If 2+√3/2-√3= a+b√3 Find a and b ​

Answer: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)

a) Formulate this problem in terms of an objective function and constraint(s).

b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.

c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2

d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?

e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?

Step-by-step explanation: A small city gets its water supply from three sources: two wells and a small upland reservoir. The well supplies require pumping, and so are more expensive. Reservoir water flows directly to the town by gravity. The town needs a total of 20 mgd (million gallons per day) of water. The cost of water is zero if obtained from the reservoir, $60/million gallons if from Well-field 1, and $30/million gallons if from Well-field 2. The reservoir can deliver 9 mgd; Well-field 1 has a capacity of 25 mgd, and Well-field 2 has a capacity of 3 mgd. (Hint: use the Lagrange multipliers for the last three questions. You can check your answers using Excel solver)

a) Formulate this problem in terms of an objective function and constraint(s).

b) Solve the problem by hand using the Lagrange Multipliers, and find the minimum total cost combination of flows from each source, and minimum total cost.

c) How much, annually, should the city be willing to pay to expand the capacity of the reservoir, Well-field 1, and Well-field 2

d) If the city decided to conserve water and the demand decreased from 20 to 19.5 mgd, how much would the city benefit from this conservation?

e) If you had a chance to expand the capacity of reservoir, Well-field 1, or Well-field 2 reservoir, Well-field 1, and Well-field 2 What would be the new cost? which one(y) would you prefer to increase, why?

Answer:

F(x)=(x+6)^2

Step-by-step explanation:

Hope this helps!

Answer:

2b. R line is lower.

2c. It is lower because the y-intercept is negative.

Answer: ill take one for you john

Step-by-step explanation:

Answer:

[tex]7x + 2 = 8x + 5 \\ collecting \: like \: terms \: \\ 7x - 8x = 5 - 2 \\ - 1x = 3[/tex]

(ecuacion primer grado para hoy. ). what does this mean..

Answer:

Recopilar términos semejantes

Answer:

7/128

Step-by-step explanation:

Answer:

just put the 25 into the equation, and you get the M, as the money she earn

2.5(25) + 12 = 74.5 that is the amount she earns

Answer: 74.5

Step-by-step explanation:

M = money = ?

f = faces she paint = 25 faces

M = 2.50(f) + 12 —> ? = 2.50(25) + 12 = 74.5

Answer:

x=25

Step-by-step explanation:

Answer:

It is not in the players favor because there is a 4/13 chance that the player will win money. That"s not even 50%. So its up to the player if they want to take that risk but its a 0.3% chance that the player will win money.

Hope this helps :)

Answer:

Simplify the expression.

Exact Form:

111129715061983798933/3

Decimal Form:

3.70432383⋅10^19

Step-by-step explanation:

Answer:

exact form is 111129715061983798933/3

decimal form 3.70432383*10^19

Step-by-step explanation:

Answer:

what is it what math

Step-by-step explanation:

um what kind of math is this high school primary school

9514 1404 393

Answer:

Step-by-step explanation:

Ms. Liu will have to pay 8p for p bags of popcorn, and 3w for w bottles of water. The amount she will have left will be these amounts subtracted from $40.

  40 -8p -3w . . . . represents the money remaining

For p=3 and w=4, this evaluates to ...

  40 -8(3) -3(4) = 40 -24 -12 = 4

Ms. Liu will have $4 left after her purchase.

Answer:

d+13=4 is wrong it would be divede because it says put one in each napkin so it is being divided

Step-by-step explanation: 13/d

Answer:

1. Triangle XYZ undergoes a translation.

2. Triangle X'Y'Z' undergoes a reflection across the x-axis

The total sunflowers and roses Lira has is 18 and 27 respectively

Let

Total flowers = x

Roses = 2/9 of x

= 2/9x

Remaining = x - 2/9x

= (9x-2x) / 9

= 7/9x

Sunflowers = 3/7 of 7/9x

= (3 × 7)/(7 ×9)x

= 21/63x

Tulips = 36

Total = roses + sunflowers + tulips

x = 2/9x + 21/63x + 36

x - 2/9x - 21/63x = 36

(63x -14x-21x) / 63 = 36

28/63x = 36

cross product

28x = 36 × 63

28x = 2268

x = 2268/28

x = 81

Therefore,

Total flowers = x

= 81 flowers

Roses = 2/9x

= 2/9 × 81

= 18 flowers

Sunflowers = 21/63x

= 21 / 63 × 81

= 27 flowers

Read More:

https://brainly.com/question/2261275

Answer:

4736

Step-by-step explanation:

1) 100 divided by 5 is 20

2) 20 times 3 is 60

3) 60 times 79 is 4740

4) 4740 subtract from 4 is 4736

5) Answer is 4736

Answer:

4736

Step-by-step explanation:

5*20 = 100

20*3 = 60

60*79 = 4740

4740 - 4 = 4736

Answer:

74 + 43[tex]\sqrt{3}[/tex]

Step-by-step explanation:

For this problem, let's say side x is 2 + [tex]5\sqrt{3}[/tex] and side y is 7 + [tex]4\sqrt{3}[/tex].

To find the area of a rectangle, you need to multiply both height and width, and in this case, x and y.

(x)(y) = 14 + 8[tex]\sqrt{3}[/tex] + 35[tex]\sqrt{3}[/tex] + 60

= 74 + 43[tex]\sqrt{3}[/tex]

Answer:

$16

Step-by-step explanation:

let x = cost of ricotta cheese

let x + 5 = cost of parmesan cheese

.5x + .25(x+5) = $9.5

now we plug that value back into x + 5 to find the cause of the cost of parmesan cheese

The cost of ricotta cheese will be $11. And the cost of parmesan cheese will be $16.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Olivia buys 0.5 pounds of ricotta cheese and 0.25 pounds of parmesan cheese. The parmesan cheese costs $5 more than the ricotta cheese. She pays a total of $9.50.

Let 'x' be the cost of ricotta cheese. Then the cost of parmesan cheese will be (x + 5). Then the equation is given as,

0.5x + 0.25 · (x + 5) = $9.5

Simplify the equation, then we have

0.5x + 0.25 · (x + 5) = $9.5

0.5x + 0.25x + 1.25 = $9.5

0.75x = 8.25

x = $11

Then the cost of parmesan cheese is given as,

x + 5 = $11 + 5

x + 5 = $16

The cost of ricotta cheese will be $11. And the cost of parmesan cheese will be $16.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Answer:

A. Anna's route is about 4 miles shorter than Alex's route, but he gets home about 20 minutes before she does because he

is traveling faster.

Step-by-step explanation:

Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fast, how far, or how long one or more objects have traveled. These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths

Answer:

98.2

Step-by-step explanation:

100 x 0.982 = 98.2

98.2 / 100 = 0.982

Step-by-step explanation:

z-score of X = 6150

[tex] \frac{6150 - 6250}{250} = - 0.4 \\[/tex]

z-score of X = 6350

[tex] \frac{6350 - 6250}{250} = - 0.4[/tex]

P(X<6150) + P(X>6350)

=P(z<-0.4) + P(z>-0.4)

=0.3446+0.3446

=0.6892

Answer:

100 mins/ 1 hour 40 mins

Step-by-step explanation:

if 5 hens are known to lay 5 eggs then each hen lays 1 egg a minute

so multiply 1 by 100

and 100 time 1 equals 100

Answer:

11

Step-by-step explanation:

17-6=11

big brain

Answer:

11

Step-by-step explanation:

17-11=6 the smallest number is 11

Answer:

3/17

Step-by-step explanation:

-2x + 3(-5x + 1)

-2x -15x +3

-17x + 3

17x = 3

x = 3/17

Rewrite the equation as

2lw+2lh+2wh=a.2lw+2lh+2wh=a

Subtract

2lh

from both sides of the equation.

2lw+2wh=a−2lh

Factor

2w out of 2lw+2wh.

2w(|+h)=w−2lh

Divide each term by

2(l+h)

and simplify.

.w=a−2lh2(l+h)

Answer:

A = (-6, 4)

B = (2,2)

C =  (-2, 2)

Step-by-step explanation:

If a coordinate (x, y) is dilated by a factor of k, the resulting coordinate will be expressed as (kx, ky). Note that each coordinate is multiplied by the scale factor  Given the coordinates (-3,2),(1,1)(-1,-1), if they are dilated by a factor of 2, the resulting coordinate will be;

A = (2(-3), 2(2)) = (-6, 4)

B = (2(1),2(1)) =(2,2)

C = (2(-1), 2(-1)) = (-2, 2)

Step-by-step explanation: It already tells you three of the coordinates. From plotting those, just create a vertical line from (0, -7) up that is equal to 16 and connect that coordinate with (8, 0).

The area of the cylinder is a function of its height (h) and radius, ([tex]\mathbf{4\sqrt 3}[/tex])

The exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]

The given parameters are:

[tex]\mathbf{Area =56\pi\sqrt 6}[/tex]

[tex]\mathbf{r=4\sqrt 3}[/tex]

The surface area of a cylinder is calculated as:

[tex]\mathbf{Area = 2\pi rh + 2\pi r^2}[/tex]

Substitute values for Area

[tex]\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}[/tex]

Divide through by pi

[tex]\mathbf{56\sqrt 6= 2 rh + 2r^2}[/tex]

Substitute value for r

[tex]\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}[/tex]

[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}[/tex]

[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}[/tex]

Collect like terms

[tex]\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}[/tex]

Make h the subject

[tex]\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}[/tex]

[tex]\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}[/tex]

Rationalize

[tex]\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}[/tex]

[tex]\mathbf{h = 7\sqrt 2- 4\sqrt 3}[/tex]

Hence, the exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]

Read more about surface areas t:

https://brainly.com/question/25131428