Answer:
a) k = 10 b) k = 7.5
Step-by-step explanation:
<h3><u><em>a)</em></u></h3>
( 5k+ 20 ) + ( 7k + 40 ) = 180
12k + 60 = 180
12k = 120
k = 10
<h3><u><em>b)</em></u></h3>
40 + ( 12k + 10) + 180 - ( 8k + 80 ) = 180
50 + 12k + 180 - 8k - 80 = 180
50 + 12k -8k - 80 = 0
50 + 4k - 80 = 0
30 = 4k
k = 7.5
The given functions appear to be ...

Of these, the exponential function g(x) will eventually exceed all others. That is the price of product 2, so ...
... The price of Product 2 will eventually exceed all others.
BC is not a line. CF and BE are lines.
Step-by-step explanation:
Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.
The Wronskian of them functions be
W = (y1y2' - y1'y2)
y1 = (e^x)/2 = y1'
y2 = (xe^x)/2
y2' = (1/2)(x + 1)e^x
W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)
= (1/4)(x + 1 - x)e^(2x)
W = (1/4)e^(2x)
Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.
Step-by-step explanation:
In trapezoid ABCF, AB || CF.
Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.

From equations (1), (2) & (3), we find:

Thus, the two triangular pieces of land are equal in area.
Hence proved.