help with calc questions

Solve the initial-value problem. dy 2 for x 2 1 with y(4) = 4 dx X The solution to the initial-value problem is y = for x 2 1.Solve the initial-value problem. dN t+4 , for t2 1 with N(1) = 5 dt The solution to the initial-value problem is N = for t2 1.Solve the initial-value problem. dW - 4t dt for t2 0 with W(0) = 3 The solution to the initial value problem is v = for t2 0.Solve the following initial value problem. dr E = Item IE3, rill] = 2 r= E {Type an exact answer: using I as needed} Solve the following initial value problem. dr do = COS (- 610), (0) = 7 The solution is r(0) = (Type an exact answer.)dL Fish are indeterminate growers; that is. their length L{t] increases with age t throughout their lifetime. If we plot the growth rate versus age t on semilog paper. a dt dL straight line with negative slope results, meaning that E =Ae_ kl where A? {l and k > E] are both coefcients that depend on the species of sh. and the habitat that it is growing in. Complete parts {a} through {:3} below. [a] Find the solution for this differential equation (your solution will include A and k as unknown constants. as well as one additional unknown constant C from the antiderivatiue). A'sKt L(t)= k +c [[1] Find the values for the constants A. k, and C, that would t the solution to the following data L(U) = 'r'. L(1}=14, and Iim L(t) = 35. lHn Az=k=. and C: (Type integers or decimals rounded to three decimal places as needed.) Elimination of ethanol from the blood is known to have zeroth order kinetics. Provided no more ethanol enters the blood, the concentration of ethanol in a person's dM blood will therefore obey the differential equation dt = - Ko, where for a certain adult ko = 0.186 g/liter/hr. Complete parts (a) through (c) below. . . . dM (a) Explain why M(t) can only obey the above differential equation if M > 0 (once M drops to 0, it is usual to assume dt =0). Choose the correct answer below. O A. M(t) =0 does not exist. O B. The differential equation becomes undefined at M(t) = 0. O C. The differential equation is positive and at M(1) = 0 there is no ethanol left in the body. D. The differential equation is negative and at M(t) = 0 there is no ethanol left in the body. (b) If a person's blood alcohol concentration is 1.6 g/liter at midnight, what will his or her blood alcohol concentration be at 3 AM? You may assume that he or she drinks no more alcohol after midnight. lis or her blood alcohol concentration will be at 3 AM. Type an integer or decimal rounded to three decimal places as needed.)