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.
2G=B+3
G=B-4
2(B-4)=B+3
2B-8=B+3
B=11
Bert possesses 11 cents
At Super Saver, 4 packs are priced at $10, which gives us 12 × 4 = 48 cans for ratio calculation. The ratio translates to 48 cans for $10, or 4.8 cans per dollar. For Shop Smart, similarly, 24 × 2 results in 48 cans priced at $9, creating a ratio of 48 cans for $9, or 5 1/3 cans per dollar. At Price Busters, 12 × 3 results in 36 cans for $9, translating to a cost of 3 cans per dollar. Overall, Shop Smart offers the best value per can, followed by Super Saver, and lastly Price Busters.
Isabella can pour a maximum of 8 full glasses. With 1.75 liters converted to milliliters being 1750, dividing that by 200 gives 8.75 cups.
