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.
Answer:
Step-by-step explanation: The error made by the student was dividing the wins by the losses.
The student should have divided the wins by the total number of games played.
Initially, the student ought to have summed 20 and 10 to conclude there were 30 games in total.
Response:
Php 973.00
Detailed explanation:
Aling Luz purchased 3/8 yards of linen priced at Php 72.00 per yard. She paid Php 1000.00 to the cashier. What will be her change?
Amount of yards acquired = 3/8
Cost per yard = Php 72.00
Total cost of the purchased yards = Amount of yards acquired × Cost per yard
= 3/8 × Php 72.00
= Php 27.00
She provided Php 1000.00 to the cashier.
What amount will she receive back?
= Amount given - total cost
= Php 1000.00 - Php 27.00
= Php 973.00
Implicit differentiation: remember that dy/dx y = dy/dx, so take the derivative of both sides. To solve for the derivative, subtract 2x from both sides, then divide by 2y. When considering the slope, solve for it and determine where the circle intersects with the line. Substitute for y and proceed by multiplying both sides. Take the square root of both sides, accounting for both positive and negative roots, leading to x = ±10. Thus, the points located are (10,-24) and (-10,24).
The applicable measurement scales are interval or ratio. In the interval measurement level, the spaces between attributes are meaningful. A prime example is temperature, where the difference between 40 to 50 degrees is the same as that between 70 to 80 degrees. Conversely, in the <span>ratio level of </span>measurement, an absolute zero exists, which is significant. This allows for meaningful fractions (or ratios) of the ratio variable to be established.
