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.
Given :
a paddle boat travels upstream = 12 miles
a paddle boat travels downstream = 20 miles
speed of the current = 2 miles per hour
Let the speed of the boat =x
Let the time taken = t
We know the distance for upstream D= (boat speed - current speed) * time
the distance for downstream D= (boat speed + current speed) * time
Plug in all the values and variables in the distance
For upstream 12 = (x-2)t, then 
For downstream 20 = (x+2)t then 
we got two equations for t, equate it and solve for x
Cross multiply it
12(x+2) = 20(x-2)
12x + 24 = 20x - 40 (subtract 12x and add 40 on both sides)
64 = 8x
x= 8
the speed of the boat in still water = 8 miles per hour
The union of the two sets is the combining of the two sets, so the correct answer is A. {4, 8, 10, 12, 14}.
Hope this helps =)
In the equation for surface area the radius is squared ( r^2)
If the radius is doubled, the radius would be 2^2 more which equals 4
The surface area would be 4 times the old surface area.
Answer:
To find the equivalent positive angle of a negative angle, just add 360 to it until it becomes positive and is between 0 and 360 degrees. -244 + 360 = 116.
Step-by-step explanation:
