Complete #10 College Algebra Question

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Mathematics

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Problem 10

oThe total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you show all your work to come up with this equation, and explain each step and what it represents.

oThe domain of the function. Explain why this domain makes sense, and show work as needed.

oGraph the function using the graphing utility on Desmos.com. Take a screenshot and make sure it is included in your document. The graph should be focused over the domain of the function.

oFind the value of x that minimizes T. Desmos.com will note this ordered pair for you automatically. If it does not, then you can click various points of the graph and it will display the ordered pair.

oWhat does the ordered pair of the minimum for T represent in our situation? I.E. what does the value of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values.

Reflection on the project as a whole

oProcess for each problem

§Did your idea for solving this work?

§Did you have to get help or try different methods?

§Was this problem easy? Hard?

§Share anything else you have to say about the problems

oWorking with a partner

§Were you and your partner able to communicate well? (YES WE COMMUNICATED THROUGH EMAIL)

§What technology did you use to meet and communicate? (EMAIL)

§How did you split up work? Did that work well? (PARTNER DID NUMBER 6 AND I DID NUMBER 10)

§Share anything else you have to say

§Your successes and failures throughout this entire project

Unformatted Attachment Preview

10. Trip Time You are in a boat 2 miles from the nearest point on the coast (see figure). You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 miles per hour. . 13. Associa Show t composit (f° (gº 14. Graph function 2 mi. an enlar X 3-X 1 mi 3 mi Not drawn to scale (a) Write the total time T (in hours) of the trip as a function of the distance x (in miles). (b) Determine the domain of the function. (c) Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. (d) Find the value of x that minimizes T. (e) Write a brief paragraph interpreting these values. 11. Heaviside Function The Heaviside function (a) f( (b) f( (c) 2f (d) f
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Explanation & Answer

Here is the final document, there is one group question I couldnt answer because I didnt do the whole project so I highlighted it for you

Problem 10
The total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you
show all your work to come up with this equation and explain each step and what it
represents.

Finding the hypotenuse (shortest distance from the Boat to Q)
22 + 𝑥 2 = 𝑐 2
𝑐 = √4 + 𝑥 2
12 + (𝑥 − 3)2 = 𝑐 2
𝑐 = √1 + (4 − 3)2
Totals
𝑐 = √4 + 𝑥 2 total water
𝑐 = √1 + (4 − 3)2 total beach
We want per hour, so we must divide each equation by the x mil...


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