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Masja [62]
2 years ago
6

Often scientists use rate of change equations in their study of population growth for one or more species. In this problem we st

udy systems of rate of change equations designed to inform us about the future populations for two species that are either competitive (that is both species are harmed by interaction) or cooperative (that is both species benefit from interaction. Which system of rate of change equations below describes a situation where the two species compete and which system describes cooperative species? Explain your reasoning.
a. dx/dt= -5x + 2xy
b. dx/dt= 4x-2xy
c. dy/dt= -4y + 3xy
d. dy/dt= 2y-xy
Mathematics
1 answer:
Elza [17]2 years ago
6 0

Answer:

a: cooperative.

b: competitive.

c: cooperative.

d: competitive.

Step-by-step explanation:

The rate of change:

dx/dt

gives information about how the quantity x changes as a function of time.

If dx/dt > 0, the population x increases as the time passes.

if dx/dt < 0, the population x decreases as the time passes.

Now, let's analyze the options:

a) dx/dt= -5x + 2xy

in this case, x represents one population and y represents the other population. Where x and y should only be positive numbers because we can not have a negative population.

Notice that in this case, if y increases, then dx/dt increases.

Then we have cooperative species because the population y helps the growth of population x.

b) dx/dt = 4*x - 2*x*y

Similar to the previous case, but now as the value of y increases, the value of dx/dt decreases, then we have competitive species.

c) dy/dy = -4*y + 3*x*y

Notice that now we have the rate of change of y, in the right side, we can see that as x increases, also the rate of change dy/dt.

Then the population x helps to increase the population y, which means that the species are cooperative.

d) dy/dt = 2*y - x*y

Now as x increases, the value of dy/dt decreases, then these species are competitive.

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The parabola with equation $y=ax^2+bx+c$ is graphed below:
Mashutka [201]

Answer:

m-n=2

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

f(x)=a(x-h)^2+k

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

f(x)=a(x-2)^2-4

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

12=a((4)-2)^2-4

Solve for a. Subtract within the parentheses:

12=a(2)^2-4

Add 4 to both sides:

16=a(2)^2

Square:

16=4a

Solve:

a=4

Thererfore, the value of a is 4.

So, our function is:

f(x)=4(x-2)^2-4

Now, let’s find our roots. Set the equation to 0 and solve for x:

0=4(x-2)^2-4

4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

4 0
3 years ago
Read 2 more answers
Please help me with question 3
zzz [600]
My gut tells me its C
5 0
3 years ago
Mika rides his bike 3 miles each way to his friend's house. He leaves his house at 4 p.m. How many miles does he ride his bike t
marusya05 [52]

Answer:

How many miles does he ride his bike there and back?

6 miles.

What information is extra?​

The hour at which he leaves his house.

Step-by-step explanation:

We know that he rides 3 miles each way.

Then he rides 3 miles from his house to his friend's house, and another 3 miles from his friend's house to his house.

So he rides 3 miles both times, if we add that, we get:

3 miles + 3 miles = 6 miles

So:

How many miles does he ride his bike there and back?

6 miles.

And to answer the other question, we need to look at the given information that we did not use in this calculation. In this case, is the hour at which he leaves his house.

Notice that we never did use the fact that he leaves his house at 4 p.m.

Then:

What information is extra?​

The hour at which he leaves his house.

6 0
3 years ago
What is -5/6 + -5/6? (its ment to be a fraction)
maks197457 [2]
The answer is:  " -5/3 " ;  or, write as:  " -1 ⅔ " .
_____________________________________________
Explanation:
_____________________________________________

   (-5/6) + (-5/6) = (-5/6) <span>− (5/6) ;  

------>  {since: "adding a negative" is the same a "subtracting a positive"} ; 

------> </span> (-5/6) − (5/6) = (-5 − 5) / 6  ;
  
                                  =   -10/6 =  (-10/2) / (6/2) ;
_____________________________________________________
                                  =   " -5/3 " ;  or, write as:  " -1 ⅔ " .
_____________________________________________________
8 0
3 years ago
Which equation(s) have x = –3 as the solution? log3(2x + 15) = 2 log5(8x + 9) = 2 log4(–20x + 4) = 3 logx81 = 4
baherus [9]

Answer:

log_3(2x+15)=2  and log_4(-20x+4)=3

Step-by-step explanation:

Plug it in and see!

log_3(2x+15)=2\\log_3(2(-3)+15)=2\\log_3(-6+15)=2\\log_3(9)=2\\\text{ This is a true equation because } 3^2=9\\\\\\log_5(8(-3)+9)=2\\log_5(-24+9)=2\\log_5(-15)=2\\\\\text{ Not true because you cannot do log of a negative number }\\\\log_4(-20(-3)+4)=3\\log_4(64)=3\\\text{ this is true because } 4^3=64\\\\\\log_x (81)=4\\log_{-3}(81)=4\\\text{ the base cannot be negative }\\\\\\\\\text{ There is only two options here} \\\\log_3(2x+15)=2 \text{ and } log_4(-20x+4)=3

6 0
3 years ago
Read 2 more answers
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