Question

Q5i). Differential equation

http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_s06_qp_3.pdf

Answer 1

@UnkleRhaukus @experimentX

Answer 2

Q5i).

Answer 3

How do you start?

Answer 4

Show that x and t satisfy the differential equation
\[\frac{\text dx}{\text dt}= 0.1(x − 250)\]

Answer 5

yes, but im not sure how to show that

Answer 6

___________________________________

\[x=x(t)\]
\[x'(t)=kx(t)-25\]
\[x(0)=x_0=1000\qquad x'_0 =75\]___________________________________

find k

Answer 7

What's x(t) i didnt use that notation before

Answer 8

the mass \(x\) of the substance in the container after \(t\) minutes

mass is a function of time

x ( t )

Answer 9

x is the dependent variable
and t is the independent variable

Answer 10

you could have the bits in brackets in the the subscript i guess
\[x(t)=x_t\]

Answer 11

did you find \(k\)?

Answer 12

yes i found it, 0.1

Answer 13

so you can solve (i)

Answer 14

thankx

Answer 15

can you do (ii) ?