These concepts become more clear when teachers use number disks instead of base ten blocks. Place value is a very important concept for elementary students because base ten is the foundation of our number system.
The corresponding homogeneous ODE has characteristic equation
with roots at
, thus admitting the characteristic solution

For the particular solution, assume one of the form



Substituting into the ODE gives



Then the general solution to this ODE is



Assume a solution of the form



Substituting into the ODE gives



so the solution is



Assume a solution of the form


Substituting into the ODE gives



so the solution is

M - 30 = 10
so the number has to be 10 more than 30.
30+ 10 = m
m = 40
Hello!
First you have to find the total of the items he bought
382 + 12 + 6.14 = 400.14
Then you apply the tax rate
400.14 * 1.0825 = 433.15155
We round this to 433.15
The answer is $433.15
Hope this helps!