# 11.6 - l t t l o ﬂat: 4/2}? n. m ._ A ' See handom‘ 0F...

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

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.

Unformatted text preview: l t t l o ﬂat: 4/2}? n. m ._ A ' See handom‘ 0F problems #ﬂéﬂﬂ’ﬂ/S/b 79000 W M Exam/Egg and Woo/ems 90°F is stood in temperature is 50°F After 5 'me If, m minmetsl denote the ﬁ : k TS T‘S ~TS m U“: LL: (3) Write a differential equation for H(t) using New- d _r' ‘E ton 3 Law of Cooling. 0’“ 0’ (b) Solve the differential e uat c: C: C: l q 1011. x I g m E E: t (C) When Will the temperature oftherice have dropped % OilSCUSS ‘ ’ PM ro6o°F7 01c K (9 (,UOHS i S S gr 3 {9‘ n I 7 f: (gr llsrtnj Var/ab 6 3 - \ £9 (9 According to a simple physiological model, an athletic r adult needs 20 calories per day per pound of body weight %- {g aLJL to maintain his weight. If he consumes more or fewer . __ calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the num- ber needed to maintain his current weight; the constant /-\ 1c amouni‘ ofproportionality is 1/3500 pounds per calorie. Suppose a O 2 K - #0 that a particular person has a constant caloric intake of m I calories per day. Let W’(t) be the person’s weight in pounds at time 25 (measured in days). (a) What differential equation has solution WU)? (b) Solve this differential equation. l ( ,_ > (c) Graph W'(t) if the person starts out weighing 160 M I I w pounds and consumes 3000 calories a day. 35 I 9(6) : dear/’9 7. Water leaks out of a barrel at a rate proportional to the square root of the depth of the water at that t1me. If the water level starts at 36 inches and drops to 35 inches in l I : ._ k ’lfy" J k hour, how long will it take for all of the water to leak out ‘ of the barrel? 94 d/scags 507/73 50 SHEETS mo SHEETS 224 4-43 200 SHEETS 22—141 22-1412 mm,” /,/ Co /. .‘BsC‘i M \ b AppltcatLQD§_1§iKJQQde/mg - M. i 1 A spherical snowball melts at a rate proportional to its surface area. —- ‘ 7. Asiath ' LI‘TH" ' ' ‘ ' ' V. ( ) Write a differential equation for its volume, . 1— 3/ (1:) If the initial volume is V0, solve the differential V - 3 equation and graph the solution. (c) When does the snowball disappear? 7 7 77 7 I” W We're told OW/d—t = -KH ) Er K70. To WNTO TWS In Terms 013 GHQ ‘H’le 1 \li anohi by subsnrtm'on. E % \$15 = “ktAr -= -I<(H‘TWZ)= -l< (LHT) It b 2cm 6 Aspheye, [i use V sphere g‘Theteq‘t/m Q! = -k VZ/3 where, R has been ' CV5 renamed (Ks k(47r)'/337/3) A chemical reaction involves one molecule of a sub- stance A combining with one molecule of substance B to form one molecule of substance C, written A + B —+ C. 0 The Law of Mass Action states that the rate at which C OF @ ta 1 is formed is proportional to the product of the quantities H I , of A and B present. Assume a and b are the initial quan- a A X tities of A and B, and 2: is the quantity of C present at time t. (3) Write a differential equation for z. 6 @ ’hm‘t: (b) Solve the equation with z(0) = 0. t\ b,“ x“ a; ram 010 ﬁrmanbn ot a = K (@uamtg at: AMQuantrg 0:116) d _ , 3.1% I k(0t—><)Cb-><7 . If the initial quantities, a and b, in Problem 15 are the ‘ same, write and solve a differential equation for it, with 2(0) = O. 7/ g};— = k (0H0 (0H) ...
View Full Document

## This note was uploaded on 03/26/2012 for the course MAC 2312 taught by Professor Bonner during the Fall '08 term at University of Florida.

### Page1 / 2

11.6 - l t t l o ﬂat: 4/2}? n. m ._ A ' See handom‘ 0F...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online