1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Julli [10]
3 years ago
8

Suppose that you are the power company and must provide power to a lighthouse on a rock one mile off shore. The nearest pole to

run the line from is 2 miles up the shore from the line straight out to the lighthouse. If the line costs $1000/mile on land and $1500/mile on water, find the path for the line that minimizes the total cost. Your answer should state how far from the pole your line leaves the shore and goes to the lighthouse. Show that this is a minimum and find the cost for the path you have chosen.
Mathematics
1 answer:
Levart [38]3 years ago
6 0
If we let x as the length of the line on line and y on water, and C as the total c ost, then we have the equation:
C = 1000x + 1500y

The figure formed by the scenario is a right triangle, so we have:
y² = 1² + (2 - x)²
Solving for y,
y = √(1 + 4 - 4x + x²)
y = √(5 - 4x + x²)

Subsituting:
C = 1000x + 1500√(5 - 4x + x²)
The minimum length of the line can be solved by taking the derivative of the equation and equating it to 0. So,
1000 + 1500(0.5)(-4 +2x)/√(5 - 4x + x²) = 0
x = 1.33 miles
From the equation: y = √(5 - 4x + x²)
y = 1.20 miles
You might be interested in
4(x+2)=4x+8 need help
alisha [4.7K]

Answer:

The answer is all real numbers

Step-by-step explanation:

4(x + 2) = 4x +8

Distribute the 4:

4x + 8 = 4x + 8

Then subtract 4x and 8 from both sides

0 = 0

This statement is true so its all real numbers

3 0
3 years ago
Read 2 more answers
If a liquid weighs 2 pounds and has a capacity of 3 gallons, what is its density?
Illusion [34]
5 gallons would be the right answer

8 0
3 years ago
How do I factor 1/4d-3/4
dolphi86 [110]
1/4d - 3/4 =
1/4(d - 3)
4 0
4 years ago
Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the
Georgia [21]

Answer: The answers are

(i) The slope of segments DE and AC is not 0.

(ii) The coordinates of D and E were found using the Midpoint Formula.

Step-by-step explanation:  We can easily see in the proof  that the co-ordinates of D and E were found using the mid-point formula, not distance between two points formula. So, this is the first flaw in the Gina's proof.

Also, we see that the slope of line DE and AC, both are same, not equal to 0 but is equal to

\dfrac{y_2}{x_2},

which is 0 only if y_2=0.

So, this is the second mistake.

Thus, the statements that corrects the flaw in Gina's proof are

(i) The slope of segments DE and AC is not 0.

(ii) The coordinates of D and E were found using the Midpoint Formula.

3 0
3 years ago
Read 2 more answers
Fifteen percent of the employees in a company have managerial positions, and 25 percent of the employees in the company have mba
Natali [406]
<h3>Given</h3>

.15 of employees are managers

.25 of employees are MBAs

.60 of managers are MBAs

<h3>Find</h3>

(a) proportion of employees who are managers with MBA

(b) proportion of MBAs who are managers

(c) whether MBA and manager are independent

<h3>Solution</h3>

(a) Your answer of 0.60×0.15 = 0.09 is correct

(b) 0.09 of the 0.25 of employees who are MBAs are managers. .09/.25 = 0.36

(c) No. P(MBA | manager) = 0.60 ≠ P(MBA) = 0.25

_____

The only calculation necessary is the one you did for part (a). Other answers can be based directly on the given data. The chart below is unnecessary.

4 0
3 years ago
Read 2 more answers
Other questions:
  • If (x) = -54 - 4 and g(x) = -3x - 2. find (f - g)(x).
    9·1 answer
  • Use the verbs in the word bank to complete the sentences. Remember that you will need to put the verb in the correct form. Watch
    11·2 answers
  • A certain line has a slope of 3/2. Select all pairs of points that may be on the line.
    5·1 answer
  • (4x+7)=(6x-63) whats value of x
    5·2 answers
  • The diameter of the circle is 12m find the circumference and leave at pi
    6·1 answer
  • 3.8,4.2,5.3,x; mean 4.8
    12·2 answers
  • Multiple Choice!!! A school bought a special type of lock for all student lockers. Every student had to create his or her own pa
    9·1 answer
  • Arrange 3<br> /4, 75%, 0.25 ​
    8·1 answer
  • Lucy earned $400 and $550 in interest the last 2 years. Describe the average interest she should earn in each of the next 3 year
    7·1 answer
  • Help please! I’ll give brainliest!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!