Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
Yes because if you do 4÷16 it is .25.
Hope it helps. If it doesn't comment on the bottom. I'll try to explain it more
In order to answer the question we need a picture of some kind
Answer:
n = 8
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
6n + 7 = 55
<u>Step 2: Solve for </u><em><u>n</u></em>
- Subtract 7 on both sides: 6n = 48
- Divide 6 on both sides: n = 8
<u>Step 3: Check</u>
<em>Plug in n into the original equation to verify it's a solution.</em>
- Substitute in <em>n</em>: 6(8) + 7 = 55
- Multiply: 48 + 7 = 55
- Add: 55 = 55
Here we see that 55 does indeed equal 55.
∴ n = 8 is a solution of the equation.
Answer:
-2
Step-by-step explanation:
use the slope formula which is y2-21/x2-x1
these are what i chose my numbers to be
-4=x1
-1= y1
-2= x2
-5= y2
-5-(-1)/-2-(-4) = -2
thats all
