2011_Solution_7 - MA 1505 Mathematics I Tutorial 7...

This preview shows pages 1–2. Sign up to view the full content.

MA 1505 Mathematics I Tutorial 7 Solutions 1. (i) As the temperature function is only valid within the hotel room, its domain is { ( x, y ) : 0 x 10 , 0 y 10 } . (ii) The heater is at the location where the temperature is highest. It is clear that the largest value of T ( x, y ) is 36 at (0 , 5). (iii) The level curve of 20 is x 2 + ( y - 5) 2 = 80 which is an arc of the circle centered at (0 , 5) with radius 80 8 . 9. The level curve of 25 is x 2 + ( y - 5) 2 = 55 which is an arc of the circle centered at (0 , 5) with radius 55 7 . 4. So the bed should be placed somewhere between the two arcs. (iv) The level curves of c is x 2 + ( y - 5) 2 = 5(36 - c ). These are circles centered at (0 , 5), the values of c decreasing as the radius increases. The largest circle intersecting the domain intersects the domain at (10 , 0) and (10 , 10), so these points have the lowest temperature which is 11. 2. V = I × R = I = V R . (i) ∂I ∂V = 1 R . If R = 15, then ∂I ∂V = 1 15 0 . 0667 A/V. (ii) ∂I ∂R = - V R 2 . If V = 120 and R = 20, then ∂I ∂R = - 120 20 2 = - 0 . 3 A/Ω.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern