The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Answer:
17
Step-by-step explanation:
27/7 or Decimal: 3.857143
Answer:
The annual percentage rate of change for the population of Oregon is of 8.125%.
Step-by-step explanation:
Total percentage change:
Change multiplied by 100 and divided by the initial value.
Change: 8.7 - 4.8 = 3.9 million
Initial value: 4.8
Percentage change: 3.9*100/4.8 = 81.25%
Annual percentage rate of change
81.25% during 10 years(from 2000 to 2010).
So, per year
81.25%/10 = 8.125%
The annual percentage rate of change for the population of Oregon is of 8.125%.
Answer:
Area of gray region = 
Step-by-step explanation:
The area covered by the furniture can be subtracted from the total area of the room to calculate the area of the gray region.
<em>Total</em> area of the room: 
Area taken up by furniture: 
Area of gray region = total area of the room - area taken up by furniture
Area of gray region = 
Remember to distribute the negative sign:
Area of gray region = 
Combine like terms:
Area of gray region =
