Answer:
Step-by-step explanation:
Given y = coskt
y' = -ksinkt
y'' = -k²coskt
Substitute this y'' into the expression 25y'' = −16y
25(-k²coskt) = -16(coskt)
25k²coskt = 16(coskt)
25k² = 16
k² = 16/25
k = ±√16/25
k = ±4/5
b) from the DE 25y'' = −16y
Rearrange
25y''+16y = 0
Expressing using auxiliary equation
25m² + 16 = 0
25m² = -16
m² = -16/25
m = ±4/5 I
m = 0+4/5 I
Since the auxiliary root is complex number
The solution to the DE will be expressed as;
y = Asinmt + Bsinmt
Since k = m
y = Asinkt+Bsinkt where A and B are constants
if there are 4 numbers that average to 60, when mutiplied they must come up to: 60*4= 240
100+30+45= 175
240-175= 65
PROOF:
100+30+45+65= 240
240÷ 4
= 60
After reflecting the points of triangle GHI over the y axis, the new points will be:
G' (3,0)
H' (5,-5)
I' (-1,-5)
The answer is B. <span>Two lines are perpendicular if they meet at one point and one of the angles at their point of intersection is a right angle. A perpendicular line has to intersect and have a 90-degree angle in order to be perpendicular.</span>
<span><span> x-4/x3-64</span> </span>Final result :<span> x4 - 64x3 - 4
—————————————
x3 </span>