Answer:
43
-161
Step-by-step explanation:
Answer:
7.(1,0) and (-4,0)
8. (-3,0) and (-2,0)
Step-by-step explanation:
7.
When the function is equal to zero, we are looking for the zeros, or the x intercepts
Where it crosses the x axis are 1 and -4
(1,0) and (-4,0)
8. When the function is equal to zero, we are looking for the zeros, or the x intercepts
Where it crosses the x axis are -3 and -2
(-3,0) and (-2,0)
So the original price is $800. And there is a 10% discount, so:
10% = 80
90% = $720
And there is also a $150 gift card applied, leaving us with a final balance of $570 (720-150)
Answer3:
Step-by-step explanation:
I do not know
Check if the equation is exact, which happens for ODEs of the form
if .
We have
so the ODE is not quite exact, but we can find an integrating factor so that
<em>is</em> exact, which would require
Notice that
is independent of <em>x</em>, and dividing this by gives an expression independent of <em>y</em>. If we assume is a function of <em>x</em> alone, then , and the partial differential equation above gives
which is separable and we can solve for easily.
So, multiply the original ODE by <em>x</em> on both sides:
Now
so the modified ODE is exact.
Now we look for a solution of the form , with differential
The solution <em>F</em> satisfies
Integrating both sides of the first equation with respect to <em>x</em> gives
Differentiating both sides with respect to <em>y</em> gives
So the solution to the ODE is