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Kryger [21]
3 years ago
12

HELP For each triangle, find x and the measure of each side.

Mathematics
1 answer:
Brums [2.3K]3 years ago
7 0

Answer:

5

Step-by-step explanation:

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Gavin needs to read at least 150 pages of his book this week. he has already read 82 pages. how many more pages p must gavin rea
Nataly_w [17]
I'm doing the same thing right now and I'm lost.
7 0
3 years ago
The revenue of a company that makes backpacks is given by the formula R = 34.S0x, where x represents the number of backpacks sol
alexgriva [62]

Answer:

Revenue = 1380

Step-by-step explanation:

Given:

Revenue means the sales or turnover of a company when it sells its products. In other words, it is nothing but the income of a company on selling the products.

Here, the company is selling backpacks. So, revenue is the amount earned by the company on selling 'x' backpacks. The linear model to represent the same is given below.

The revenue received from selling 'x' backpacks is given as:

R=34.50x

Number of backpacks sold (x) = 40

Now, in order to find the revenue received on selling 40 backpacks, we need to plug in 40 for 'x' in the equation above and solve for the revenue, 'R'.

On plugging 40 for 'x', we get:

R=34.50\times 40\\\\R=1380

Therefore, the revenue received by the company on selling 40 backpacks is 1380.

8 0
3 years ago
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 ​people, while each carton of c
lutik1710 [3]

Answer:

  233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

  40f +25c ≤ 21000

The other expresses the limit on volume.

  20f + 5c ≤ 7000

_____

<u>Feasible Region vertex</u>

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

  5(20f +5c) -(40f +25c) = 5(7000) -21000

  60f = 14000

  f = 233 1/3

The second boundary line equation can be rearranged to find c:

  c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

  (f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

<u>Check of Integer Solution</u>

Trying these in the constraint inequalities gives ...

  • 40·233 +25·467 = 20,995 < 21000
  • 20·233 +5·467 = 6995 < 7000

<u>Selection of the Answer</u>

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

  p = 13f + 6c

The values of p at the vertices are ...

  p = 13·233 + 6·467 = 5831

  p = 13·0 + 6·840 = 5040

  p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

7 0
2 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
Polynomial division (-12m^2-49mn-44n^2)/(-3m-4n)
Ket [755]
First factor -12m^n - 49mn - 44n^2 to get -(4n+3m)(11n + 4m) then the equation would be:
-(3m + 4n)(4m + 11n) / (-3m - 4n)
Then, cancel out the like terms and the final answer would be
4m + 11n
7 0
3 years ago
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