Newton's 3 Laws of Motion are probably the most recognized.
His universal law Gravitation.
He paved the way for advances in Integral and Differential Calculus.
Answer:
It will take Lin an hour and 25 minutes at her constant speed, and it will take Jada at her constant speed an hour and 30 minutes.
SO, Lin will arrive at 4:25
and Jada will arrive at 4:30
There is a 5 minute difference in time.
Step-by-step explanation:
From the facts given, Lin can walk 13 miles in 5 hours which when you divide means she can walk 2.6 mph (miles per hour), and Jada can walk 2.5 mph.
To get these answers you divide the current speeds into the total distance
For example, in Lin's case...
3.25 (The 3 and 1/4 mile converted to decimal form)
2.6 (Lin's Average speed per hour)
3.25/2.6=1.25
1.25 (1 hour and 25 minutes)
GFC is 8. Use a tree of 88 and 48. 88= 2^3 x 11 or 2 x 2 x 2 x 11
48=2^4 x 3 or 2 x 2 x 2 x 2 x 3 see how many groups count as the number once and multiply and bam GFC. Hope I helped! (:
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
