Answer:
Find the midpoint between the two points.
(4,4),(-1,2)
Answer: I am not sure exctly what the question is here but if you are wondering how many butterflies tatal for all species here it is:
North American Butterfrlies: 30
South American Butterflies: 18
Europe Butterflies: 12
Step-by-step explanation: To get the total number of butterflies per species you need to mulitply to find the correct ratio given the total number of North American Butterflies is 30
North American Butterflies to South American Butterflies is 5 to 3 so 30/5=6, you then multiply 3*6 to get 18 South American Butterflies.
Then since we now know there are 18 South American Butterflies and the ratio of those to Europe Butterflies are 3 to 2 we take 18/3=6, then multiply 2*6 to get 12 Europe Butterflies.
Explanation:
Differentiating the solution, we have ...
y' = c1 +8c2x^7
y'' = 56c2x^6
Putting this into the DE, we have ...
x^2y'' -8xy' +8y = 16 . . . . . . . different from your problem statement
x^2(56c2x^6) -8x(c1 +8c2x^7) +8(c1x +c2x^8 +2) = 16
56c2x^8 -8c1x -64c2x^8 +8c1x +8c2x^8 +16 = 16
x^8(56c2 -64c2 +8c2) +x(-8c1 +8c1) +16 = 16
0 +16 = 16 . . . . QED
