(a) Suppose Y1(t) is a solution of an autonomous system dY/dt = F(Y). Show that Y2(t) = Y1(t +t0) is also a solution for any con
stant t0. (b) What is the relationship between the solution curves of Y1(t) and Y2(t)?
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Answer: We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.
We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.
Step-by-step explanation:
Given: A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice.
Since, for recipe of sparkling grape juice , they should be used in same proportion.
Let x be the amount of sparkling water need to mix with 9 quarts of grape juice, then
We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.
Let y be the amount of grape juice need to mix with 3.75 quarts of sparkling water, then
We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.
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