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:
y = - 2x + 110
Step-by-step explanation:
The equation of a line in slope- intercept form is
y + mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 110) and (x₂, y₂ ) = (20, 70) ← 2 points on the line
m = 
= 
= - 2
the line crosses the y- axis at (0, 110) ⇒ c = 110
y = - 2x + 110 ← equation of line
The answer is -16 - 10i.
Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)
Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²
Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i
Answer:
The answer is six
Step-by-step explanation:
12 3/5 = 63/5
2 1/10 = 21/10
63/5 divided by 21/10 is equal to 63/5 multiplied by 10/21 which is equal to 630/105 = 6 <-- answer
angles BAC and BCA are equal = 69
69 +69 = 138
angles in a triangle =180
180-138 = 42
5x + 2 = 42
5x = 40
x = 8
