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3 years ago

10

Brendan and Marie are each assigned a paper for a class they share. Brendan decides to write 41 pages at a time while Marie deci

des to write 18 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?

1 answer:

hram777 [196]3 years ago

7 0

Answer:

18+18=38, since they did the same number that's the least it could be

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The height of the rectangle and the triangle are the same. The base of the triangle is half the base of the rectangle.

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<h2>Answer: C 375 cm²</h2>

Step by step explanation: The last answer i wrote was wrong, so i retook the quiz and got 100% and this was right.

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2 years ago

Your price on a particular model is $125 however to get a service contract you offer to sell it for $115 how much discount are y

Arisa [49]

It would be an 8 percent discount because 115 is 92 percent of 125.

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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

A crew has paved 3/4 of a mile of road. If they have completed 50% of the work, how long is the road they are paving?

mel-nik [20]

Answer:

1.5

Step-by-step explanation:

Let the value be x,

(3/4) = 50% * x

x = 1.5

Thenks and mark me brainliest :))

3 0

2 years ago

HELP PLEASE. A pizza shop charges customers based on the area of the pizza they order. The cost of a pizza in dollars can be rep

san4es73 [151]

For this case we have that the cost of each pizza is given by the following function:

$S (r) = 0.1 \pi * r ^ 2$

Where:

r: It's the radius of the pizza

IF a pizza cost $26.32 we have:

$26.32 = 0.1 \pi * r ^ 2$

We cleared the radius, using $\pi = 3.14$ :

$\frac {26.32} {0.1} = \pi * r ^ 2\\263.2 = 3.14r ^ 2\\\frac {263.2} {3.14} = r ^ 2\\83.82 = r ^ 2\\r = \pm \sqrt {83.82}$

We choose the positive value:

$r = 9.15$

So, the radius of the pizza is $9.16 \ in$

Then, the diameter is: $2r = 2 * 9.15 = 18.30 \ in$

Finally, the diameter of the pizza is: $18.30 \ in$

Answer:

Option B

4 0

3 years ago

Read 2 more answers