I estimate that it would be about an hour and 15 minutes, but I'm not entirely sure.
Answer:
Dependent: Total cost of the ride.
Independent: Amount of rides.
Step-by-step explanation:
The independent variable represents what is adjusted, while the dependent variable signifies what alters as a result of that adjustment.
In this case, the total expense for rides fluctuates with any variation in the number of rides taken.
Therefore, the amount of rides is the independent variable whereas the total cost for rides is the dependent variable
Answer:
The formula representing the penny's height as a function of time is:
After 7 seconds, the height of the penny will reach 667 feet.
Step-by-step explanation:
The penny experiences free fall.
With an initial velocity of zero and an initial height of h(0)=1,451.
Gravity acts as the acceleration, measured as g=32 ft/s^2.
The model can be initiated by analyzing speed:
Then, the height is expressed as:
The height of the penny at approximately 7 seconds can be calculated as:
After 7 seconds, the penny will stand at a height of 667 feet.
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.
