y2 = C1xe^(4x) Step-by-step explanation: Knowing that y1 = e^(4x) satisfies the differential equation y'' - 8y' + 16y = 0, we need to derive the second solution y2 using the reduction of order technique. Let y2 = uy1. Since y2 is a solution to the differential equation, it holds that y2'' - 8y2' + 16y2 = 0. By substituting for y2, its derivatives become y2 = ue^(4x), y2' = u'e^(4x) + 4ue^(4x), and y2'' = u''e^(4x) + 8u'e^(4x) + 16ue^(4x). Plugging these into the differential equation gives us u''e^(4x) = 0. Let w = u', so w' = u''. This results in w' e^(4x) = 0, leading to w' = 0. Integrating gives w = C1. Since w = u', this implies u' = C1, and integrating once more results in u = C1x. Therefore, y2 = ue^(4x) becomes y2 = C1xe^(4x), which is the second solution.
$29,580. Breaking it down: 29000/4 equals 7250. So, 7250 plus 2% of 7250 calculates as follows: 7250 + (2/100) * 7250 gives us 7250 + 145, totaling $7395 with four payments resulting in $29,580.
Among the options provided, the correct choice is: D 7y^4-13x^3 inches
1000 g = 1 kg
5,000 g = 5 kg
825 kg - 5 kg = 820 kg
<span>The pumpkin that set the world record in 2011 weighs __820 kg___ more than an average pumpkin.</span>
