Answer:
247
Step-by-step explanation:
1,4,11,26,57,120. see the pattern that emerges from the series:
4–1 = 3; 3–1 = 2 = 2^1
11–4 = 7; 7 - 3 = 4 = 2^2
26 - 11 = 15; 15 - 7 = 8 = 2^3
57 - 26 = 31; 31 - 15 = 16 = 2^4
120 - 57 = 63; 63 - 31 = 32 = 2^5
so the next number should be 64+63 = 127+120 = 247.
check: 247–120 = 127; 127–63 = 64 = 2^6. correct.
so the next number is 247. 2^n+(n-1)
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:
The expression showing how many more meters Mathieu ran than Edgar ran during that time is 
.
Step-by-step explanation:
Edgar ran 'e' meters per second, and Mathieu ran 'm' meters per second. The boys ran for 't' seconds.
The expression describes how many more meters Mathieu ran than Edgar ran during that time.
We can also use the expression 
represent the same quantity.
We know that,
Distance covered by Edgar = te
Distance covered by Mathieu = tm
Difference in distance 
The expression showing how many more meters Mathieu ran than Edgar ran during that time is .
Answer:
<u>Hours in first month = 8</u>
Step-by-step explanation:
AS it is given
He volunteered fr the first month = x hours
He volunteered for the second month = 12/3 times of first month
which will be = 12/3 * x
Total Hours volunteered = 40 hours
Now according to the given conditions
Volunteered first month + volunteered second month = total
putting this gives
x + 12/3 8 x = 40
as 12/3 = 4 so
it becomes
x + 4x = 40
solcing it will gives
5x = 40
x = 40/5
x = 8
<u><em>So Numbers of hours worked in first month are 8</em></u>
<u><em></em></u>
<u>I hope this help you! :)</u>
She has a difference of $2.75, she may have subtracted something wrong while balancing out the check book.
