The concentrations of two chemicals A and B as functions of time are denoted by x and y respectively. Each alone decays at a rate proportional to its concentration. Put together, they also interact to form a third substance, at a rate proportional to the product of their concentrations. All this is expressed in the equations:

dx/dt = −2x−xy,

dy/dt = −3y−xy.

Note that (x, y)=(0,0) is the only equilibrium state (both concentrations must be positive or zero).

(a) Find an equation for y(x):
dy/dx =

(b) Solve your equation to obtain a relationship between x and y. Letting x(0)=5 and y(0)=10, give the relationship as an equation involving x and y:

(Your answer will be an equation involving x and y.)

Note that one implication of your relationship should be that if x and y are positive and very small (so that x is very much smaller than ln(x)), y2/x3 is roughly constant.

(c) Suppose that x=y. From your equation, what are x and y in this case?
x = y=

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

if she was to only spend a dollar she can get 1lb

step-by-step explanation: