The 15% tip would be 50*0.15=$7.5
Let 
. Then
and substituting these into the ODE gives
Let 
, so that 
. Then the ODE is linear in 
, with
Multiply both sides by 
, so that the left side can be condensed as the derivative of a product:
Integrating both sides and solving for 
gives
Integrate again to solve for 
:
and finally, solve for 
by multiplying both sides by 
:
already accounts for the term in this solution, so the other independent solution is 
.
The answer is 10 2/3, 5
Proof:
Solve the following system:
{x/2 + y/3 = 7 | (equation 1)
{x/4 + (2 y)/3 = 6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{x/2 + y/3 = 7 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 1 by 6:
{3 x + 2 y = 42 | (equation 1)
{0 x+y/2 = 5/2 | (equation 2)
Multiply equation 2 by 2:
{3 x + 2 y = 42 | (equation 1)
{0 x+y = 5 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{3 x+0 y = 32 | (equation 1)
{0 x+y = 5 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 32/3 | (equation 1)
{0 x+y = 5 | (equation 2)
Collect results:
Answer: {x = 10 2/3, y = 5
Answer:
it would be 7/10
Step-by-step explanation:
7 over 10.
Hope this helps:)
To find the sum, add. To find the difference, subtract. It's simple terminology in mathematics. Hope I helped!
