need help with some calc questions.

Solve the following initial value problem. dr do = Isin TO, r(0) = 2 (Type an exact answer, using it as needed.)Solve the initial-value problem. dw - 4t =e for t 2 0 with W(0) = 3 dt The solution to the initial value problem is y = for t2 0.\fdL dL Fish are indeterminate growers. that is. their length L(t) increases With age 1 throughout their lifetime. it we plot the growth rate E versus age t on semilog paper. a straight line With negative slope results meaning that E : Ae' N where A > n and k> 0 are both coefcients that depend on the speCies ofsh' and the habitat that it is grouting in Complete parts (a) through (c) 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 antiderivative) A_kt K L{t): 7 +c (I!) Find the values for the constants A' k and or that would t the suiutiun to the roiiowrng data LtD) = 7. l.(l)=14. and Ilm L(t) = 35 tim A : , K: , and C : (Type integers or decimals rounded to three decimal places as needed ) GM 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 blood will therefore obey the differential equation F : , k0. where for a certain adult icD : 0155 gflitertt'ir Complete parts (a) through (c) below [1M (a) Explain why Mtt) can only obey the above differential equation if M > 0 (once M drops to 0, it is usual to assume E : 0) Choose the correct answer below. Mtt) : 0 does not exist The differential equation becomes undefined at M0) = O The differential equation is positive and at Mt): El there is no ethanol left in the body \" The differential equation is negative and at Mtt) : 0 there is no ethanol left in the body. (b) lr a person's blood alcohol concentration is 1.6 gtliterat 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. His or her blood alcohol concentration will be at 3 AM. (Type an integer or decimal rounded to three decimal places as needed)