(1 point) Consider the system of equations =»(1- * -x), taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (-)nullcline: (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) (c) Use a phase plane plotter (such as pplane) to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (2,), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Answers

Answer 1

(a) An equation for the (non-zero) vertical (x -)nullcline of this system is  and for the (non-zero) horizontal (y-)nullcline is y = 1 - x/3 and x = 1 - y/4

(b) The equilibrium points for the system are (0,0) and (1,1).

c) If we start at the initial position (2,2), trajectories approach the point (1,1).

The system of equations we will consider is:

dx/dt = x(1 - x/3 - y)

dy/dt = y(1 - y/4 - x)

To find the vertical (x-)nullcline, we set dx/dt to 0 and solve for y. This gives us:

1 - x/3 - y = 0

y = 1 - x/3

Similarly, to find the horizontal (y-)nullcline, we set dy/dt to 0 and solve for x. This gives us:

1 - y/4 - x = 0

x = 1 - y/4

The nullclines represent the points in the phase plane where either dx/dt or dy/dt is zero.

Therefore, any trajectory that passes through a nullcline will be tangent to that nullcline.

To find the (non-zero) vertical (x-)nullcline, we set x = 0 and solve for y. This gives us y = 1/x.

Therefore, the equation of the vertical nullcline is y = 1/x.

Similarly, to find the (non-zero) horizontal (-)nullcline, we set y = 0 and solve for x. This gives us x = y.

Therefore, the equation of the horizontal nullcline is x = y.

Next, we want to find the equilibrium points of the system, which are the points in the phase plane where both x and y are zero.

To find the equilibrium points, we set x = 0 and y = 0 and solve for x and y. This gives us two equilibrium points: (0,0) and (1,1).

To confirm that these are indeed equilibrium points, we can substitute them into the original equations and verify that x and y are both zero at these points.

Finally, we want to estimate trajectories in the phase plane using a phase plane plotter.

Suppose we start at the initial position (2,2). We can use the phase plane plotter to draw the trajectory that passes through this point. We observe that the trajectory approaches the equilibrium point (1,1) as t goes to infinity.

Therefore, we can complete the sentence as follows: If we start at the initial position (2,2), trajectories approach the point (1,1).

To know more about equilibrium points here

https://brainly.com/question/30843966

#SPJ4

Complete Question:

Consider the system of equations

d x / d t = x ( 1 − x / 3 − y )

d y / d t = y ( 1 − y / 4 − x ) . taking (x, y) > 0.

(a) Write an equation for the (non-zero) vertical (x -)nullcline of this system; And for the (non-zero) horizontal (y-)nullcline:

(b) What are the equilibrium points for the system? (Enfer the points as comma-separated (x.y) pairs, e.g., (1, 2), (3,4).) (

c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position ( 2 , 1 2 ) . trajectories the point (Enter the point as an (x.y) pair. o.g.. (1, 2).) Analysing s


Related Questions

jane spend $42 for her for shoes this was $14 less than twice what she spent for a blouse how much was the blouse​

Answers


42=2b-14 where b=price of the blouse
42+14=2b
56=2b
b=56/2
b=$28 is the price of the blouse



Please help answer all please thank you

Answers

Answer:

The answers are, in order:

1. Isolate

2. substitute

3. variable

Step-by-step explanation:

You're welcome :)

answer choices:90ft square inches, 45ft square inches, 80ft square inches ​

Answers

Answer:

CAUSE I FEEL THE BREK FEEL THE BREK FELLLLLLL THE BREKK

Step-by-step explanation:

1)y=4
2)y=4x
3)y=4x+4
4)x=4

Answers

Answer:

I think number letter shape 14

Answer:

I am pretty sure that the answer is y=4x

find an equation of line containing (3, -4) and having slope -2. if this line contains the points (a, 8) and (5, b) find a and b

Answers

Answer:

a = -3

b = -8

Step-by-step explanation:

Equation for a line is:

y-coordinate = (slope * x-coordinate) + y-intercept

For (3, -4): -4 = (-2 * 3) + y-intercept

y-intercept = 2

Equation for all points on this line is:

y = -2*x + 2

For (a, 8): 8 = (-2 * a) + 2

For (5, b): b = (-2 * 5) + 2

Which triangle makes this statement true?

Answers

Answer:

Step-by-step explanation:

The question is kind of confusing but I think the answer is A.

Answer:

C is the correct answer

Step-by-step explanation:

I did this exact one and it was right I hope this helps! Have a good day! :)

Proof:

Enter a digit in each box to complete the division problem.

Please answer i’ll give brainliest

Answers

Step-by-step explanation:

2527 is the first line so 5 in the box

then 47 so a 4 in that box

top answer row

315 E7 so a 5 in that box.

What does y = 1/3x + 5 look like on a graph?

Answers

It’s gonna cross the 5 on the y axis, and it’ll be decreasing because the rise/run is 1/3

HELP ANSWER FAST!!!!

Answers

D = -2, -1, 3, 5
R = -7, 0, 4
Function? Yes

Find the equation of the line with slope −15 and y-intercept (0,−2).

Answers

Answer:

y = -15x - 2

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

Write and equality for an each situation .

Gary has at least 25 blue t shirts
The room can hold no more than 50 people .

Answers

Answer:

50-25? so the answer is twenty five?

Step-by-step explanation:

25 hope this helps!!!

Jasmine had some candy to give to her three children. She first took four pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

Answers

Answer:

10 pieces

Step-by-step explanation:

She gave herself 4 pieces, and each child 2 pieces. If she has 3 children, she gave them 6 pieces.

(3*2=6) and then you add with the amount she gave herself, (6+4) that would be 10.  She started with 10 pieces.

An equation would be:

x= 4+(2*3)

I hope this helps!

(Also this equation seems a bit easy, am I reading it wrong? If I am be sure to correct me :) )

The length of what line segment would be multiplied by pi to find the circumference of Circle P?

Answers

9514 1404 393

Answer:

  QS

Step-by-step explanation:

The circumference is pi times the diameter. The only segment shown that is a diameter is QS.

Omg pls help in my math. It is 6th grade

Answers

Answer:

1. You have to shade 38/100 squares

2. You have to shade 65/100 squares

3. 3/5=15/25, 6/10, 9/15

Yes he’s right or she ?

Please help, I beg of y'all

FIND BD -

Answers

9514 1404 393

Answer:

  14 units

Step-by-step explanation:

The angle bisector divides the sides proportionally.

  BD/BA = CD/CA

  (x+4)/8 = (2x+1)/12

  3(x +4) = 2(2x +1) . . . . . multiply by 24 (the least common denominator)

  3x +12 = 4x +2 . . . . . . . eliminate parentheses using the distributive property

  12 = x +2 . . . . . . . subtract 3x

  10 = x . . . . . . . . . subtract 2

Then the length of BD is ...

  BD = x +4

  BD = 10 +4 . . . . substitute the value of x

  BD = 14

pls help soon reward brainiest

Answers

Answer:

x=-6

Step-by-step explanation:

please help picture attached ​

Answers

Answer:

triangle B and D

what equation represents the table ?

Answers

Answer:

y=x-2

Step-by-step explanation:

we know that y-intercept is -2

y=?x-2

So now we would have to find slope

the slope would be 1

soo that makes the equation would be

y=x-2

I hopes this helps.

Have a good day!!

Evaluate the formula for distance to solve the problem. Then use the drop-down menus to complete the statements.

Distance = rate times time

During a big race, Jeff races his car at a rate of 125 miles per hour for 3.2 hours. What is the distance of the race?

First, write the
.

Next, use parentheses when you substitute
in for r and
in for t.

Now, simplify by
125 and 3.2.

Jeff raced for a distance of
miles.

Answers

Answer:

First, write the  

✔ formula: d = rt

.

Next, use parentheses when you substitute  

✔ 125

in for r and  

✔ 3.2

in for t.

Now, simplify by  

✔ multiplying

125 and 3.2.

Jeff raced for a distance of  

✔ 400

miles.

Step-by-step explanation:

Which is closest to the quotient 4,367 divided bye 0.004?


A. 1,000
B. 10,000
C. 100,000
D. 1,000,000

Answers

Answer:

6.) 1,000,000

Step-by-step explanation:

Answer:

ye

Step-by-step explanation:

y=-3x-5
y=4x+30
PLS HELP ASAP

Answers

{y,x} = {10,-5}

Step-by-step explanation:

sorry if this dont make sense

solve equation [2] for the variable y

y = 4x +30

plug this in for variable y in equation [1 ]

(4x+30) +3x= -5

solve [1] for the variable x

7x= - 35

x= - 5

by now we know this much

y= 4x+30

x= - 5

use the x value to solve for y

y=4 (-5) + 30 = 10

solution

{y,x} = {10,-5}

Tito builds a model of the solar system. In his model, the diameter of the sphere representing Jupiter is 7
inches. What is the circumference of a cross section through the center of the model of Jupiter? Use 3.14
for π


Answers

Answer:

21.99

Step-by-step explanation:

C = 2 * Pi * (r)

Diameter = 7

Radius = 3.5

Pi

21.99

A store wants to mark up
their prices by 12%.
What would the markup
be on a $40 lamp?
What is the final price?
And how did you solve it

Answers

Answer:Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...

Step-by-step explanation:

Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...

Answer:

$44.80

Step-by-step explanation:

Here' s  an equation to help you with percent problems:    part            %

                                                                                               -------    =    -----

                                                                                              whole         100

Because you want to find 12%, the % in the equation would be replaced with 12. The part would be x because that's what u need to find. The whole would be 40. Cross multiply to get 100x = 480. Divide 480 by 100 to get x = 4.80. Add 4.80 to 40.00 to get the final price. The final price is $44.80.

McKenzie earns $15 per lawn mowed she also earned $10 for babysitting she earned 100 total, what does that look like in algebra form? Please help.

Answers

Answer:

15a + 10b = 100

Step-by-step explanation:

Given:

Cost of each lawn mowed = $15

Cost of each babysitting = $10

Total money earned = 100

Find:

Algebra form

Computation:

Assume;

Number of lawn mowed = a

Number of babysitting = b

So,

15a + 10b = 100

Write your own Algebraic expression with four terms that can simplify to 12x+4​

Answers

Answer:

11x+1x + 2+ 2

Step-by-step explanation:

2
1
X 46
7. Find the m 2 JKL
in rhombus JKLM

Answers

Step-by-step explanation:

since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.

Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account balance be after 8 years if the interest is compounded 6 times each year?
URGENT PLEASE

Answers

Answer:

We conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

[tex]A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}[/tex]

[tex]\:A=2500\left(1+\frac{0.05}{6}\right)^{48}[/tex]

[tex]A=2500\times 1.48935[/tex]      ∵  [tex]\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935[/tex]

[tex]A=\:3723.38[/tex] $

Therefore, we conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

I need help with this assignment please help me ​

Answers

Answer:

Step-by-step explanation:

a. 7*7*7= 7 cubed(when we divide powers we subtract them)

Enola surveyed 300 of the students in her school about their favorite color. 78 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?

Answers

Answer:

26%

Step-by-step explanation:

I did some simple math here: a percentage represents a number over 100.

To find the percentage, I just divided 78 by 300 and got 0.26

I then multiplied by 100 to get 26%

Hope this helps! Have a great day!

A man with a height of 5ft casts a shadow of 2ft. What will be the height of a tree that casts a shadow of 40ft at the same time?

Answers

Answer:

19

Step-by-step explanation:

Answer:

100 ft.

Step-by-step explanation:

Let x = height of tree

height/height = shadow length/shadow length

5/x = 2/40

2x = 200

x = 100 ft.

Other Questions
You are a recent Berkeley College graduate and you are working in the accounting department of Macys. Next week, you are required to attend an inventory meeting for the store located in the Paramus Park mall. You know this store well because you shop there frequently. One of the managers of the store feels that the mens shoe department is unprofitable because the selection is poor, there are few sizes available, and there just arent enough shoes. The manager is pushing for a very large shoe inventory to make the department more desirable to shoppers and therefore more profitable. Explain in this discussion why it is good or bad to have a large inventory of shoes. 2. Do the terms LIFO, FIFO, and Weighted Average have anything to do with the actual physical flow of the items in inventory? Please explain Compare the presentations about desalination in the two passages. Explain how they are alike different. Describe how the authors use similar and different facts to achieve their unique purposes. Use at least TWO details from the texts in your responce Find the distance from point X to line p. Compare the amount of current entering a junction in a parallel circuit with that leaving the junction. (A junction is a point where three or more conductors are joined.) plssConsidering that the figure shows a square and congruent quarter circles, then the shaded area in the figure corresponds to (consider = 3) A RewardsChargeCard must use ChargeCard as its base class. Such a card has a reward rate - the percentage of money the user gets back as rewards for each charge transaction. The rewards are accumulated until used. When rewards are used, the accumulated reward amount is deposited into the card and accumulated reward amount is reset to zero. A ChargeCard must support the following calling syntaxes:ConstructorThe constructor should accept two required parameters, designating the spending limit on the card and the reward rate (as a float). Additionally, the constructor must accept an optional parameter that designates an initial balance (with the balance being 0 by default). For example, the syntax# using default value of balancecard = RewardsChargeCard(1000, 0.01)would create a new card, with spending limit of 1000, reward rate of 0.01, and an initial balance of zero.# specifying the value of balance explicitlycard = RewardsChargeCard(1000, 0.01, 100)would create a new card, with a spending limit of 1000, reward rate of 0.01, and an initial balance of 100.charge(amount)The RewardsChargeCard should override the parent class implementation of this method by:First calling the parent class implementation ofcharge(amount)Updating the value of accumulated rewards. Each charge transaction earns (amount * reward rate) toward the accumulated rewards. Rewards will only be added on valid transactions (if the charge is accepted).Returning True if the amount does not exceed the sum of the current card balance and the card limit, and False otherwise.For example, the following operations would result in the accumulated reward value 10.card=RewardChargeCard(10000, 0.01)card.charge(1000)If the charge is invalid (over the limit) the rewards are not added. For example, the following operations would result in no rewardscard = RewardChargeCard(10000, 0.01, 1000) # inital balance is 1000card.charge(10000) # charge is over the limit+balance, invalid operation, no rewardsgetRewards()A call to this method returns the value of accumulated rewards.useRewards()A call to this method applies the currently accumulated rewards to the balance and then sets the rewards total to 0. Applying rewards to the balance is identical to depositing money to the card, and a convenient way to apply accumulated rewards to the balance is by using the parent class deposit(amount) method and then setting the reward total to 0.To help you test your implementation of RewardsChargeCard, we provide you with a sample session that uses the RewardsChargeCard class:from RewardsChargeCard import RewardsChargeCard# spending limit of 10000, reward rate 0.03, initial balance 0visa = RewardsChargeCard(10000, 0.03)# returns True, as charge is accepted; new balance is 100.# accumulated reward value is 3visa.charge(100)# return value of 3.0 is displayedprint(visa.getRewards())# new balance is 1100# accumulated 30 for this transaction# total accumulated reward value is 33visa.charge(1000)# return value of 33.0 is displayedprint(visa.getRewards())# balance is adjusted to 1067# accumulated reward value is set to 0visa.useRewards()# return value of 1067.0 is displayedprint(visa.getBalance())# return value of 0 is displayedprint(visa.getRewards())# return False, as the amount we are charging is larger than the limit# no rewards should be addedvisa.charge(100000)# return value of 0 is displayedprint(visa.getRewards()) Additionally, we provide you with TestRewardsChargeCard.py script that uses Python unittest framework. Save ChargeCard.py, TestRewardsChargeCard.py and your implementation of RewardsChargeCard.py in the same directory. Then Run the TestRewardsChargeCard.py script and fix any errors that the script finds.Submit the single file, RewardsChargeCard.py, which should contain your implementation of the RewardsChargeCard class.PreviousNext A cone without a base is made from a quarter- circle. The base of the cone is a circle of radius 3 cm. What is the volume of the cone? Explain your reasoning. in 1971, when the consumer price index was 40.48, women earned a median income of $2,408 per year. if the consumer price index in 2012 was 229.6, how much was $2,408 in 2012 dollars? Suppose AD = Im (the m x m identity matrix). Show thatfor any b in Rm , the equation Ax = b has a solution.[Hint: Think about the equation AD b = b.] Explain why A cannothave more rows than columns. What is the current yield on $1000 par value bond that sells for $900 with the coupon rate is 10%? which of the following organizational structures best represents al capones illegal enterprises? PLEASE HELPPPThe Beginning of Brown James and Noel sat on the steps of their new house. It was going to be a hot day, but the boys preferred sitting outside to unpacking more boxes inside. Their mom was unpacking kitchen stuff, and the boys had grown tired of hearing her exclaim every time she unwrapped another of the teapots she hadn't seen in months."You'd think she'd have enough teapots by now," said James."Yeah," said Noel, "I don't get that excited about my Godzilla collection and that is way more interesting than any teapot.""And I'm sorry," said James, "but I know way too much about teapots for a boy my age."James then started listing all the things he knew about teapots. "There's the spout and the pouring angle," he began. But Noel had already tuned James out. The heat was rising and as tired as he was of his mother's teapots, he was more tired of James' complaining.Besides, there was a raggedy old dog down the street. Noel could tell, even from far away, this was a dog that belonged to no one. Its coat was matted. It had no collar. All he could see of the dog's face was its nose sticking out. Its coat was all brown, but a dirty, grayish brown, not the deep dark warm brown that made you feel safe."And there's that teapot with the flowers. The brown one with the little dots all in a row," James continued on his rant, now listing all the teapots he had unwrapped for Mom. Noel continued ignoring James and watched the dog.It was moving slowly in their general direction. It stopped at various spots along the curb to smell things. Sometimes the smelling took a very long time. Every now and then it would sit down to scratch behind its ear. Noel wondered if it was looking for something to eat.James jabbered on and Noel began to wonder how a dog came to be in such a sad condition as this one. Did no one ever want it? Even as a puppy, was this fellow not cute enough to find a good family? Had it always been this ugly? Hadn't anyone ever been kind to it? The dog was across the street now, one house over. It seemed to be particularly attracted to mailboxes and the plants around them. To Noel's mind, it appeared that the dog was greeting each family on the street.Noel watched the dog cross the street heading in their direction. He hadn't noticed it before, but the dog's head seemed rather large. It swung back and forth in front of its body, much like the bears Noel had seen at the zoo and on television. Noel could not see any eyes through all the matted hair. He could see gnats and flies hovering over the poor thing, waiting for it to sit down again.It lumbered toward them. Noel noticed that James had stopped talking. He looked over at his brother. Staring at the dog, James seemed to be a bit shocked or surprised, maybe even stunned."What is that?" James whispered.Instead of sniffing their mailbox and moving on like before, the dog started up the sidewalk toward the steps where they were sitting. Noel could hear the flies buzzing and see not just a few gnats, but a whole swarm around the dog. Bits of leaves and twigs hung in its hair. The dog continued toward them. Was it going to stop, wondered Noel. Should I get up and get in the house? But then, just when Noel felt a twinge of panic, the dog sat down, wagged its tail, and smiled. Noel had never seen anything like it before. It was as if the dog, flies and all, were posing for a photographer. It is going to be an interesting summer, thought Noel. Part A: Which of the following best summarizes the character of James as presented in this excerpt? Fill in blank 1 using A, B, or C.(A) Annoyed (B) Ill-tempered (C) Sympathetic Part B: Select one quotation from the text that supports your answer to Part A. Enter your selection in blank 2 using E, F, or G.(E) Their mom was unpacking kitchen stuff, and the boys had grown tired of hearing her exclaim every time she unwrapped another of the teapots she hadn't seen in months.(F) itd coat was all brown, but a dirty , grayish brown, not the deep dark warm brown that made you feel safe.(G) Noel began to wonder how a dog came to be in such a sad condition as this one. Did no one ever want it? Part CSelect another quotation from the text that supports your answer to Part A. Enter your selection in blank 3 using H, I, or J. (H) Even as a puppy, was this fellow not cute enough to find a good family? Had it always been this ugly? Hadn't anyone ever been kind to it? (I) Noel watched the dog cross the street heading in their direction. (J) He hadn't noticed it before, but the dog's head seemed rather large. rumor has it a new restaurant is coming to town called italia noodles. however, the owners are waiting to compare market commonalities and resource similarities to other local italian restaurants. italia noodles is conducting a: Why, in your opinion, would business executives shy away from the new approval process? 1911THE MATCHThere never was a time when the world was without fire, but there was a time when men did notknow how to kindle fire; and after they learned how to kindle one, it was a long, long time beforethey learned how to kindle one easily. In these days we can kindle a fire without any trouble,because we can easily get a match; but we must remember that the match is one of the mostwonderful things in the world, and that it took men thousands of years to learn how to make one.Let us learn the history of this familiar little object, the match.Fire was first given to man by nature itself. When a forest is set on fire by cinders from a neighboringvolcano, or when a tree is set ablaze by a thunderbolt, we may say that nature strikes a match. In theearly history of the world, nature had to kindle all the fires, for man by his own effort was unable toproduce a spark. The first method, then, of getting fire for use was to light sticks of wood at a flamekindled by nature-by a volcano, perhaps, or by a stroke of lightning. These firebrands were carried tothe home and used in kindling the fires there. The fire secured in this way was carefully guarded andwas kept burning as long as possible. But the flame, however faithfully watched, would sometimesbe extinguished. A sudden gust of wind or a sudden shower would put it out. Then a new firebrandwould have to be secured, and this often meant a long journey and a deal of trouble.In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate ofpotash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggisthad discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemicalbecause it is made by mixing certain chemicals together and rubbing them. Although Walker's matchidid not require the bottle of acid, nevertheless it was not a good one. It could be lighted only by hardrubbing, and it sputtered and threw fire in all directions. In a few years, however, phosphorus wassubstituted on the tip for antimony, and the change worked wonders. The match could now belighted with very little rubbing, and it was no longer necessary to have sandpaper upon which to rubit. It would ignite when rubbed on any dry surface, and there was no longer any sputtering. This wasthe phosphorus match, the match with which we are so familiar,How does the author develop the idea that relying on nature was problematic? Please respond inthree to five complete sentences, using evidence from the text to support your answer. (5 points) find two numbers whose sum is 15 and whose product is 44. write the answers as integers or simplified fractions. D(x+2)(x+6)=0In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:O zero product propertyO division propertyO transitive propertyO multiplication propertyHOI All the following were original members of the European Community, the predecessor to the European Union,EXCEPT(A) France (D) Italy(B) Belgium (E) The Netherlands(C) United Kingdom Please answer and explain so I can understand Following circuits are two implementations of 2-input AND gate. Which one is faster, and explain why? Is it consistent with your intuition? Assume = k = 2, Cgate = C X 2-NAND 2-NOR 6C A B When it comes to mate selection, too much choice is not always the best thing. in the book, paradox of choice, schwartz described two types of people. those who spend a lot of time and energy researching options often ended up less satisfied when they finally make a decision. schwartz labeled those people:___________. i. satisficers ii. sufficers iii. maximizers iv. decisionizers