A 100-gallon barrel, initially half-full of oil, develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at time t. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. The mathematical model is:. (a) =kA, A(0) = 0
(b) A = ktA, A(O) = 50
(c) A tA, A(0) = 100
(d) A = két +A), A
(e) = 50 None of the above.

the mathematical model is :

Step-by-step explanation:

Given that:

Let A(t) to be the amount of oil in the barrel at time t.

However; Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel.

Then,

Initially the 100 -gallon barrel is half-full of oil

So, A(0) = 100/2 = 50

The variable is now being separated as:

Taking integral of both sides; we have:

However; since A(0) = 50; Then

t = 0  ; A =50 in the above equation

Thus; the mathematical model is :

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

60°

step-by-step explanation:

the measure angle of c in an isosceles triangle abc is 60° because in isosceles triangle,the measures of all the angles is 60°.