Answer:
I'm not completely sure but in my opinion I think the answer is that the Associated store has the better buy for oranges! :-)
Step-by-step explanation:
Because they have $3.00 for five pounds and the shoprite store has 2.59 for 4 pounds, but if you where to buy a fifth one at the Shoprite store then you would have to pay more for 5 pounds of oranges then you would for the 5 pounds of oranges at the Associated store.
Hope this helps! Please mark me brainliest! :-)))))))
Answer:
57×6 is 342 ,not sure what you mean by the word expression
Answer:
y =
+ ![\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)
Step-by-step explanation:
y''- 9 y' + 18 y = t²
solution of ordinary differential equation
using characteristics equation
m² - 9 m + 18 = 0
m² - 3 m - 6 m+ 18 = 0
(m-3)(m-6) = 0
m = 3,6
C.F. = ![C_1e^{3t}+C_2e^{6t}](https://tex.z-dn.net/?f=C_1e%5E%7B3t%7D%2BC_2e%5E%7B6t%7D)
now calculating P.I.
![P.I. = \frac{t^2}{D^2 - 9D +18}](https://tex.z-dn.net/?f=P.I.%20%3D%20%5Cfrac%7Bt%5E2%7D%7BD%5E2%20-%209D%20%2B18%7D)
![P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=P.I.%20%3D%20%5Cdfrac%7Bt%5E2%7D%7B%28D-3%29%28D-6%29%7D%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%281-%5Cfrac%7BD%7D%7B6%7D%29%5E%7B-1%7D%28t%5E2%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%281%2B%5Cfrac%7BD%7D%7B6%7D%2B%5Cfrac%7BD%5E2%7D%7B36%7D%2B....%29%28t%5E2%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281%2B%5Cfrac%7BD%7D%7B3%7D%2B%5Cfrac%7BD%5E2%7D%7B9%7D%2B....%29%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)
hence the complete solution
y = C.F. + P.I.
y =
+ ![\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)