Find the points of inflection of the curve y = (1 + x)/(1 + x2).
Answers
The points of inflection of the curve can be found by determining the values of "x" where the concavity of the curve changes. The points of inflection of the curve are located at x = √(1/2) and x = -√(1/2).
To find the points of inflection, we need to consider the second derivative of the function y = (1 + x)/(1 + \(x^2\)) and identify the values of "x" where the concavity changes.
Let's start by finding the first and second derivatives of y with respect to x:
First derivative:
dy/dx = [(1 + x)(d/dx)(1 + \(x^2\)) - (1 + \(x^2\))(d/dx)(1 + x)] / \((1 + x^2)^2\)
= (1 + x)(2x) - (1 + \(x^2\))(1) / \((1 + x^2)^2\)
= (2x + 2\(x^2\) - 1 - \(x^2\)) / \((1 + x^2)^2\)
= (\(x^2\) + 2x - 1) / \((1 + x^2)^2\)
Second derivative:
\(d^2\)y/d\(x^2\) = [(1 + \(x^2\))(d/dx)(\(x^2\) + 2x - 1) - (\(x^2\) + 2x - 1)(d/dx)(1 + \(x^2\))] /\((1 + x^2)^4\)
=\((1 + x^2)(2x + 2) - (x^2 + 2x - 1)(2x) / (1 + x^2)^4\)
=\((2x + 2x^3 + 2 + 2x^2 - 2x^3 - 4x^2 + 2x) / (1 + x^2)^4\)
= \((4x^2 + 2) / (1 + x^2)^3\)
To find the points of inflection, we need to solve the equation\(d^2y/dx^2\)= 0. Setting \((4x^2 + 2) / (1 + x^2)^3\)= 0, we find that 4\(x^2\) + 2 = 0. Solving this quadratic equation, we get x = ±√(2/4) = ±√(1/2).
Therefore, the points of inflection of the curve y = (1 + x)/(1 +\(x^2\)) are located at x = √(1/2) and x = -√(1/2).
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Related Questions
PLEASE HELP DUE SOON 25 POINTS
Answers
Answer:
135.
A. 5
B. 7
C. 2
D. 15
E. 24
F. 2
143: 15
144: ( A even/odd number)
Explanation:
Did it in a rush cause i gotta do mines. if wrong, I'll try better next time.
Answer:
Five years ago, cheryl was d years old
a. cheryl is (d+5) years old
b. Brandon is two years older than Cheryl
so bradon = (d+5+2) = d+7 years old
c. sum of their ages now = d+5+d+7 = 2d+12
d. sum of their ages two years from now
= (d+5+2) + (d+7+2) = 2d+16
143.
Age of sarah = 5 years
clayton age = 5+x
according to questiom
5+x= 3*5
5+x = 15
x= 15 -5 = 10 years
144.
age of Adam = d years
age of Brandon = (d+b)
accordind to question
d+b = 2d
2d-d = b
d = b years
solve the system of equations using the substitution method. state the solution as an ordered pair, (x,y). x+y=2 y=5x-4
Answers
Answer:
(1, 1)
Step-by-step explanation:
x+y=2
y=5x-4
x + 5x - 4 = 2
6x - 4 = 2
6x = 6
x = 1
x + y = 2
1 + y = 2
y = 1
(1, 1)
Round your answers to the nearest integer.) (a) 20 to 40 (b) 15 to 45 (c) % (d) 18 to 42 (e) 13 to 47 %
Answers
(a) When rounding 20 to the nearest integer in the range of 40, the result is 20.
(b) When rounding 15 to the nearest integer in the range of 45, the result is 20.
(c) The symbol "%" does not provide any specific value or context for rounding, so it is not possible to determine the rounded value.
(d) When rounding 18 to the nearest integer in the range of 42, the result is 20.
(e) When rounding 13 to the nearest integer in the range of 47, the result is 10.
(a) To round 20 to 40 to the nearest integer, we look at the digit in the tens place, which is 0. Since it is less than 5, we keep the tens digit as it is, resulting in 20.
(b) To round 15 to 45 to the nearest integer, again, we examine the digit in the tens place, which is 5. When the digit in the ones place is 5 or greater, we round up the tens digit. Thus, the rounded value is 20.
(c) The given statement "%" does not provide any specific value or context for rounding, so it is not possible to determine the rounded value.
(d) Rounding 18 to 42 to the nearest integer, we consider the tens digit, which is 2. Since it is less than 5, we keep the tens digit as it is, resulting in 20.
(e) Rounding 13 to 47 to the nearest integer, the tens digit is 4. Since the digit in the ones place is 5 or greater, we round up the tens digit. Hence, the rounded value is 50.
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Someone pls tell me the answer to this5(6.2+z);z=3.8
Answers
Answer:
30.2 is the answer (use distrubutyion in this problem)
Step-by-step explanation:
someone help answer the bottom 4 pls I'll brainlist u !!
Answers
Which of the following is the equation in slope-intercept form for the line that passes through points (- 4, 1) and \ -3,0\; y = - x + 5; y = - x - 3; y = x + 2 None of these choices are correct
Answers
Answer:
there y= -x - 3 is correct
Step-by-step explanation:
(-4,1) ; (-3,0)
y= -x - 3
with (-4,1)
1 = -(-4) - 3 = 4 - 3 = 1. left = right
with (-3,0)
0 = -(-3) - 3 = 3 - 3 = 0. left = right
so the line y = -x - 3 is passes through points (-4,1) and (-3,0)
A vase contains 60 marbles, all of which are red or orange. if the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?
Answers
The total number of red marbles in the vase are 10.
What is the ratio?A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.
Now, according to the question;
Let 'x' be the red marbles in the vase.
Let 'y' be the orange marbles in the vase.
The total number of marbles in the vase are 60
x + y = 60 (equation 1)
The ratio of red marbles to orange ones is 1:5.
Thus, x/y = 1/5
cross multiplying;
5x = y
or y = 5x
substitute the value of y in equation 1;
x + y = 60 (equation 1)
x + 5x = 60
6x = 60
x = 10 (red marbles)
Thus, the number of red marbles in the vase are 10.
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Activity: Find three different single digit numbers that
multiply together to give 120.
Answers
Answer:
Step-by-step explanation:
5,4,6
5×4=20 and 20×6=120
I NEED HELP PLEASE!!!
Answers
Step-by-step explanation:
Slope , m , betwen the two points
(y1-y2) / (x1-x2) = (-2 -2) /(5-7) = -4/-2 = 2
SO y = mx + b form would be
y = 2x + b
sub in one of the points to calculate 'b'
-2 = 2(5) + b shows b = -12
so equation is y = 2x -12
Identifying Products Resulting in a Sum or Difference of
Cubes
Sum of cubes:
(a + b)(a²-ab + b²) = a³ + b³
Difference of cubes:
(a-b)(a² + ab + b²)=a³-b³
4) Intro
Which products result in a sum or difference of cubes?
Check all that apply.
(x-4)(x2+4x-16)
□ (x-1)(x²-x+1)
(x-1)(²+x+1)
(x+1)2+x-1)
(x+4)(x²-4x+16)
□ (x+4)(x2 + 4x + 16)
Answers
The products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
What is sum or difference of cubes?
The term "sum of cubes" refers to a polynomial with the formula a^3 + b^3. The term "difference of cubes" refers to a polynomial with the form
a^3 - b^3.
The formulas for sum of cubes and difference of cubes are given:
Sum of cubes: (a + b)(a²-ab + b²) = a³ + b³
Difference of cubes: (a-b)(a² + ab + b²)=a³-b³
We have to check which products result in a sum or difference of cubes.
Consider,
(1) (x - 4)(x^2 + 4x - 16)
(x - 4)(x^2 + 4x - 16) = x^3 - 8x^2 + 32x - 64
It is not a sum or difference of cubes.
(2) (x-1)(x²-x+1)
(x - 1)(x² - x + 1) = x^3 - 2x^2 + 2x - 1
It is not a sum or difference of cubes.
(3) (x - 1)(x² + x + 1)
(x - 1)(x² + x + 1) = x^3 - 1
This is the difference of cubes.
(4) (x + 1)(x^2 + x - 1)
(x + 1)(x^2 + x - 1) = x^3 + 2x^2 - 1
It is not a sum or difference of cubes.
(5) (x + 4)(x² - 4x + 16)
(x + 4)(x² - 4x + 16) = x^3 + 64
This is the sum of cubes.
(6) (x + 4)(x^2 + 4x + 16)
(x + 4)(x^2 + 4x + 16) = x^3 + 8x^2 + 32x + 64
It is not a sum or difference of cubes.
Hence, the products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
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Use the graph to find the solution.
Given the graph of w(x), w(2) = ?
(the graph is below)
THE FIRST ANSWER WILL GET BRAINLIEST OR 5 STARS! PLEASE ANSWER QUICK :)
Answers
Answer:
W(2) = 5
Step-by-step explanation:
Because when you look at the graph, the y value is 5 when the x value is 2.
Answer:
w(2) = 5
Step-by-step explanation:
by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept
to calculate w(2):
w(2) = 4(2) - 3
w(2) = 8 - 3
w(2) = 5
or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)
what is the slope of a line parallel to the function graphed
Answers
Answer
To find the slope of a line parallel
1. Calculate the line slope
The slope m = ( y2 - y1 ) / ( x2 - x1 )
You can select two different point
For example,
(x1 , y1 ) = (-4, 0)
(x2, y2 ) = (0, 6)
_______________________________
So then, the slope,
m = ( y2 - y1 ) / ( x2 - x1 )
Replacing with the two points chosen
m = ( 6 - 0) / ( 0 - (-4) )
m=6/4
m= 3/2
___________
The parallel lines have the same slope.
_____________
The slope of a line parallel to the given line is 3/2
What are the steps to solve 2x^2+5x-12=0
Answers
In order to solve a quadratic equation, the first step is identifying the parameters a, b and c of the standard form:
\(\begin{gathered} ax^2+bx+c=0\\ \\ 2x^2+5x-12=0\\ \\ a=2,\text{ }b=5,\text{ }c=-12 \end{gathered}\)Now, the next step is using the quadratic formula to find the values of x:
\(\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-5\pm\sqrt{5^2-4\cdot2\cdot(-12)}}{2\cdot2}\\ \\ x=\frac{-5\pm11}{4}\\ \\ x_1=\frac{-5+11}{4}=\frac{6}{4}=1.5\\ \\ x_2=\frac{-5-11}{4}=\frac{-16}{4}=-4 \end{gathered}\)Therefore the solutions are x = 1.5 and x = -4.
In a mixed school, the number of girls is 375. if the boys to girls is 4:5.how many boys are in the school
Answers
Answer:
300
Step-by-step explanation:
375 divided by 5=75
Each “1”=75
4x75=300
There are 300 boys.
Hope this makes sense
Answer:
300 boys
Step-by-step explanation:
Let the number of boys = x
Girls: 375
boys : girls = 4 : 5
total in the ratio is 9
girls are 5/9 of total, and are 375
boys are 4/9 of total
5/9 x = 375
x = 375 × 9/5
x = 675
Boys are 4/9 of total.
4/9 × 675 = 300
PLEASE HELP ME
6 x 6 x ? = 261
Answers
Answer:
7.25
Step-by-step explanation:
Simplify
36x = 261
Divide both sides by 36
x = 261/36
Simplify
x = 7.25
Hope this helps!
Answer:
7.25 or 7\(\frac{1\\}{4}\)
Step-by-step explanation:
261 ÷ 6 ÷ 6 = 7.25
Severe hand or wrist pain due to an inflammation of the tendons in a user's hand and wrist is called ____.
Answers
Severe hand or wrist pain due to inflammation of the tendons is commonly referred to as tendinitis.
Tendinitis is a condition characterized by inflammation or irritation of the tendons, which are the fibrous tissues that connect muscles to bones. It commonly occurs in the hand and wrist area, leading to pain, swelling, and discomfort. Tendinitis can be caused by repetitive motions, overuse of the hand or wrist, injury, or certain medical conditions.
The inflammation of the tendons can result in severe pain in the affected hand or wrist, making it difficult to perform everyday activities that involve gripping or moving the hand. The pain may worsen with movement or after prolonged use of the hand. Rest, ice, immobilization, and anti-inflammatory medications are often recommended for managing tendinitis symptoms.
It is important to note that while tendinitis is a common cause of hand and wrist pain, there could be other underlying conditions or injuries that may require further evaluation and medical intervention. Consulting a healthcare professional for an accurate diagnosis and appropriate treatment is recommended for individuals experiencing severe hand or wrist pain.
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A farmer has only goats and hens in his farm,on a particular day,he sold 12 animals (goats and hens) and the total number of their legs was 32. how many goats and how many hens did he sell that day?
Answers
The number of goats sold is 4 and hens sold is 8.
What is an Equation ?An equation is a mathematical statement which equates two algebraic expression with an equal sign.
Let the total number of goats sold be g
Let the total number of hens sold is h
g + h = 12
The total no. of legs of a goats sold will be 4g
and the total number of legs of a hens sold will be 2h
and it is given that
4g +2h = 32
The system of equation formed is
g + h = 12
4g +2h = 32
Multiplying equation (1) by 2 and then (1) - (2)
-2g = -8
g = 4
Therefore the number of goats sold is 4 and hens sold is 8.
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QUESTION FOR FOR LIH04
Answers
92, 63, 22, 80, 63, 71, 44, 35
Mean:? Median:? Mode:? Range:?
Answers
Answer:
92
−
22
=
70
.
70
Step-by-step explanation:
subtract and add
The mean is 58.75 . The median is 63. The mode is also 63 . And the range is 70
when testing the observed value of the z-score was found to be −2.15. then, the p-value for this test would be a. .0316 b. .9842 c. .0158 d. .9684
Answers
When the observed z-score is -2.15, we can find the p-value by looking up the value in a standard normal (z) table or using a calculator or software that provides p-values.
Step 1: Identify the z-score
The given z-score is -2.15.
Step 2: Find the p-value
To find the p-value, look up the z-score in a standard normal table or use a calculator. In this case, the p-value is approximately 0.0158.
So, the correct answer is:
c. 0.0158
This p-value represents the probability of observing a value as extreme or more extreme than the observed z-score in the standard normal distribution, assuming the null hypothesis is true.
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How do I find x in this problem?
Answers
Answer:
125
Step-by-step explanation:
Since its a hexagon the interior angles equal to 720 degrees.
Because (n-2)180 equals the number of sides. So, (6-2)180 = 720.
Now for x,
120 + 130 + 100 + x + 135 + 110 = 720
595 + x = 720
x = 125
PLS HURRY WILL GIVE BRANLIEST AS USUAL
A row of desks in a classroom has 6 seats. How many seats are in 5 rows?
A= ___
Answers
Answer:
30
Step-by-step explanation:
write the equation of the line that passes through the given points. (0,-1) and (-11,-4)
Answers
Answer:
Line equation
y=0.2727272727272727x−1 Slope 0.27 Intercept -1
Step-by-step explanation:
5
Drag the tiles to the correct boxes.
Put the equations in order from least to greatest number of solutions.
Answers
In order from least to greatest number of solutions, the equations are 1/2|x|+3=3, 3-|x+4|=10, and |x-8|-4=-1.
What is an equation?The expressions are usually separated by an equal sign (=). Equations are used to solve problems and to describe relationships between different variables.
The first equation, 3-|x+4|=10, has two solutions.
We can do this by subtracting 3 from both sides: |x+4|=7.
Now, the absolute value expression can be split into two equations: x+4=7 and x+4=-7.
Solving each equation results in x=3 and x=-11.
The second equation, |x-8|-4=-1, also has two solutions.
We can do this by adding 4 to both sides: |x-8|=3.
Now, the absolute value expression can be split into two equations: x-8=3 and x-8=-3.
Solving each equation, we get x=11 and x=5.
The third equation, 1/2|x|+3=3, has one solution.
We can do this by subtracting 3 from both sides: 1/2|x|=0.
Now, the absolute value expression can be split into two equations: x=0 and x=-0.
Since -0 is the same as 0, this equation has only one solution: x=0.
1/2|x|+3=3, 3-|x+4|=10 or |x-8|-4=-1 is the correct order.
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Example 1: Marcus buys a varsity jacket from a clothing store in Arlington. The price of the jacket is $80 and the sales tax is 8%. What is the total cost of the jacket?
Answers
Answer:
$86.40
80 + 8%= 86.40
Answer:
$86.40..
Step-by-step explanation:
80 + 8%= 86.40
What do you get when you divide the circumference of your jack-o-lantern by its diameter?.
Answers
On dividing the circumference and the diameter of our Jack-o-Lantern we will get π.
A Jack-o-Lantern can be considered spherical in shape.
The circumference of a #D shape is the intersection of the 3D shape with any plane passing through its center.
Hence the circumference of a jack-o-lantern will be the perimeter of the circle that has been cut through its center.
Let the radius of our Jack-o-lantern be r cm.
The formula of a circumference of a sphere is 2πr
where r is the radius of the sphere.
The diameter of a sphere is twice its radius.
Therefore, the diameter of our jack-o-lantern will be
2r cm.
By dividing the circumference and the diameter we get
2πr cm / 2r cm
= π
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Is x=4 a solution to the equation 9x = 32 + x?
Answers
Answer:
yes
Step-by-step explanation:
because 9*4=36 and well it's 36=32*? so 36-32 is 4
So well the solution is x=4
Answer:
Yes, it is.
Explanation:
For x = 4 to be a solution of the given eqⁿ, it must satisfy it. That is,
9x = 32 + x => 8x - 32 = 0
=> f(x) = 8x - 32
At x = 4,
f(4) = 8(4) - 32 = 32 - 32 = 0
Since, f(4) = 0, thus, x = 4 is a solution to the given eqⁿ.
find the probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea.
Answers
The probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea is 0.1317, or 13.17%
The number of subjects experiencing nausea follows a binomial distribution with parameters n=250 (number of trials) and p=0.1 (probability of success, i.e., experiencing nausea). The probability of exactly k subjects experiencing nausea is given by the probability mass function:
P(X=k) = (n choose k) * \(p^k\) * \((1-p)^{(n-k)\)where (n choose k) is the binomial coefficient "n choose k", which represents the number of ways to select k subjects out of n.
Using this formula with n=250, p=0.1, and k=10, we get:
P(X=10) = (250 choose 10) * (0.1)^10 * \((0.9)^{240\)This gives a probability of approximately 0.1317, or 13.17%.
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please help
khan academy videos are confusing and dont help at all
Answers
Answer:
12
Step-by-step explanation:
y = 2x + 0
6x + 4y = 3xy
y = 4 - x2
7xy = 12
Notes:
It's okay and completely understandable you might not be able to understand Khan Academy much. We all have our own struggles. I highly recommend using Brainly more. It's a much bigger community, with millions of other users always online to help. Oh - and don't forget about the moderators! I heard they're always on the look out and super hungry for question answering!
A Brainliest or Thank You is always appreciated! Please make sure to rate this answer and Heart it so we can easily help grab more attention for any other users who might also need help.
Cheers,
Chris.
answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
Answers
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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