Suppose a student carryinga virus returns toan isolated college campus o 1000 students. Determine a differential equation for the number x(t) who have contracted the fluif the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the fluand the number of students show have not been exposed to it.

= k.x.[1000 - x] ;  

where k is the proportionality  constant

Step-by-step explanation:

Let

The number of people who are infected with the flu = x(t)

Total number of students = 1000

So,

Total number of student who do not expose with the flue = 1000 - x(t)

As given,

We have to find the differential equation such that

The rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students show have not been exposed to it.

⇒ ∝ x(t) . [ 1000 - x(t) ]

⇒ = k.x.[1000 - x] ; where k is the proportionality  constant

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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