Give the substitution that converts the given nonlinear equation into a linear equation then solve the initial value problem. v+=y=t²y²², v(1)=1 a. y(t)=√1+ b. y(t)=. c. y(t) = d. y=3 e. y²= 2 1+e-21 1 e¹[t+1+e] to +1 2t3 5t 2+5ct5

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3Q

Evaluate. to dt

Simplify. 21) V3(5 – V6) 23) 4V15(5+ V3-

-7 -8 T -5. 6 -4 10 -4 +A = 5 9 8 3 2

Arrange these steps in the correct order to prove that if you have an 8-gallon jug of water and two empty jugs with capacities of 5 gallons and 3 gallons, respectively, then you can measure 4 gallons by successively pouring some of or all of the water in a jug into another jug in the correct order. Rank the options below. Fill the 3-gallon jug from the 5-gallon jug, leaving (3, 2, 3). Empty the 5-gallon jug's contents into the 3-gallon jug, leaving (6, 0, 2), and then fill the 5-gallon jug from the 8-gallon jug, producing (1, 5, 2). Fill the 5-gallon jug from the 8-gallon jug, leaving the contents (3, 5, 0), where the ordered triple is used to record the amount of water in the 8-gallon jug, the 5-gallon jug, and the 3-gallon jug, respectively. Top off the 3-gallon jug from the 5-gallon jug, and there will be (1, 4, 3), with four gallons in the 5-gallon jug. Pour the contents of the 3-gallon jug back into the 8-gallon jug, leaving (6, 2, 0). ❤ ← ←

Simplify each series of additions and subtractions