-step explanation:

Given

4x - 2y = 12 ( subtract 4x from both sides )

- 2y = 12 - 4x ( divide all terms by - 2 )

y = - 6 + 2x

4 0

3 years ago

Read 2 more answers

Ivahew [28]

Answer:

A

D

Step-by-step explanation:

6 0

3 years ago

A. Developer. Owns. 54. Acres. Of land. If he. Plans. To use. 3.2. Acres. Of the land. For an entrance. Into a housing developme

lukranit [14]

How much of the land is available to be divided into lots?

4 0

3 years ago

Read 2 more answers