Suppose f(x) is a function such that for some positive integer n, f has n linearly dependent derivatives. In other words, if f(x
),f′(x),…,f(n−1)(x),f(n)(x) are all linearly dependent functions, then f(x) is expressible in terms of a,xk,eax,sin(ax),cos(ax), and any combination of such functions, where a is a constant and k is a positive integer. Prove this statement
1 answer:
Answer:
See explaination for the prove of the statement.
Step-by-step explanation:
To establish this prove, lets refer back to what we already know.
We know that "If the set of reactions {d1,d2,d3,......dn} in a vector space V over a field f be linearly dependent, then atleast one of the vectors of the set can be expressed as a linear combination of the remaining others.
Please kindly go to attachment for a detailed step by step explaination of the prove.
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Answer:
Step-by-step explanation:
Eek! Let's give this a go. Things we know:
acceleration of Bond in free fall is -9.8 m/s/s
velocity of the truck is 25 m/s
displacement Bond will travel when he jumps is -10 m
What we are looking for is the time it will take him to hit the top of the truck, knowing that the truck can travel from one pole to the next in 1 second.
Our displacement equation is
Δx = v₀t + 1/2at²
Filling in we have
Simplifying we get
This is a quadratic that needs to be solved however you personally solve quadratics. When you do that, you find that the times it will take Bond to drop that displacement is either -.37 seconds or 5.47 seconds. Many things in physics can be negative, like velocity and acceleration, but time NEVER will be. So it takes Bond 5.5 seconds to drop to the roof of the moving truck. That means that he needs to jump when the truck is between the 5th and the 6th poles away from him.
Good luck with this!
Cheers!