Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of the cable by arranging the cable in a Y-shaped configuation. Centerville is located at ( 10 , 0 ) in the x y -plane, Springfield is at ( 0 , 5 ) , and Shelbyville is at ( 0 , − 5 ) . The cable runs from Centerville to some point ( x , 0 ) on the x -axis where it splits into two branches going to Springfield and Shelbyville. Find the location ( x , 0 ) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
To solve this problem we need to minimize the following function of x : f ( x ) =
We find that f ( x ) has a critical number at x =
To verify that f ( x ) has a minimum at this critical number we compute the second derivative f ' ' ( x ) and find that its value at the critical number is ,
a positive number. Thus the minimum length of cable needed is

Answers

Answer 1

Answer:

hi i dont understand this

Step-by-step explanation:

sorry

Answer 2

The function will be

[tex]f(x) = 9 - x + \sqrt[2]{ {x}^{2} + 9} [/tex]

and minimum value required will be

[tex]9 + \sqrt[3]{3} [/tex]

How to solve this problem?

The steps are as follow:

[tex]f(x) = (9 - x) + \sqrt[2]{ (x^2 + 3^2) } \\ =(9 - x) + \sqrt[2]{ (x^2 +9)} \\ f(x) = \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 \\ f(x) = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9}} = 1 \\ 2x = \sqrt{ {x}^{2} + 9} \\ 4{x}^{2} = { x}^{2} + 9 \\ 3 {x}^{2} = 9 \\ {x} = \sqrt{3} [/tex]

so putting value of in f(x) we will get

[tex]f( \sqrt{3} ) = 9 - \sqrt{3} + \sqrt[2]{ { (\sqrt{3} )}^{2} + 9} \\ = 9 + 2 \sqrt{3} [/tex]

So The function will be

[tex]f(x) = 9 + \sqrt[2]{ {x}^{2} + 9}[/tex]

and minimum value required will be

[tex]9 + \sqrt[3]{3} [/tex]

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Related Questions

The solids are similar. Find the missing dimension.

Answers

Answer:

i need the picture

Step-by-step explanation:

To find the missing measure of similar solids, set up a proportion of corresponding dimensions. Then, cross multiply and divide. To find the surface are of similar solids, set up a ratio of surface area equal to the squared ratio of given linear measures. Then cross multiply and divide.

I need to know this answer it’s very important. It’s on a test and if I don’t get an answer I’ll have to go to summer school!!!

Answers

28/24 = 42/AC
28.AC = 42.24
AC = 42.24/28
AC = 36 ft

Solve the equation please

Answers

Answer:

y = 14

Step-by-step explanation:

| y + 3 | = 17

simplify:

y + 3 = 17

subtract 3 on both sides:

y + 3 - 3 = 17 - 3

y = 14

I need help asap please someone help

Answers

Answer:

yes,yes,no,yes

Step-by-step explanation:

Please help! I dont have much more time to do school today

Answers

Answer:

B

Step-by-step explanation:

Answer:

put the numbers in order, cross off low/high pairs, add the leftover numbers, divide the sum by two

Step-by-step explanation:

In UVW, the measure of ZW = 90°, UV = 96 feet, and VW = 58 feet. Find the
measure of V to the nearest degree.

Answers

Answer:

V=52.831≈ 53

Step-by-step explanation:

cosV=

hypotenuse

adjacent

=

96

58

\cos V = \frac{58}{96}

cosV=

96

58

V=\cos^{-1}(\frac{58}{96})

V=cos

−1

(

96

58

)

V=52.831\approx 53^{\circ}

V=52.831≈53

weeeeeeeeeeeeeee3seeeeeeehehejdurut

Answers

Answer:

huh....is there a problem

......are you good-?

I need help plzzzzzzzzz​

Answers

Answer is:

a= 90-70

=20

Answer:

The missing angle is 20°

Step-by-step explanation:

The square by the vertex indicates that this is a right angle. A right angle measures 90°. So what you can do is subtract the 70° from the 90°, to get 20°.

Hope this helps! Have a great day! :)

HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER

Answers

Answer:

B 53

Step-by-step explanation:

what is the value expression 26+22÷12 pls help me​

Answers

The answer is 23 .833333

Answer:

As a decimal : 27.833

As a fraction : 167/6

Step-by-step explanation:

26 + 22/12

=

26/1 + 22/12

=

26/1 + 11/6

=

156/6  + 11/6

156 + 11 / 6

=

167/6

or as a decimal 27.833

Hope this helps!

6 out of 13 of your
friends are on the
basketball team. What
percent of your friends
are on the basketball
team? Round to the
tenths place.

Answers

Answer:

46.2%

Step-by-step explanation:

6/13 x 100% = 46.1538461538% (rounded to the nearest tenth: 46.2%)

Hope that helps!

Answer:

(A) Theoretical

Step-by-step explanation:

bec this is the real answer

it cost $5.25 for a bottle of 150 vitamins. if the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?

Could you please give me the equation and show me how you got it please so I could understand... thanks.

Answers

Answer:

8.75

Step-by-step explanation:

if a bottle of 150 vitamins is 5.28...then that of 250 vitamins

x is the value of a single vitamin, therefore

5.25- 150

x- 1

150x divide by 5.25=0.035

therefore 250*0.035= 8.75

lan makes 60 cakes.
He gives à of the cakes to Helen.
He gives 20% of the 60 cakes to Sue.
What fraction of the 60 cakes does he have left?

Answers

Answer:

4/5

Step-by-step explanation:

there are 5 20s in 100 so 20 % is equal 1/5 so take 1/5 away and you get 4/5

si se opta por la primera modalidad cuanto de dinero se abra pagado al sexto mes

Answers

Answer:Los contratos de opciones se pueden tasar utilizando modelos matemáticos como los modelos de precios Black-Scholes o Binomial. El precio de una opción se compone principalmente de dos partes distintas: su valor intrínseco y su valor temporal. ... El valor temporal se basa en la volatilidad esperada del activo subyacente y el tiempo hasta el vencimiento de la opción.

Step-by-step explanation:¡espero que esto ayude!

Btw's I speak english too!

Pls help this is due today ! Find the value x:

Answers

Answer:

x = 12

Step-by-step explanation:

180° = (3x - 6) + (8x + 4) + 50°  because all interior angles of a triangle add up to 180°

180° = 11x +48°

11x = 132°

x = 12

The temperature was very cold.
Then the temperature tripled.
Then the temperature dropped by 14 degrees.
Then the temperature increased by 32 degrees.
The temperature is now 51 degrees.
What was the starting temperature?
Do NOT write degrees.

Answers

Answer:

51-32+14=33

33÷3=11

answer is 11

What is the distance, in a radical form, between the points (5,-6) and (2,5).

Answers

Answer:

L²=(x1-x2)²+(y1-y2)²

L2=(5-2)²+(-6-5)²

L²=3²+(-11)²

L²=9+121

L²=130

L=✔130

3 4/7 minus 2 1/5 by rounding to the nearest half

Answers

Answer:

[tex]1 \frac{13}{35}[/tex]

Step-by-step explanation:

[tex]3 \frac{4}{7} - 2 \frac{1}{5}[/tex]

you can solve for the fractions first, but you have to give them a common denominator

[tex]\frac{20}{35}- \frac{7}{35}[/tex]

[tex]= \frac{13}{35}[/tex] which is in simplest form

then solve for the whole numbers

3-2=1

therefore, the answer is [tex]1 \frac{13}{35}[/tex]

A closing is March 5 for a rental property with an annual tax bill of $2800. Calculate and show the debit and credits for the tax proration between the buyer and seller using the 365 day method, the day of closing belongs to the buyer.

Answers

Answer:

The debit and credits for the tax proration will be as follows:

Debit seller for $483.29; and Credit buyer for $483.29.

Step-by-step explanation:

The assignment of how much is owed to the responsible party is the major reason of a proration.

For the days owned by the seller, the buyer needs money from the seller since the buyer will pay the taxes at end of the year.

Amount per day = Annual tax bill / 365 = $2800 / 365 = $7.67

Total number of days from January 1 to a day before March 5 = Number of days in January + Number of days in February + Number of days from March 1 to March 4 = 31 + 28 + 4 = 63

Amount the seller owes for the time he owned = Amount per day * Total number of days from January 1 to a day before March 5 = $7.67 * 63 = $483.29

Therefore, the debit and credits for the tax proration will be as follows:

Debit seller for $483.29; and Credit buyer for $483.29.

The sum of two numbers is 25. one number is twice the second number plus 7. what are the two numbers

Answers

Answer:

6 and 19

Step-by-step explanation:

x+y=25

2x+7=y

x+2x+7

3x+7=25

3x=18

x=6.

25-6=19.

y=19

what does 4n+3(n-5)+2 equal

Answers

4n+3n-15+2,
7n-13 is what it equals

Answer:

7n-13

Step-by-step explanation:

Simplify

4n+3(n-5)+2

4n+3n-15+2

Add The Numbers

4n+3n-15+2

4n+3n-13

Combine Like Terms

4n+3n-13

7n-13        Solution 7n-13

what is the opposite of –|−8|?

Answers

Answer:

it should be |8| or just 8 because there can not be a negative in the absolute value sign. pretty sure but not 100%

Answer:

|8|

Step-by-step explanation:

that is your answer :D

Please help I put a screenshot of the assignment

Answers

Answer:

78.5ft^2

Step-by-step explanation:

calculations done on a calculator

Answer:

78.5

Step-by-step explanation:

4 x 2.5 = 10 ft

4.5 x 2.5 = 11.25

4.5 x 4 = 18

18 + 10 + 11.25 = 39.25

39.25 x 2 = 78.5

solve for X


please answer will give brainliest!!!

Answers

x = 9.25
This is because you have to subtract 3.5 from both sides of the equal sign in order for x to be by itself on the left side. 12.75 minus 3.5 equals 9.25

A school needs to buy new notebook
and desktop computers for its
computer lab. The notebook
computers cost $400 each, and the
laptop
computers cost $150 each. How
much would it cost to buy 13
notebooks and 19 desktop
computers? How much would it cost
to buy
n notebooks and d desktop
computers?
Total cost, 13 notebooks and 19
desktop computers:
Total cost, n notebooks and d desktop
computers:

Answers

Answer:

so if they need 400 nc and they need 13 you need to multiply which is 5200 alr now same thing with the other 150 and they need 19 you get 2850 now all together you get that's 8050 hope this helped

The bar graph shows the number of each kind of pet owned in Critter City. How many more cats are pets in Critter City than fish?
A)
5
B)
10
15
D)
30

Answers

Answer:

i need the photo to answer

Step-by-step explanation:

When you factor a trinomial, you are undoing what process?

Answers

I think it’s FOIL not fs tho...

Answer:

you would be undoing the FOIL process

Find the distance between the points (-5,5) and (-6,-4).

Answers

Answer:

distance = 9.06 units

Step-by-step explanation:

x difference = -1

y difference = -9

using the Pythagorean theorem:

-1² + -9² = d²

d² = 1 + 81 = 82

d = 9.06

Plz help yo boi out thank u

Answers

Answer:

either the first or second but id go with the second one!

Step-by-step explanation:

It’s the second one :-)

Write the fraction 28 in its simplest form.
70​

Answers

Answer: 2/5

Step-by-step explanation: 28/70 ÷ 12/12 = 2/5

The simplest form of the given fraction is 2 / 5

What is a fraction?

A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.

Given is a fraction, 28 / 70, we have to convert it into its simplest form,

28 / 70

= 2(14) / 5(14)

= 2 / 5

Hence, the simplest form of the given fraction is 2 / 5

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