Please help with the final quesion this is all the info i have and I am very stuck. there are two images We need to minimize the cost (measured in units of $100,000) of the pipeline,C(x) = 20✔205 x + 10√x² +1.Step 3We haveC'(x) = -5 +Step 4Solving 0 = C'(x) leads to5√²+1 10x10xwhich can be re-written asx² + 1 = 4x²X =Step 6√x² + 13✓Step 5Therefore, since x must be non-negative, we have1√31We must compare the costs for x = 0,√3'Step 7Evaluate= 4( √5).( √5) - (20-5 15310x20 +1520Step 8Round your answer to two decimal places.and 4. C(0) = 3015The minimum of these costs occurs when x = and so P should be1√3'30 and C(4) = 10√17.X km east of the refinery. An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 4 km east of the refinery. The cost of laying pipe is $500,000/km over land to a point P on the north bankand $1,000,000/km under the river to the tanks. To minimize the cost of the pipeline, how far (in km) from the refinery should P be located?Step 1If x measures the distance from the point directly across the river from the storage tanks to the point P where the underwater pipe reaches the opposite shore, then there are m = 4-xunderwater.refinerymP1storage tanks-xkm of pipe over land and n =+1x² +1km of pipe

Answered: Image /qna-images/answer/52a06f67-5a91-4be7-8f8d-b29f6f876443.jpg

We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 20✔ 20 5 x + 10√x² +1. Step 3 We have C'(x) = -5 + Step 4 Solving 0 = C'(x) leads to 5√²+1 10x which can be re-written as x² + 1 = 4x² X = Step 6 10x Step 5 Therefore, since x must be non-negative, we have 1 Step 7 3 √x² + 1 Evaluate = 4( √5). ✓ 1 We must compare the costs for x = 0, √3' 10x √3 √(√) - (20 - ✓ E) √3 20 3 and 4. C(0) = 30 30 and C(4) = 10√17.

We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 20✔ 20 5 x + 10√x² +1. Step 3 We have C'(x) = -5 + Step 4 Solving 0 = C'(x) leads to 5√²+1 10x which can be re-written as x² + 1 = 4x² X = Step 6 10x Step 5 Therefore, since x must be non-negative, we have 1 Step 7 3 √x² + 1 Evaluate = 4( √5). ✓ 1 We must compare the costs for x = 0, √3' 10x √3 √(√) - (20 - ✓ E) √3 20 3 and 4. C(0) = 30 30 and C(4) = 10√17.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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