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Alex787 [66]
3 years ago
13

Write in expression form. 8 times the quantity of a number and 6​

Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Answer:

8(x+6)

Step-by-step explanation:

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Use the zeros and the labeled point to write the quadratic function
Anarel [89]

Answer:

y = 2x2 - 10x + 12

Step-by-step explanation:

5 0
2 years ago
ANSWER ASAP What is the volume of this right triangular prism? A. 180 cubic centimeters B. 120 cubic centimeters C. 90 cubic cen
Bess [88]

Volume of the right triangular prism 90 cube cm.

Step-by-step explanation:

Given,

In the right triangular prism

Length (l) = 6 cm

Base (b) = 5 cm

Height (h) = 6 cm

To find the volume of the right triangular prism

Formula

Volume of the right triangular prism = \frac{1}{2}bhl

Now,

Volume of the right triangular prism = \frac{1}{2}×6×6×5 cube cm

= 90 cube cm

5 0
3 years ago
A data set consists of the following data points:
aleksley [76]
<span>(3,5),
(5,8),
(6,13)
------
(14,26)/3
 
then use the point slope form of a line to find equation of line

</span>y-y_1=m(x-x_1)&#10;\\y -  \frac{26}{3}  = 2.5(x- \frac{14}{3})&#10;\\y -  \frac{26}{3}  =  \frac{5}{2} (x- \frac{14}{3})&#10;\\y -  \frac{26}{3}  =  \frac{5}{2} x-  \frac{5}{2}\times\frac{14}{3}&#10;\\y -  \frac{26}{3}  =  \frac{5}{2} x-  \frac{35}{3}&#10;\\6y-52=15x-70&#10;\\15x-6y-18=0
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Find y-intercept for x = 0.

</span>15x-6y-18=0&#10;\\15\times0-6y-18=0&#10;\\-6y=18&#10;\\y=-3<span>

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4 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
PLEASE HELP 20 POINTS PLEASE HELP BROOO
Ulleksa [173]

Answer: 31700 sq mi

Step-by-step explanation: Well in order to find out the sq mi for Lake Superior you will add 7340 and 24360 which equals 31700 sq mi.

7 0
3 years ago
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