Shown above is a slope field for the differential equation dydx=y2(4−y2). If y = g(x) is the solution to the differential equation with the initial condition g(−2)=−1, then, limx→∞g(x) is
The value limx→∞g(x) is zero option (c) is correct.
What is a differential equation?The differential equation involves the function and its derivative to represent a relationship between the functions and their derivative. In simple words, the differential equation is the mathematical relation that consists of one or more functions with its derivative.
We have a differential equation:
[tex]\rm \frac{dy}{dx} =y^2(4-y^2)[/tex]
[tex]\rm\frac{dy}{y^2(4-y^2)} = dx[/tex] (rearranging the equation to solve)
[tex]\int \rm\frac{dy}{y^2(4-y^2)} = \int dx[/tex]
[tex]\rm \frac{ln(|y+2|)}{16} -\frac{1}{4y} -\frac{ln(|y-2|)}{16} = x+c[/tex] (after integrating both sides)
For the given initial condition g(-2) = -1
When x = -2, y = -1
[tex]\rm \frac{ln(|-1+2|)}{16} -\frac{1}{4(-1)} -\frac{ln(|-1-2|)}{16} = -2+c[/tex]
[tex]\rm \frac{1}{4} -\frac{ln(|-3|)}{16}+2 = c[/tex]
The value of c = 2.18
The equation we get:
[tex]\rm \frac{ln(|y+2|)}{16} -\frac{1}{4y} -\frac{ln(|y-2|)}{16} = x+2.18[/tex]
As we can see the value of g(-2) is negative and from the graph of the above equation it goes to infinity and it touches the x-axis at the infinity.
The value [tex]\displaystyle \lim_{x \to \infty}g(x)[/tex] when x reaches infinity the value of function g(x) becomes zero. ie.
[tex]\displaystyle \lim_{x \to \infty}g(x) =0[/tex]
Thus, the value [tex]\displaystyle \lim_{x \to \infty}g(x)[/tex] is zero option (c) is correct.
Learn more about the differential equation here:
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Find cot theta if 180° < theta < 270° and cos theta = - sqrt 3/2
Answer:
cot theta = -√3
Step-by-step explanation:
we are given that cos theta = - √3/2 within the range 180° < theta < 270° and
since cos theta = adj/hyp
adj = - √3
hyp = 2
Get the opposite using the pythagoras theorem
hyp^2 = opp^2 + adj^2
2² = opp² + (-√3)²
4 = opp² + 3
opp² = 4-3
opp² = 1
opp = 1
tan theta = opp/adj
tan theta = - 1/√3
Recall that cot theta = 1/tan theta
cot theta = 1/(-1/√3)
cot theta = -√3
An army of clone warriors is quadrupling every year. If the army started with only one warrior
named Clone Alpha, how many clones will there be in a decade?
A) 262,144 clones
B) 4,194,304 clones
C) 1,048,576 clones
D 10,485,760 clones
Answer:
C) 1,048,576 clones
Step-by-step explanation:
An army of clone warriors is quadrupling every year.
This means that the amount of clone warriots after t years is given by:
[tex]A(t) = A(0)4^t[/tex]
Started with only one warrior:
This means that [tex]A(0) = 1[/tex], so:
[tex]A(t) = 4^t[/tex]
How many clones will there be in a decade?
A decade is 10 years, so this is A(10).
[tex]A(10) = 4^{10} = 1,048,576[/tex]
The correct answer is given by option C.
Write 9/5 as a decimal number.
Answer:
1.8
Step-by-step explanation:
you have to divide 9 from 5 to get 1.8
Answer:
Decimal 1.8
Percentage 180%
Step-by-step explanation:
i need this fast thank you! :)
Answer:
C
Step-by-step explanation:
Hope this helps! Good Luck!
a
explanation
1/5280 = 5/x
the 1 and 5 represent the miles
5280 and x represent the total ft
so 5280 x 5 would be how to solve x because whatever you do the top you do the bottom which 1 x 5 being 5 so 5280 x 5 being 26400The mean number of points in 1977 was 1189 points with standard deviation of 397 points. With a roughly normal distribution, what percent of performances would fall between 395 and 1983 points?
Your answer
A. 100%
B. 68%
C. 95%
D.99.7%
Answer:
C. 95%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1189 points, standard deviation of 397 points.
Percentage between 395 and 1983 points?
395 = 1189 - 2*397
1983 = 1189 + 2*397
So within 2 standard deviations of the mean, which by the Empirical Rule is approximately 95%, and the answer is option C.
Find the volume of a pyramid that has a rectangular base that is 12 inches 10 inches and a vertical height of 9 inches.
Please help!? Work out the size of angle x. 42 degrees and 123 degrees?
Answer:
x° = 99°
Step-by-step explanation:
Sum of angles on a straight line is 180°.
180° - 123° = 57° (sum of angles on a straight line)Sum of angles in a triangle is 180°. Let u be the value of the unknown angle in the triangle.
57° + 42° + u° = 180°u° = 180° - 57° - 42°
u° = 81°
Sum of angles on a straight line is 180°.
x° + 81° = 180°x° = 180° - 81°
x° = 99°
what is 13 more than 3 times a number is 34 and what is the solution
Answer:
13 + 3x = 34
Variables:
x = random number
When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,465 times in a given year.
This question is not complete, the complete question is;
When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,465 times in a given year.
a) What is the expected number of diversions
b) What is the probability of at least 400 diversions
c) What is the probability of fewer than 450 diversions?
Answer:
a) expected number of diversions μ is 406.32
b) the probability of at least 400 diversions is 0.6368
c) the probability of fewer than 450 diversions is 0.9861
Step-by-step explanation:
Given the data in the question;
n = 8465
π = 4.8% = 0.048
so expected number of diversions μ = nπ = 8465 × 0.048 = 406.32
and
σ = √(π(1 - π ) = √(8465 × 0.048(1 - 0.048 ) = √( 406.32 × 0.952 )
σ = √386.81664
σ = 19.6677
b) the probability of at least 400 diversions
P(at least 400 diversion ) = P( X ≥ 400 )
= P( X ≥ 399.5 )
so
z = (X - μ) / σ
we substitute
z = (399.5 - 406.32 ) / 19.6677
z = -6.82 / 19.6677
z = -0.35
so
P(Z > -0.35 ) = 0.500 + p( -0.35 ≤ z ≤ 0 )
= 0.5000 + p( 0 ≤ z ≤ 0.35 )
= 0.5000 + 0.1368
= 0.6368
Therefore, the probability of at least 400 diversions is 0.6368
c) the probability of fewer than 450 diversions
P(fewer than 450 diversion ) = P( X ≤ 450 )
= P( X ≤ 449.5 )
so
z = (X - μ) / σ
we substitute
z = (449.5 - 406.32 ) / 19.6677
z = 43.18 / 19.6677
z = 2.20
so
P(Z ≤ 2.20 ) = 0.500 + p( 0 ≤ z ≤ 2.20 )
= 0.5000 + 0.4861
= 0.9861
Therefore, the probability of fewer than 450 diversions is 0.9861
Betsy started a business 2 years ago. She had 8 customers in the first year. She added 18
customers in the second year. Betsy's goal is that in each of the next 4 years, she will have
three times as many customers as the year before. Betsy says her calculations in the table
below show that if she meets this goal each year, she will have 312 customers 4 years from
now. Is Betsy correct? Use the drop-down menus to explain your reasoning.
I need help !
Answer:
Step-by-step explanation:
If im correct it will be no because...
18 x 3 = 54
Now you do
54 + 54 = 216
I might be right or wrong (sorry if i got it wrong)
Answer:
Betsy's Calculations in step 1 are Incorrect because she should have multiplied 18*3^4 before adding 3
Betsy's Calucations in step 2 are Incorrect because she did not find the correct value of 3^4
If Betsy reaches her goal each year, she will have 1,466 customers 4 years from now.
Step-by-step explanation:
God helped me plus i had this question on the Iready 7th grade math diagnostic
Question 30
What was the median annual earnings for all U.S. civilian workers in 2016?
O $51,980
O $49,630
O $41,778
O $46,230
if x is 6 what is x + 4
Answer:
put six on the place of x..
Step-by-step explanation:
So 6+4 =10 Answer
hope it helps
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Graph the polygon and its image after a reflection in the line x=4.
you are going to have to zoom in
Is 4/5 closer to 0,1/2, or 1?
Answer:
1
Step-by-step explanation:
4/5 is closer to 1
The critic rating and audience score for 8 movies are shown in the table.
Critic Rating 72 80 65 23 28 60 41 35
Audience Score 64 92 90 48 55 70 44 80
An owner of a movie theater is investigating whether critic rating can be used to predict the mean audience score of movies. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in audience score for each 1 point increase in the critic rating?
A. A one-sample t-test for means
B. A linear regression t-interval for slope
C. A two-sample t-interval for a difference between means
D. A matched-pairs t-interval for a mean difference
E. A two-sample Z-interval for a difference between proportions
Answer:
B. A linear regression t-interval for slope
Step-by-step explanation:
Given the data for the critic rating and audience score, the relationship between this vmaues acb be modeled using regression, the slope value helps give the average change in the dependent variable (audience svi per unit change in the value of the independent variable (critic rating). The t distribution is employed due to the relatively small sample size which
does not form an approximately normal distribution according to the Central limit theorem.
b→ = ⟨−1,3⟩ and c→ = ⟨−11,−2⟩.
What is c→ + b→ in component form?
Enter your answer by filling in the blanks.
c→+b→ = ⟨ __ , __ ⟩
Answer:
-12,1
(-12î, 1j)
is the ans
Answer:
The answer is, (-12î, 1j)
Step-by-step explanation:
Definition of component form:The ordered pair that describes the changes in the x- and y-values is the component form of a vector. the ordered pair that describes the changes is [tex](x_{2} -x_{1} ,y_{2} -y_{1} )[/tex].
According, to the question:
= (-11-1),(-2+3)
= -12,1
= (-12î, 1j)
The component form are (-12î, 1j)
To know more component form here, https://brainly.com/question/13450744
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8. The difference between two numbers is 33 and the ratio
between them is 5:2. Find the numbers
Answer:
Step-by-step explanation:
x - y = 33
x/y = 5/2 Multiply both sides by y
y*x/y =5y/2
x = 5y/2 Multiply both sides by 2
2x = 5y Multiply the top equation by 2. Bring 5y to the left
2x - 2y = 66
====================
2x - 5y = 0
2x - 2y = 66 Subtract
-3y = - 66 Divide by - 3
y = 22
x - y = 33
x - 22 = 33 Add 22 to both sides
x = 22 + 33
x = 55
The Nutty Professor sells cashews for $7.10 per pound and Brazil nuts for $4.60 per pound. How much of each type should be used to make a 32 pound mixture that sells for $6.24 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
Answer:
Pounds for cashew- 20.96
Pounds for Brazilian nut- 11.04
Step-by-step explanation:
Let c be the pounds of cashew
Let b ne the pound of Brazilian but
32×6.24
= 199.68
7.1c + 4.60b= 199.68.......equation 1
c + b= 32..........equation 2
From equation 2
c= 32-b
Sub 32-b for c in equation 1
7.1(32-b) + 4.60b= 199.68
227.3-7.1b+4.60b, = 199.68
227.3-2.5b= 199.68
-2.5b= 199.69-227.3
- 2.5b= -27.61
b= 27.61/2.5
b= 11.04
Sub 11.04 for b in equation 2
c+b= 32
c + 11.04= 32
c= 32-11.04
c= 20.96
Plsss help mark brain list
Answer:
105
Step-by-step explanation:
42 * 2 = 84
360 - ( 84+171 ) = 105
Answer:
arc RS = 105°
Step-by-step explanation:
arc RT = 2(42°) = 84°
arc RS = 360° - 84° - 171° = 105°
Please help, I'll mark the correct answer as brainiest!!!
Answer:
$1612
Step-by-step explanation:
12% of 2400
12/100 * 2400
0.12 * 2400 = 288
Amount to be paid :
2400 - 288 = 2112
Down payment = $500
Amount owed =
Amount to be paid - Down payment
$2112 - $500
= $1612
Hence, amount owed for installment loan = $1612
40 pts please help (:
Find the geometric probability of throwing a dart and hitting the yellow ring. You may assume the dart will not miss the target entirely.
Answer:
c
Step-by-step explanation:
Answer:
i think it d
Step-by-step explanation:
sorry if it turn out wrong
Suppose the point (3,-1) is changed to (3,0) on this rectangle. Change a second point
so the figure remains a rectangle. What is the area of the new rectangle?
Answer:
10 units I believe......
Answer:
The area is 10 sq. units
Step-by-step explanation: (-2, 1) would change to (-2, 0). So the width changes to 2 and the length becomes 5, making the area 10 sq. units
help please Im bout to fail.....
Answer:
it's the second to last one on the right side
Answer: (Not if I'm involved!)
Move the dot to the fourth tick mark to the right of zero.
Step-by-step explanation:
Each of the tick marks represent two, & 8 is the fourth positive multiple of 2. So move the dot to the fourth tick mark to the right of zero, which will represent 8.
Find the area of this circle.
6 in.
Use 3.14 for
A side of 6 feet, and a 120° angle
A. One
B. None. C. Many
Answer:
C. Many ang sagot............
6 - 7x
a) constant binomial
b) linear binomial
c) quadratic binomial
d) cubic trinomial
Answer:linear binomial
Step-by-step explanation:
Answer:
B) Linear binomial.
Step-by-step explanation:
????
Allison used 2 cups of flour to make a
cake, and of a cup of flour to make
a pie. If she started with 4 cups of
flour, how many cups of flour does she
have left?
Answer:
wouldnt she have 1
Step-by-step explanation:
well there might be a typo with and of a cup of flour but ya
I think it would be one
It's free!
Enjoy! :)
A triangular pyramid is 30 meters tall and has a base area of 500 square meters. What is the volume of the pyramid?
A) 7,500
B) 5,000
C) 15,000
D) 6,200
Answer:
C
Step-by-step explanation:
if it has a base area that means 500/4 = 125 so each side is 125 on the base.
The formula for the volume of a triangular pyramid is 1/3lwh.
if L=125 and w=125 and H= 30
we multiply 125·125·30=468750
and 468750/3=156250
so rounding that, our base would be C)15,000