2. First show that for the completely insulated bar

ut = c2uxx; 0 < x < L; t > 0:
ux(0; t) = 0; t > 0
ux(L; t) = 0; t > 0
u(x; 0) = f(x); 0 < x < L

the separation of variables gives the solution

u(x; t) = A0 + 1 Ancos n x e ( cn )2t
L

n=1 L
X
where
2 Z0 L n x
An = f(x)cos dx; n = 1; 2; 3:::;

L L
then nd the temperature in the bar with L = ; c = 1; and f(x) = x

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

positive

step-by-step explanation:

the quadrant is facing upwards

answer: 16

step-by-step explanation: first you would add 6+6 which equals 12 then add 2+2 which equals 4. then add 12 + 4 which is 16.

hope this ^_^

the answer is "add 2y and y"

step-by-step explanation:

you need to collect the like terms first.