Answer:
a) 
b) 
Step-by-step explanation:
By definition, we have that the change rate of salt in the tank is 
, where 
is the rate of salt entering and 
is the rate of salt going outside.
Then we have, 
, and
So we obtain. 
, then
, and using the integrating factor 
, therefore 
, we get 
, after integrating both sides 
, therefore 
, to find 
we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions 
, so 
Finally we can write an expression for the amount of salt in the tank at any time t, it is
b) The tank will overflow due Rin>Rout, at a rate of 
, due we have 500 L to overflow 
, so we can evualuate the expression of a) 
, is the salt concentration when the tank overflows
You need to divide-4 on both sides which will get you 8.hope this helps
Answer:
See below
Step-by-step explanation:
Here we need to prove that ,
Imagine a right angled triangle with one of its acute angle as 
.
- The side opposite to this angle will be perpendicular .
- Also we know that ,
And by Pythagoras theorem ,
Where the symbols have their usual meaning.
Now , taking LHS ,
- Substituting the respective values,
Since LHS = RHS ,
Hence Proved !
I hope this helps.
As you've got 15%, the best thing to do is to find 10%, then multiply it by 1.5. Once you've found the tip, you add this onto the cost of the meal.
Therefore, the total cost of $25 meal with a 15% tip is $28.75
Hope this helps :)
