C(X)= 2.7X +4.7 SQRT OF [400^2 + (780-X)^2]
The first term's derivative is 2.7. Use the chain rule for the second term.
Are you sure there is no x after 400?
d/dx 4.7*[400^2 + (780-X)^2]^1/2
= (4.7)*(1/2)*[400^2+(780-X)^2]^-1/2
* d/dx [780-X)^2]
A common problem encountered by the oil industry is to determine the most cost-effective route to connect various wells in an oil fertile area. The attached map is a copy of a section of a U.S. Geographical Survey contour map with a wetland area outlined. An existing oil well is located approximately at the point labeled A. A new well is to be dug at point B, requiring that the pipeline installation company be given plans for laying connecting pipe from A to B. In consultation with the installation company, the following information has been obtained:
• Straight, two-inch coated pipe must be used, at a cost of $ 1.50 per foot.
• A maximum of one elbow joint may be used. The elbow joint may be fabricated with any angle measure and will not be included in the cost.
• On normal terrain, installation cost is $ 1.20 per foot.
• Installation in the wetland area requires the use of a special , at an additional installation cost of $ 60 per hour over and above normal installation cost.
• In a 10-hour day, this special can dig approximately 300 feet of trench.
Write up your investigation as a report to your supervisor, who should be able to understand your report without reference to this sheet. Demonstrate that you and your partner(s) have considered the costs of what you believe to be several viable pipeline routes connecting the existing well at A to the new well at B. Discuss your selection for the route that incurs the least cost and mathematically justify that your selection will give the least cost of all possible routes from A to B. Be sure to explain why minimum distance may not yield minimum cost.
Hints:
• Since the wetland separating A and B is very irregular in shape, simplify your work from the beginning by making some (slightly exaggerated) assumptions. You are to assume that the entire wetland is in the shape of a rectangle. How far to the east will your rectangle go? How far to the west? To the north? To the south?
• Reduce the number of paths you consider before calculating anything. Should you consider a path around the swamp to the north of A (with only one elbow joint)? What about to the south of B? Can you really go due south of A only on normal terrain?
• Do some measuring and calculating of costs of various paths, but be sure you consider the case where the pipeline is laid some distance southeast of A on wetland terrain and then turns due south on normal terrain to B. Perhaps this is where calculus comes in?
If you type in this :Engineering Applications in Differential and Integral Calculus* onto google on page four you will see the map. Please help
the title of this lab is designing a pipeline with minimum cost
* MATH (CALCULUS) PLZ HELP - Damon, Thursday, April 1, 2010 at 7:02am
Route 3: I think the hypotenuse is wrong in the text
d = d1-d3
cost = 2.7 x + 4.7 [(d-x)^2 +d2^2 ]^.5
dc/dx = 2.7 +4.7(1/2)[(d-x)^2 +d2^2 ]^-.5 *2(d-x)(-1)
now set that to zero and solve for x
http://www.ijee.dit.ie/articles/Vol18-1/Ijee1262.pdf
The expression C(X) = 2.7X + 4.7√[400^2 + (780-X)^2] represents a mathematical function. To understand how to use this function, let's break it down step by step:
1. C(X): This is the dependent variable, which means it depends on the value of X. In other words, the function C(X) will give us a different value for every unique value of X.
2. 2.7X: This term represents the linear component of the function. It means that 2.7 times the value of X will be added to the result.
3. 4.7√[400^2 + (780-X)^2]: This term represents the square root of the sum of two squared quantities. Let's break it down further:
a. [400^2 + (780-X)^2]: Inside the square brackets, we have the sum of two terms: 400^2 and (780-X)^2. The caret (^) symbol represents exponentiation, so 400^2 means 400 raised to the power of 2, and likewise, (780-X)^2 means (780-X) raised to the power of 2.
b. √: This symbol represents the square root operation. It means we need to find the positive square root of the value inside the square brackets.
c. 4.7: This coefficient is multiplied by the square root value to scale the result.
To evaluate the function, you need to substitute a specific value for X and perform the calculations step by step using the order of operations (PEMDAS/BODMAS).
For example, if you want to find the value of C(100), you would substitute X = 100 into the function:
C(100) = 2.7(100) + 4.7√[400^2 + (780-100)^2]
Now, calculate each part step by step. First, simplify within the square brackets:
[400^2 + (780-100)^2] = 400^2 + 680^2
Next, calculate the sum within the square brackets:
[400^2 + (780-100)^2] = 160,000 + 462,400
Now, take the square root of the result:
√[400^2 + (780-100)^2] ≈ √622,400 ≈ 788.97 (rounded to two decimal places)
Now, substitute this value back into the function:
C(100) = 2.7(100) + 4.7(788.97)
Finally, calculate this expression:
C(100) ≈ 270 + 3,705.719 ≈ 3,975.72 (rounded to two decimal places)
Therefore, when X is 100, the value of C(X) is approximately 3,975.72.