"Predator - Prey"Consider the following systems of rate of change equations:System A(dx/dt)= 3x(1-(x/10))- 20xy(dy/dt)= -5y+(xy/20)System B(dx/dt)= 0.3x-(xy/100)(dy/dt)= 15y(1-(y/17))+25xyIn both of these systems, x and y refer to the number of two different species at time t. In particular, in one of these systems the prey are large animals and the predators are small animals, such as piranhas and humans. Thus it takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey.* Figure out which system is which and explain the reasoning behind your decision. Try to develop more than one way to reach a conclusion.
Answers
Answer:
The responses to this questin can be defined as follows:
Step-by-step explanation:
Take system A. The predator must be there. If we feel the attacker is x, that drop in y (a further prey eaten) must raise by x. Growing x could render y falling much quicker because more predators become available. See the equation of \(\frac{dx}{dt}\).
\(\frac{dx}{dt} = 3x(1- \frac{x}{10})-20xy\)
It will see that dx/dt is an x both y function. It is indeed difficult to tell something about the dependence among \(\frac{dx}{dt}\) and x, but it is quite easy: the higher to y, its higher the 20xy (since x and y are positive numbers). And therefore -20xy is much more negative, but \(\frac{dx}{dt}\) is much worse. Going to find: the larger y, the less or even more negative \(\frac{dx}{dt}\), the less x.
Test: It implies that higher y means less x (more prey) (fewer predators). Then, does the assumption which x is a predator confirmed? No, because more prey, and thus more predators, would mean better lunch for both the predators, People could see that x is now a prey as well as y a predator, even though more predators(y) exist.
They use the second equation to check this:
\(\frac{dy}{dt} = -\frac{5y+xy}{20}\)
Perhaps, now we're just talking about basic dependency as of now: one is from dy/dt to x. A larger x means that the y (predator) is growing faster. For System B we are using the same rationale.Thus, x is a predator and y a predator (as high x indicates higher 25 x but this results in increased y population increase (EQ.2), as higher x means lower \(\frac{XY}{100}\) and reduces x) Afterwards, we would like to learn which system has big and small predators. To conclusion, they must realize that this piranha does not impact that population of humans in the case of piranhas. However in cases where y = I and y = i+1 would not significantly differ from \(\frac{dx}{dt}\) (alter in the number of individuals) (i is an arbitrary number of piranhas)
This function of system B can be seen: \(\frac{dx}{dt} = 0.3x - \frac{xy}{100}\). And what's the reason? Given the fact that the element beside y is \(\frac{1}{100}\), another tiger shark is no worse than \(\frac{dx}{dt}\) and therefore not willing to make a significant contribution to the elimination of global life. Through system A, they could see that the predator is huge because one predator implies a major shift in \(\frac{dx}{dt}\) almost. I belive that, this message has been observed by you. But I also hope that throughout the end I have created no error:) This should try to not learn with your heart, since it is helpful when you grasp the task. Another way to approach the problem might be to try to consider \(\frac{dy}{dt}\) instead of \(\frac{dx}{dt}\) for both systems and then to see that what prey is tiny or large. This big predator should not imply many hunters with one location or each other and will eat a meal (System A seems to have this feature: \((\frac{dy}{dy} = -5y)\)
Related Questions
Write 11/2 as a mixed number
Answers
Answer:
5.5 or 5 1/2
Step-by-step explanation:
Is 16/60 and 4/15 equivalent ratio
Answers
Answer:
Yes
Step-by-step explanation:
4 x 4 =16
____ _____
15 x 4 = 60
Can someone help me Solve:
-2√3+√75=
Answers
Answer:
\(3\sqrt{3}\)------------------
Simplify in below steps:
\(-2\sqrt{3} +\sqrt{75} =\)\(-2\sqrt{3} +\sqrt{25*3} =\)\(-2\sqrt{3} +\sqrt{5^2*3} =\)\(-2\sqrt{3} +5\sqrt{3} =\)\(3\sqrt{3}\)A state lotto has a prize that pays $900 each week for 20 years.
Find the total value of the prize: $
If the state can earn 5% interest on investments, how much money will they need to put into an account
now to cover the weekly prize payments?
Reminder: There are 52 weeks in a year.
Answers
The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
Read more about state lotto
brainly.com/question/28988219
#SPJ1
what type of scale is used on the map?
Answers
The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.
The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.
There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.
Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.
Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.
Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.
It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.
for such more question on graphic scale
https://brainly.com/question/13473114
#SPJ11
Ben sees a game at a city
Answers
The complete question is in the attachment. 60 percent are likely to be the ones that would have to succeed.
How to solve the problemWhole chance of receiving blue here is represented by receiving blue on the first spin, blue on the second spin, and blue on the third spin.
= 2 + 1 + 3
=6
The odds of obtaining a blue or red are equal to the total odds of getting a blue or red in the first spin plus the total odds of getting a blue or red in the second spin plus the total odds of getting a blue or red in the third spin.
= 4 + 2 + 4
= 10
Total chance of receiving blue / Total chances is the probability of getting blue in three spins.
=6/10
=3/5
=60 %
60% are likely to succeed.
Here, the likelihood of victory is lower than 80%
Ben shouldn't therefore play
Read more on probability here:https://brainly.com/question/24756209
#SPJ1
a courtroom spectator merely looks at the defendant and says, “He’s guilty, i tell you.”
Answers
Answer:
hes lyin prolly
Step-by-step explanation:
On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answers
Nathaniel drinks 3 glasses of water in one hour.
To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.
In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.
Let's convert the mixed number of hours to an improper fraction:
\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)
\(=\frac{12}{5}\)
Now, we can set up a proportion to find his drinking rate per hour.
We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.
Let's assign "x" as the number of glasses he drinks in one hour.
The proportion is then
\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)
Cross-multiplying gives us
\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)
Simplifying, we get
\(\frac{12}{5} =\frac{4}{5}\times x\)
Dividing both sides by \(\frac{4}{5}\), we find x:
\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)
\(x=\frac{12}{4}\)
\(x = 3.\)
Therefore, Nathaniel drinks 3 glasses of water in one hour.
For such more such question on glasses
https://brainly.com/question/11980886
#SPJ8
8th grade math. I think. This is not a test just reviewing. Just saying.
Answers
Answer:
I'm pretty sure its 50.24. like 95%
The average rate of growth for human hair is about 0.3 millimeters per day. How many days will it take a hair that is 12 millimeters long to grow to be 16.5 millimeters?
Answers
It will take 15 days for the hair to grow from 12mm to 16.5mm
What do you mean by average rate?By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.
Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):
16.5mm - 12mm = 4.5mm
Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:
4.5mm ÷ 0.3mm/day = 15 days
Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.
To know more about average rate:
https://brainly.com/question/17219001
#SPJ1
5 years ago, Cheryl was d years old, Brandon is 2 years older than Cheryl.
a. how old is Cheryl
b. how old is Brandon
c. what was the difference in their ages 5 years ago?
d. what is the sum of their ages now?
e. what will the sum of their ages be two years from now?
f. what will the difference of their ages be two years from now
will mark the brainliest.
Answers
Answer: See explanation
Step-by-step explanation:
a. how old is Cheryl?
Cheryl's age = d + 5
b. how old is Brandon?
d + 5 + 2
= d + 7
c. what was the difference in their ages 5 years ago?
Cheryl age five years ago = d
Brandon's age five years ago = d + 2
Difference = d + 2 - d = 2 years
d. what is the sum of their ages now?
Cheryl's age = d + 5
Brandon age = d + 7
Sum = d + 5 + d + 7
= 2d + 12
e. what will the sum of their ages be two years from now?
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Sum = d + 7 + d + 9
= 2d + 16
f. what will the difference of their ages be two years from now
Two years from now,
Cheryl's age = d + 5 + 2 = d + 7
Brandon age = d + 7 + 2 = d + 9
Difference = Brandon age - Cheryl age
= (d + 9) - (d + 7)
= 2 years.
I’ll give Brainly!
A bunch of bananas cost $4, a pineapple cost $2 more than a bunch of bananas, and 4 apples cost one-half of a pineapple.
Question:
1. Write an equation that shows the cost of a pineapple (p) in terms of bananas (b). Use this equation to find the cost of a pineapple.
2. Write an equation that shows the cost of 4 apples (a) in terms of a pineapple (p). Use this equation to find the cost of 4 apples.
3. Write an equation that shows how much more a bunch of bananas cost compared to 4 apples where x is the unknown value. Then, solve the equation.
Answers
Answer:
Step-by-step explanation:
1. b+2=p
b=4
4+2=6. 6=p
2. 1/2p=4a
p=6
1/2(6)=4a
3=4a
.75=a
3. 4(.75)+x=4
3+x=4
x=1
the sum and product of zeroes are 4 and 1 respectively then the quadratic equation is
A. x² - 4x + 1 =0
B. x + 1=0
C 4x² +x +1 =0
D . x² + 7x+1 =0
Answers
Answer:
A. x²- 4x+ 1
option A is the answer
According to the Centers for Disease Control
and Prevention, kids should get
at least 10 minutes of exercise each day
at least 30 minutes of exercise each day
at least 60 minutes of exercise each day
Dat least 3 hours of exercise each day
Answers
According to the Centers for Disease Control
and Prevention, kids should get C) at least 60 minutes of exercise each day.
What's exerciseExercise is a movement activity that has an important role for health. With exercise, one's body becomes healthier and stronger. Not only maintaining physical health, exercise also affects spiritual health.
The aim of exercise is to improve one's health. In addition to improving physical fitness, exercise can also improve and improve the performance of the human brain so that it can work more optimally. Therefore, exercise is considered to be able to increase one's self-confidence.
Learn more about exercise at
https://brainly.com/question/13128077
#SPJ1
A student bought 11 pencils and a pad of paper.
The pencils each cost the same amount.
The pad of paper costs $4.99.
The student spent a total of $18.74, not including tax
Answers
Answer:
Each pencil costs $1.25
Step-by-step explanation:
$18.74 - 4.99=13.75
13.75/11=$1.25
You have to take the total amount and subtract how much the paper pad costs then you get 13.75 and that is how much the student paid for all 11 pencils so you divide it by 11 and you get $1.25
please help me with math i’ll give you brainlist
Answers
Answer: False
Step-by-step explanation:
25% of the data is between Q1 and the median.
Cilia cycles 4.2 km every morning. How many feet are in 4.2 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet?
Answers
Answer:
13,780.8 feet
Step-by-step explanation:
1 mile = 1.609km
1 mile = 5,280ft
Convert 4.2km to miles
1.609km = 1 mile
4.2km = 4.2/1.609 miles
= 2.610 miles
Convert 2.610 miles to feet
1 mile = 5,280ft
2.610 miles = 2.610 × 5,280
= 13,780.8 feet
13,782.47 feet is the correct answer i just did this test DUUUH LOL
Solve using substitution.
y = –6
–8x − 7y = –6
Answers
Okay so you put -6 in where y is then solve and youll get your answer
-8x-7(-6)=-6
ramon makes a spinner with 4 colors. he colors 25% of the spinner red, 15% blue, 40% orange, and the rest green. ramon then spins the spinner. which outcome would be most likely to happen?
a. the spinner landing on green or red
b. the spinner landing on green or blue
c. the spinner landing on orange or red
d. the spinner landing on orange or blue
Answers
Answer:
c. the spinner landing on orange or red
Step-by-step explanation:
So first you find how much is green
25 + 15 + 40 = 80
100 - 80 = 20
So the amount green is 20%
Then you choose the color that has the biggest percentage because it has a higher change of being chosen
25% is red
15% is blue
40% is orange
20% is green
orange and red is the biggest amount/ has the biggest percentage
c is your answer
Put the quadratic into vertex form
Answers
The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.
How to find the vertex formTake a look at the quadratic function:
f(x) = 2x^2 + 8x + 7
In this situation, a = 2 and b = 8, yielding:
f(x) = 2(x^2 + 4x) + 7
It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:
f(x) = 2(x^2 + 4x + 16 - 16) + 7
The expression inside the parenthesis can now be written as a perfect square:
f(x) = 2((x + 2)^2 - 16) + 7
Finally, the phrase is simplified by spreading the 2:
f(x) = 2(x + 2)^2 - 32 + 7
f(x) = 2(x + 2)^2 - 25
Learn more about functions on
https://brainly.com/question/10439235
#SPJ1
What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7
Which of the following is a Pythagorean triple?
A. (5, 5, 10)
O B. (3,4,6)
C. (6, 8, 10)
D. (10, 12, 15)
Answers
Answer:
its c
Step-by-step explanation:
There where four times as many trucks as vans. What is the ratio of the statements could compare the number of trucks to vans .
Answers
Answer:
4:1
Step-by-step explanation:
4 trucks for 1 van
write the algorithm for the following tasks. to calculate the sum of 9 and 4.
Answers
The algorithm to calculate the sum of 9 and 4. is:
Input 9Add 4 to 9Prnt the result 13How to determine the algorithmFrom the question, we have the following parameters that can be used in our computation:
algorithm to calculate the sum of 9 and 4
This implies that we write the steps to calculate the sum of 9 and 4
So, the steps are
Input 9Add 4 to 9Prnt the result 13Read more about algorithm at
https://brainly.com/question/24793921
#SPJ1
how would I find the equation of this graph
Answers
Answer:
y = sec(x-2) - 1
Step-by-step explanation:
We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.
How is a system of two linear inequalities in two variables different from a system of two linear equations in two variables?
Answers
Answer:
A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.
There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:
Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).
The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.
The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.
The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.
Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.
I will give brainliest
Jared is going to plant 20 small plants around the edge of a circular garden that is 8 feet in diameter. If he spaces the plants evenly, how much distance will be between the plants?
25.12 feet
12.56 feet
2.5 feet
1.26 feet
Answers
Answer:
2.5 feet
Step-by-step explanation:
20/8=2.5
answer these 2 qns if possible or atleast one
Answers
1. The percentage of maize flour is given as 16.7 %
2. The common ratio of the GP is r = 1.5.
How to solve for the common ratio1. We have to set up equation
60x + 90(1 - x) = 85
60x + 90 - 90x = 85
now we have to solve for the value of x
-30x = -5
x = 5 / 30
x = 0.167
Hence percentage of maize flour is given as 16.7 %
2. a + ar = 20 (1)
ar + ar^2 = 30 (2)
We can rearrange equation (1) to get an expression for a:
a = 20 / (1 + r)
Now, we can substitute a into equation (2) to get an equation only in terms of r:
\(20r / (1 + r) + 20r^2 / (1 + r) = 30\\20r + 20r^2 = 30(1 + r)\\20r + 20r^2 = 30 + 30r\\20r^2 - 10r - 30 = 0\\2r^2 - r - 3 = 0\)
Solving this quadratic equation, we get:
We have two solutions, r = 1.5 and r = -1. But since the GP is increasing, we discard the negative solution. Therefore, the common ratio of the GP is r = 1.5.
Read more on common ratio here:https://brainly.com/question/1509142
#SPJ1
Calculate the surface area
Answers
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
Learn MoreTo learn more about the surface area of shapes, refer to:
https://brainly.com/question/31978573
https://brainly.com/question/32198861
https://brainly.com/question/26883871
https://brainly.com/question/30816589
https://brainly.com/question/27847638
https://brainly.com/question/15476432
https://brainly.com/question/14001755
https://brainly.com/question/29298005
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
Answers
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
Learn more about speed here:
brainly.com/question/13943409
#SPJ1
what is (1/2 + isqrt3/2)^5?
Answers
Answer:
\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
Step-by-step explanation:
Convert 1/2 + i√3/2 to rectangular form
\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)
Use DeMoivre's Theorem
\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)