Answer:
124.8
Step-by-step explanation:
52 divided by 5 = 10.4
then, multiply by 12 = 124.8
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:
They are parallel because their slopes are equal
Step-by-step explanation:
Answer:
SP = Quadrant 3 FP = Quadrant 4
Step-by-step explanation:
sp = (−5.4, 3) fp (3, −5.4) this means the line is decreasing as point y coordinate changes fro 3 to 5.4 and will be a negative slope gradient- The quadrants at top left to right are 3 and 1 and bottom left to right is 2 and 4 Labels are Quadrant 3 = R Quadrant 1 = P Quadrant 2 = Q Quadrant 4 = S The starting point is Left top side as y is positive and can only be 3 or 1 and x is negative SP = Quadrant 3 The finishing point is bottom quadrants as y is negative this time and x is positive FP = Quadrant 4 You can remember that it is often start of origin then quadrant 1 in straight line positive colorations
Answer:
A.
Step-by-step explanation:
we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.
and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?
7 × s = 0.5 = 1/2
s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14
=> answer A is correct
