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

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.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

95.03 is the answer. hope this !