Answer:
3m² + 2mn + 7n²
Step-by-step explanation:
Subtract m² + 3mn - n² from 4m² + 5mn + 6n², that is
4m² + 5mn + 6n² - (m² + 3mn - n²)
= 4m² + 5mn + 6n² - m² - 3mn + n² ← collect like terms
= 3m² + 2mn + 7n²
Answer:
-x³ + 3x² - 14x + 12
Step-by-step explanation:
Area of outer rectangle = (x² + 3x - 4) * (2x - 3)
= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)
=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)
=2x³ + 6x² - 8x - 3x² - 9x + 12
= 2x³ + <u>6x² - 3x²</u> <u>- 8x - 9x</u> + 12 {Combine like terms}
= 2x³ + 3x² - 17x + 12
Area of inner rectangle = (x² - 1)* 3x
= x² *3x - 1*3x
= 3x³ - 3x
Area of shaded region = area of outer rectangle - area of inner rectangle
= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)
= 2x³ + 3x² - 17x + 12 -3x³ + 3x
= 2x³ - 3x³ + 3x² - 17x + 3x + 12
= -x³ + 3x² - 14x + 12
Cost Price for oil change =$27
Charge for the customers =$40
Markup cost = Difference between selling price and cost price =$40-$27=$13
To find the percent of markup, divide the markup cost by the cost price and multiply it by 100.
Markup percent = (13/27)*100
=48.15%
Divide both sides by 
to get
Substitute 
, so that 
. Then
The remaining ODE is separable. Separating the variables gives
Integrate both sides. On the left, split up the integrand into partial fractions.
Then
On the right, we have
Solving for 
explicitly is unlikely to succeed, so we leave the solution in implicit form,
and finally solve in terms of 
by replacing :
