Answer:
4/11 as a repeating decimal is 0.3636…
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:
Answer:
D) y = -5x + 5
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 1/5x + 5. Its slope is 1/5. A line parallel/perpendicular to this one will have a slope of -5.
Plug this value (#) into your standard point-slope equation of y = mx + b.
y = -5x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -5). Plug in the x and y values into the x and y of the standard equation.
-5 = -5(2) + b
To find b, multiply the slope and the input of x (2)
-5 = -10 + b
Now, add 10 to both sides to isolate b.
5 = b
Plug this into your standard equation.
y = -5x + 5
This equation is parallel/perpendicular to your given equation (y = 1/5x + 5) and contains point (2, -5)
Hope this helps!