Answer:
y2 = C1xe^(4x)
Step-by-step explanation:
Given that y1 = e^(4x) is a solution to the differential equation
y'' - 8y' + 16y = 0
We want to find the second solution y2 of the equation using the method of reduction of order.
Let
y2 = uy1
Because y2 is a solution to the differential equation, it satisfies
y2'' - 8y2' + 16y2 = 0
y2 = ue^(4x)
y2' = u'e^(4x) + 4ue^(4x)
y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)
= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)
Using these,
y2'' - 8y2' + 16y2 =
[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0
u''e^(4x) = 0
Let w = u', then w' = u''
w'e^(4x) = 0
w' = 0
Integrating this, we have
w = C1
But w = u'
u' = C1
Integrating again, we have
u = C1x
But y2 = ue^(4x)
y2 = C1xe^(4x)
And this is the second solution
Answer:
$2.00
Step-by-step explanation:
If you divide 12 by 24 you get 2. So $2 cookies.
Hope it helps :)))
∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices a
koban [17]
To get the length of each side,
use the distance formula with equation:
Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
Solving
<span>AB = 8 units BC = 6 units AC = 10 units
</span><span>MN =8units NO = 6 units MO = 10 units
</span><span>XY = 6.32 units YZ = 6.32 units XZ = 8.94 units
</span>JK = 4.47 units KL = 4.47 units JL = 6 units
1 The
right answer is the letter b) triangle ABC and Triangle MNO are Congruent
<span>triangles
ABC and MNO are triangles that have the same lengths of its three sides.
</span>2 The answer is the letter c)
rotation
There
is a rotation of
90º about ABC and MNO the origin is B=N
B=N
C----------O
A----------M
slope is $0.10 <em>($1.00 per 10 tokens = $0.10)</em>
y-intercept is $60 <em>($60 is the annual fee)</em>
y = .10x + 60 <em>(y = mx + b)</em>
domain is x ≥ 0 <em>(you can't buy a negative number of token)</em>
range is y ≥ 60 <em>(input the domain (x ≥ 0) to find the range)</em>
Answer: the y-intercept of the function is $60
