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3 years ago

If f(x) is a third degree polynomial function, how many distinct complex roots are possible?

Mathematics

2 answers:

Valentin [98]3 years ago

7 0

Answer:

0 or 2

Step-by-step explanation:

Allisa [31]3 years ago

5 0

The answer is 0 or 2 i believe

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(1 point) A very large tank initially contains 100L of pure water. Starting at time t=0 a solution with a salt concentration of

Paraphin [41]

1. dy/dt is the net rate of change of salt in the tank over time. As such, it's equal to the difference in the rates at which salt enters and leaves the tank.

The inflow rate is

(0.4 kg/L) (6 L/min) = 2.4 kg/min

and the outflow rate is

(concentration of salt at time t) (4 L/min)

The concentration of salt is the amount of salt (in kg) per unit volume (in L). At any time t > 0, the volume of solution in the tank is

100 L + (6 L/min - 4 L/min) t = 100 L + (2 L/min) t

That is, the tank starts with 100 L of pure water, and every minute 6 L of solution flows in and 4 L is drained, so there's a net inflow of 2 L of solution per minute. The amount of salt at time t is simply y(t). So, the outflow rate is

(y(t)/(100 + 2t) kg/L) (4 L/min) = 2 y(t) / (50 + t) kg/min

and the differential equation for this situation is

$\dfrac{dy}{dt} = 2.4 \dfrac{\rm kg}{\rm min} - \dfrac{2y}{50+t} \dfrac{\rm kg}{\rm min}$

There's no salt in the tank at the start, so y(0) = 0.

2. Solve the ODE. It's linear, so you can use the integrating factor method.

$\dfrac{dy}{dt} = 2.4 - \dfrac{2y}{50+t}$

$\dfrac{dy}{dt} + \dfrac{2}{50+t} y = 2.4$

The integrating factor is

$\mu = \displaystyle \exp\left(\int \frac{2}{50+t} \, dt\right) = \exp\left(2\ln|50+t|\right) = (50+t)^2$

Multiply both sides of the ODE by µ :

$(50+t)^2 \dfrac{dy}{dt} + 2(50+t) y = 2.4 (50+t)^2$

The left side is the derivative of a product:

$\dfrac{d}{dt}\left[(50+t)^2 y\right] = 2.4 (50+t)^2$

Integrate both sides with respect to t :

$\displaystyle \int \dfrac{d}{dt}\left[(50+t)^2 y\right] \, dt = \int 2.4 (50+t)^2 \, dt$

$\displaystyle (50+t)^2 y = \frac{2.4}3 (50+t)^3 + C$

$\displaystyle y = 0.8 (50+t) + \frac{C}{(50+t)^2}$

Use the initial condition to solve for C :

$y(0) = 0 \implies 0 = 0.8 (50+0) + \dfrac{C}{(50+0)^2} \implies C = -100,000$

Then the amount of salt in the tank at time t is given by the function

$y(t) = 0.8 (50+t) - \dfrac{10^5}{(50+t)^2}$

so that after t = 50 min, the tank contains

$y(50) = 0.8 (50+50) - \dfrac{10^5}{(50+50)^2} = \boxed{70}$

kg of salt.

7 0

2 years ago

Which of the following best describes the delian problem?

Alex777 [14]

Answer: B

Step-by-step explanation:Because I tried every other answer can I found out that B was right

4 0

3 years ago

A factory has three machines making energy drinks. When all three machines are running, 520 drinks are made each hour. When only

Vinil7 [7]

Let A, B and C be the amount machines A, B and C, respectively, produce each hour alone.

With all three machines together produce 520 drinks each hour, we know that the addition of the amount that each produces each hour is equal to 520, that is.

$A+B+C=520_{}$

Now, similarly, machines A and B produce together 320 drinks each hour, so the sum of the amounts A and B produce each hour is equal to 320, so:

$A+B=320$

If machine C produce 30 more drinks than B each hour, than the amount of B plus 30 will be the amount of C:

$C=B+30$

So, we got the system of equations:

$\begin{gathered} A+B+C=520 \\ A+B=320 \\ C=B+30 \end{gathered}$

To solve, notice that A + B is known, because of the second equation, so we can substitute A + B by 320 in the first equation:

$\begin{gathered} (A+B)+C=520 \\ 320+C=520 \\ C=520-320=200 \end{gathered}$

Now, we can substitute C into the third equation and solve for B:

$\begin{gathered} C=B+30 \\ 200=B+30 \\ B+30=200 \\ B=200-30=170 \end{gathered}$

And, finally, we can substitute B into the second equation and solve for A:

$\begin{gathered} A+B=320 \\ A+170=320 \\ A=320-170=150 \end{gathered}$

Answers:

First box:

$A+B+C=520$

Second box:

$A+B=320$

Third box:

$C=B+30$

Fourth box:

$150$

3 0

1 year ago

Solve for p.<br> p-3.1/6.7 = 4.5/5

inna [77]

Answer:

$5x - 15.5 = 6.7 \times 4.5 \\ 5x = 30.15 - 15.5 \\ 5x = 14.65 \\ 2 .93$

6 0

2 years ago

Determine which of the following points lies on the line y= 5/4 x + 2

Katyanochek1 [597]

The point (4,7) is the only one that can be plugged into the equation and work. in this case when 4 is plugged in as X & Y is plugged in at 7 we get that 7=7, which is a true statement.

3 0

3 years ago