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2 answers:
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Answer:
Step-by-step explanation:
The general solution will be the sum of the complementary solution and the particular solution:
In order to find the complementary solution you need to solve:
Using the characteristic equation, we may have three cases:
Real roots:
Repeated roots:
Complex roots:
Hence:
Solving for :
Since we got complex roots, the complementary solution will be given by:
Now using undetermined coefficients, the particular solution is of the form:
Note: was multiplied by x to account for
and
in the complementary solution.
Find the second derivative of in order to find the constants
and
:
Substitute the particular solution into the differential equation:
Simplifying:
Equate the coefficients of and
on both sides of the equation:
So:
Substitute the value of the constants into the particular equation:
Therefore, the general solution is:
1) First, you would need to create an equation for this problem. Let x represent the unknown percentage.
= 
Next, you would cross multiply.
185x = 3,500
Now, all you would have to do is isolate the x. To do this, you would divide both sides by 185.
x = <span>18.918%
Your answer was correct!
2) </span>First, you would need to create an equation for this problem. Let x represent the unknown 85%.
<span> = </span>
<span>
</span>Next, you would cross multiply.
100x = 16150<span>
</span>Now, all you would have to do is isolate the x. To do this, you would divide both sides by 100.
x = 161.5
3) First, you would need to create an equation for this problem. Let x represent the unknown percentage.
=
Next, you would cross multiply.
128x = 2,400
Now, all you would have to do is isolate the x. To do this, you would divide both sides by 128.
x = 18.75%
I hope this helps!
Next, you would cross multiply.
185x = 3,500
Now, all you would have to do is isolate the x. To do this, you would divide both sides by 185.
x = <span>18.918%
Your answer was correct!
2) </span>First, you would need to create an equation for this problem. Let x represent the unknown 85%.
</span>Next, you would cross multiply.
100x = 16150<span>
</span>Now, all you would have to do is isolate the x. To do this, you would divide both sides by 100.
x = 161.5
3) First, you would need to create an equation for this problem. Let x represent the unknown percentage.
Next, you would cross multiply.
128x = 2,400
Now, all you would have to do is isolate the x. To do this, you would divide both sides by 128.
x = 18.75%
I hope this helps!