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-Dominant- [34]
3 years ago
10

A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The near

est power source is on land, 10 miles due east of the bird nesting beach. Surveying for electricity construction costs $250 per mile over the water and $150 per mile on the ground. As a surveyor, the cheapest price (in dollars) for which you can bill the job involves surveying above the water to a point inbetween the nesting beach and the power source, and then from the nesting beach to the power source. Find the least expensive price for which you can bill the job
Mathematics
1 answer:
Serga [27]3 years ago
6 0

Answer:

T.C ( 1.1007 ) = T.C_min = $2252  

Step-by-step explanation:

Given:

- Cost of electricity construction over water C_w = $250 / mile

- Cost of electricity construction over ground C_w = $150 / mile

- The distance from hotel island = 3.5 miles

- The distance from beach to power source = 10 miles

Find:

Find the least expensive price for which you can bill the job

Solution:

- This problem requires cost optimization. So we need to develop a cost function as follows

Total Cost = C_w*(distance from island to x) + C_g*( distance from x to power)

- Now calculate the relevant distances using Pythagoras theorem:

              Distance from island to x = sqrt ( x^2 + 3.5^2 )

              Distance from x to power station = 10 - x

- Input the distances in the cost function:

              T.C ( x ) = C_w*sqrt ( x^2 + 3.5^2 ) + C_g*(10 - x )

- Input the relevant rates:

              T.C ( x ) = 250*sqrt ( x^2 + 3.5^2 ) + 150*(10 - x )  

- Simplify:

              T.C ( x ) = 250*sqrt ( x^2 + 12.25 ) + 1500 - 150x

- Next, we will optimize the cost to minimum. We need the distance x that would give us the minimum cost. To minimize the function, set its derivative with respect to x equals to zero.

                T.C' ( x ) = 500*x*( x^2 + 12.25 )^( -0.5 ) - 150

- Set the derivative to zero and solve for x:

                            sqrt ( x^2 + 12.25 ) = 10x/3

Squaring both sides:

                           9*x^2 + 110.25 = 100*x^2

Simplify and solve:

                      x = sqrt (110.25 / 91) = 1.1007 miles

- The cost function is minimized at x = 1.1007 miles. We will input this back into our function and evaluate the minimum cost as follows:

                 T.C ( 1.1007 ) = 250*sqrt ( 1.1007^2 + 12.25 ) + 1500 - 150*1.1007

                 T.C ( 1.1007 ) = T.C_min = $2252  

                                 

- So the minimum cost associated with this plan is $2252.

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Answer:

V( 3, -8 )

Step-by-step explanation:

Parable equation is of the form:

( x - h )² = 4p*(y - k)

In that expression, vertex has coordinates V ( h, k )

Then all we have to do is transform the given equation

y = x² - 6x + 1       or     x² - 6x  = y - 1          (1)

We can get a  perfect square trinomial in the first member of the equation according to:

x²  -  6x   =   ( x - 3 )²  - 9

(x - 3 )²   = x² - 6x  + 9

By substitution  en equation (1)

( x - 3 )² - 9 = y - 1

( x - 3 )² = y -1 + 9

( x - 3 )² = y + 8

( x - 3 )² = (y + 8 )

Then vertex coordinates are

V( 3 , -8)

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3 years ago
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2 years ago
Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for r
butalik [34]

The missing part of the question is show in bold format.

Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it

once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube, 1 chance for all any of the 6 numbers.

You roll it 500 times and get the following data:

Outcome 1 2 3 4 5 6

Frequency 77 92 75 90 76 90

Exercises 1–2

1. If the equality model was correct, about how many of each outcome

would you expect to see if the cube is rolled 500 times

2. Based on the data from the 500 rolls, how often were odd numbers observed? How often were even numbers observed?

Answer:

Step-by-step explanation:

1.

If the equally likely model was correct,  about how many of each outcome

would you expect to see if the cube is rolled 500 times.

The probability of rolling any of the numbers from 1 to 6 is  p(1/6)

The number of each of the outcomes expected to be seen in 500 rolls of the number cube is np

= 500 * \frac{1}{6}  \\ \\ = \frac{500}{6} \\ \\  = 83.333 \\ \\ \approx 83

2.  From the given data in the roll;

The odd numbers 1, 3 and 5, were obtained at  77, 75 and 76 times respectively.

Thus, the total number of times odd number were rolled = 77 + 75 + 76 = 228

Probability of an odd number turning up = \frac{ number \ of  \ required  \ outcome}{ total \  number  \ of  \ possible \ outcome}

= \frac{228}{500}

= 0.456

= 45.6%

The even numbers, 2, 4 and 6, were obtained 92, 90 and 90 times respectively.

The total number of times even number were rolled = 92 + 90 + 90 = 272

Probability of an even number turning up  = \frac{ number \ of  \ required  \ outcome}{ total \  number  \ of  \ possible \ outcome}

= \frac{272}{500}

= 0.544

= 54.4%

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natka813 [3]
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18.194 rounded to the nearest hundredths
ehidna [41]
18.19
-you're welcome
5 0
3 years ago
Read 2 more answers
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