Let the amount invested with 5% interest be x
Therefore, the amount invested with 6% interest will be (6000-x)
It is given that the total interest earned yearly is $337.5. Thus, the equation of interest will be:
Multiplying both sides by 100 we get:
Subtracting both sides by 36000 we get:
Thus, the amount invested at 5% is $2250
Therefore, the amount invested at 6% will be $(6000-2250)=$3750
Answer: The required solution of the given system is
(x, y) = (3, 1) and (4, 0).
Step-by-step explanation: We are given to solve the following system of equations :
From equation (i), we have
Substituting the value of y from equation (iii) in equation (ii), we get
When, x = 3, then from (iii), we get
And, when x = 4, then from (iii), we get
Thus, the required solution of the given system is
(x, y) = (3, 1) and (4, 0).
Answer:
Step-by-step explanation:
Let:
This is an exact differential equation because:
With this in mind let's define f(x,y) such that:
and
So, the solution will be given by f(x,y)=C1, C1=arbitrary constant
Now, integrate with respect to x in order to find f(x,y)
where g(y) is an arbitrary function of y
Let's differentiate f(x,y) with respect to y in order to find g(y):
Now, let's replace the previous result into :
Solving for
Integrating both sides with respect to y:
Replacing this result into f(x,y)
Finally the solution is f(x,y)=C1 :