6. does the initial value problem tion in the neighborhood of x = 4 = 3y^2/3 where y(0) = 10-7 have a unique solu- 7. consider y 4 - 4x = 0. a) does theorem 1 imply the existence of a unique solution that satisfies y(xo) = 0? b) show that when xo + 0, there can not be a solution in any neighborhood of x = 20 such that y(xo) = 0. c) show that there are two distinct solutions to this ode satisfying y(0) = 0.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

is there supposed to be a diagram or a graph for this one? ?

step-by-step explanation: