Consider the system of differential equations
dx/dt= x+ y=1
dy/dt =1- x^2 +y^2
Required:
Sketch the x-nullcline, where solutions must travel vertically. Identify the regions in the plane where solutions will move toward the right, and where solutions move toward the right.
Answers
Answer:
Step-by-step explanation:
Given that:
the differential equations:
[tex]\dfrac{dx}{dt}= x+y = 1 \\ \\ \dfrac{dy}{dt}= 1-x^2+y^2[/tex]
For x-nullcline;
[tex]\implies \dfrac{dx}{dt} =0 \\ \\ \implies x+y-1[/tex]
From the image attached below, the sketch of the x-nullcline was carefully drawn and the regions were identified.
So, x-increases at the time when [tex]\dfrac{dx}{dt}>0[/tex]
[tex]\implies x+y -1 >0[/tex]
Thus, the solution move towards the right for x+y>1
Related Questions
What is the slope of the line that goes through (0,0) and (6, 3)?
Answers
Answer:
0.5
Step-by-step explanation:
so the slope is also known as the gradient in y=mx+c
A manager at a gas station realized that there appeared to be a quadratic relationship between the price he charged for a doughnut and the number he sold for the day.
Using a quadratic regression model base on the data, how many doughnuts would be predicted to sold if he charges $0.85 for a doughnut?
Answer choice:
a) ≈22
b) ≈25
c) ≈29
d) ≈30
Answers
He sold 28 at 0.75 cents and sold 21 at 0.99 cents.
0.85 is between 0.75 and 0.99 so he sells between 21 and 28 donuts.
0.85 is closer to 0.75 ,so the number should be closer to28.
The answer should be b)25
Destinee bought a tablet for $599 and enrolled in a data plan for $25
per month. The total amount y Destinee has paid towards the tablet after x months is found using an equation in the form y = mx + b.
What is the value of m and b?
Answers
Value of b=599
y=25x+599
Will you please help me with my math?
Answers
Answer:
isn't it just 4?
Step-by-step explanation:
according to the table it's just asking you to name what is with x of f(x). I might be wrong though
8. Carol and Curtis are running a half mile race. Curtis finished the race in 11 minutes and 8
seconds. Carol completed the race in 9 minutes and 3 seconds. What is the difference
between their average speed per mile?
Answers
Answer:
Step-by-step explanation:
curtis is 22 min 16 sec carol is 18 min 6 sec
4 mins and 10 seconds it the difference
STOP SENDING ME LINKS BUT I NEED HELP RN
a company has a machine that produces 1080 pounds of sand in 24 hours the machine puts the sand in 5lbs bags how many 5lbs bags can the machine produce in one hour
Answers
1080 divided by 24
45
45 5lbs per hour
PLEASE ANSWER ASAP FOR BRIANLEST DUE IN 3 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: 3rd one
Step-by-step explanation:
A new car is purchased for \$18,000$18,000 and over time its value depreciates by one half every 3.5 years. How long, to the nearest tenth of a year, would it take for the value of the car to be \$900$900?
Answers
Answer:
15.1
Step-by-step explanation:
Rounding equation up to the nearest hundred dollars, the car's value 19 years later will be around $2,500.
What is equation?In mathematics, an equation is a statement stating the equality or two expressions. An equation consists of two sides split by an algebraic equation (=). For illustration, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal to the value "9".
Given that new car is purchased for $18,000 and over time its value depreciates by one half every 3.5 years Because the car depreciates by half every six years, the car's value after t years is provided by:
To determine the worth of the car 19 years after purchase, we have to analyse V(19):
y = 2000
y = a(1/2) ^t/h
q = 18000
h= 3.5
t=19
Therefore,
y = 18,000
y=2,500.52211582
y≈2,500
Thus the car's value 19 years later is around $2,500.
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The Chandlers are moving across the country. Mr. Chandler leaves 4.5 hours before Mrs. Chandler. If he averages 60 mph and she averages 85 mph, how many hours will it take Mrs. Chandler to catch up to Mr. Chandler?
Answers
Answer:
3
Step-by-step explanation:
9514 1404 393
Answer:
10.8 hours
Step-by-step explanation:
Mr. Chandler has a head start of ...
(4.5 h)(60 mi/h) = 270 mi
Mrs. Chandler is closing the gap at the rate of ...
(85 mph) -(60 mph) = 25 mph
At that rate, she will close the 270 mile gap in ...
(270 mi)/(25 mi/h) = 10.8 h
It will take Mrs. Chandler 10.8 hours to catch up.
__
After 15.3 hours, Mr. Chandler will have driven 918 miles.
After 10.8 hours, Mrs. Chandler will have driven 918 miles.
Maria cut a rectangular piece of fabric. The area was 8/10 of a meter. The width was 6/10 of a meter. What was the length of the fabric?
Answers
Answer:
its A
Step-by-step explanation:
help I have already published it 3 times and nobody helps me, could someone help me and explain how to do it? Thank you
Answers
9514 1404 393
Answer:
3) 74°
4) 260°
Step-by-step explanation:
3) Angle CAE is vertical to angle FAB, which is shown as 121°. Vertical angles are congruent. So, we have ...
∠DAE +∠DAC = ∠EAC
∠DAE + 47° = 121° . . . . . . . fill in known values
∠DAE = 121° -47° . . . . . . . . subtract 47°
∠DAE = 74°
__
4) arc MJL is the long arc that completes the circle along with short arc MJ. Short arc MJ has the same measure as its central angle, 100°. Then long arc MJL is 360° -100° = 260°.
arc MJL = 260°
what is the inverse operations of -5x + 10 = 40
Answers
Answer:
x=-6
Step-by-step explanation:
−5x+10=40
−5x+10−10=40−10
−5x=30
−5x/5=30/5
x=−6
Lynda was a horrible waitress. She spilled a drink on you and she brought you the wrong food. The bill came to $56.35 so you left her $3. What was the percent of tip you left her?
Answers
Answer:
5.32 percent of the tip
Someone please help me!!! I’m stuck and need help!
Answers
Answer:
12
Step-by-step explanation:
These triangles are similar using the AA theroem. This means there sides are in corresponding proportion.
Side AR and Side TE are corresponding. Use this proportion.
[tex] \frac{6}{8} [/tex]
This side the triangle SAR side lengths are 3/4 of side lengths of triangle SET.
We know that RS+ST=21
And that RS=3/4(ST).
[tex] \frac{3}{4} x + x = 21[/tex]
[tex]1.75x = 21[/tex]
x=12.
Side ST is 12
A=bh, find A when b=93 and h=69 A=
Answers
Answer:
A= 6417
Step-by-step explanation:
A = bh
b = 93
h = 69
A = 93*69
Please help!! I will venmo
Answers
Answer:
30 cm^2
Step-by-step explanation:
the triangle is 36
the rectangle is 6
36-6=30
Classify the angle pair using all names that apply
Answers
Answer:
Vertical
Step-by-step explanation:
Answer:
∠1 and ∠3 = vertical
Step-by-step explanation:
vertically opposite angles are equal
the opposite sides of rectangles parallel.
Answers
Answer:
TRUE
Step-by-step explanation:
If that's not the answer you wanted just comment if you need help
Work out the size of angle x
Answers
Answer:
65°
Step-by-step explanation:
A ladder needs to reach a second-story window that is 15 feet above the ground and make an angle with
the ground of 66°. How far out from the building does the base of the ladder need to be positioned?
Round your answer to the nearest tenth.
The base of the ladder needs to be feet away from the wall.
Answers
Answer:
6.7 ftStep-by-step explanation:
Given:
Vertical distance = 15 ftHorizontal distance = xAngle with ground = 66°Use tangent to solve:
tan 66° = 15/xx = 15 / tan 66°x = 6.7 ft (rounded)Answer:
Solution given:
In right angled triangle ABC
relationship between perpendicular and base is given by tan angle
tan66°=15/AB
AB=15/tan66°=6.678 ft is your answer.
Which of the following statistics is used to measure inflation?
Answers
Answer:
.....................
Step-by-step explanation:
As an economic indicator. The CPI is the most widely used measure of inflation and is sometimes viewed as an indicator of the effectiveness of government economic policy.
Which statement compares the product 9/9 x 5,208, the product 19/20 x 5,208, and the product 13/6 x 5,208?
Answers
Answer:
C
Step-by-step explanation:
[tex]\frac{9}{9}=1[/tex]
[tex]1=\frac{20}{20}[/tex]
[tex]\frac{19}{20} <\frac{20}{20}[/tex]
[tex]\frac{13}{6}=2\frac{1}{6}[/tex]
[tex]1<2\frac{1}{6}[/tex]
A family is trying to pick from different shades of paint for their living room. They have narrowed it down to 10 colors: 3 different blues and 7 different greens. The family decides to just randomly select a color from these. What is the probability they will pick a shade of blue? Choose the answer in percent form. Question 3 options: 50% 100% 70% 30%
Answers
Answer:
30%
Step-by-step explanation:
A family is trying to pick from different shades of paint for their living room. They have narrowed it down to 10 colors: 3 different blues and 7 different greens. The family decides to just randomly select a color from these. What is the probability they will pick a shade of blue? Choose the answer in percent form. Question 3 options: 50% 100% 70% 30%
First, we need to convert the probability of picking a blue shade into a fraction.
= 3/10
Since this is by 10, we need to times 0.3 (numerator) by 10 (the number of outcomes) Whatever you do to the numerator, you do to the denominator. This means that you also times 10 by 10
This gives you 30/100
Since a percentage is out of 100, you don't need to change anything, just take away the 100 and put a percentage sign.
=30%
Answer: It is 30%, and i got proof right here.
Step-by-step explanation: I got AN (A) on my test so give the first person all those great rating he needs.
Susan invests $Z at the end of each year for seven years at an annual effective interest rate of 5%. The interest credited at the end of each year is reinvested at an annual effective rate of 6%. The accumulated value at the end of seven years is $X. Lori invests $Z at the end of each year for 14 years at an annual effective interest rate of 2.5%. The interest credited at the end of each year is reinvested at an annual effective rate of 3%. The accumulated value at the end of 14 years is $Y.
Required:
Calculate Y/X.
Answers
Answer:
2.02955
Step-by-step explanation:
Given that:
Susan invests $Z as each year ends for seven years.
So we assume that Z = 1
Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.
The cashflow interest:
The cashflow of Susan interest payments are:
Payments Time
0 1
0.05 2
2(0.05) 3
3(0.05) 4
4(0.05) 5
5(0.05) 6
6(0.05) 7
The accumulated value of this cash flow is:
[tex](0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653[/tex]
So Susan accumulated values is:
X = 7 + 1.1653
X = 8.1653
Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.
The cashflow of Lori interest payments are;
Payments 0 0.025 2(0.025) 3(0.025) ......... 13(0.025)
Time 1 2 3 4 .......... 14
The accumulated value of cash flow is:
[tex](0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719[/tex]
Now, Lori's accumulated value is:
Y = 14 + 2.5719
Y = 16.5719
Since; Susan value X = 8.1653
Lori's value Y = 16.5719
∴
[tex]\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}[/tex]
= 2.02955
Six eggs sat in a basket overnight. A fox
came and took an unknown amount, and
a raccoon came and took an unknown
amount. In the morning, there were only
two eggs left. Write an equation showing
how six eggs were reduced to two eggs.
Use 'f for the number the fox took and 'r
for the number the raccoon took.
Answers
Answer:
6 - F - R = 2
Step-by-step explanation:
Since six eggs sat in a basket overnight, and a fox came and took an unknown amount, and a raccoon came and took an unknown amount, with which in the morning there were only two eggs left, to write an equation showing how six eggs were reduced to two eggs the following reasoning must be raised:
6 = Starting number
F = Eggs stolen by the fox
R = Eggs stolen by the raccoon
6 - F - R = 2
If f(x) = 4x + 2, what is the value of f(3)?
O 8
O 14
O 45
O 66
Answers
Answer:
14
Step-by-step explanation:
Please help me ASAP really need help!!!
Answers
Answer:
2.7
Step-by-step explanation:
the scale factor should be consistant as you scale up and down. So you can divide 4.59 by its corresponding side of 1.7 in order to get the scale factor of 2.7. When repeated with the other sides this number should remian consitant.
in what number base is the addition 456+24+225=1050
Answers
This additition is false
the true answer is 705
Its base on my understanding:)
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For brainly user:Just please, idols ,if we are going to answer questions here on brainly, don't do the ones from the internet, then just copy and paste
Just please, idols ,if we are going to answer questions here on brainly, don't do the ones from the internet, then just copy and paste You can search on the internet but make your own sentence okay? Thank you
Evaluate :
[tex] \frac{3}{8} + \frac{2}{9} [/tex]
[tex] \frac{4}{9} + \frac{1}{2} [/tex]
Answers
The second one is 17/18
Find the length, width and perimeter of 3 possible different rectangles given the area of 12 square units, Fill out the table below. PLS HELP
Answers
Answer:
Bussy
Step-by-step explanation: