(a) Find the vertical and horizontal asymptotes. (b) Find the intervals of increase or decrease. (c) Find the local maximum and minimum values. (d) Find the intervals of concavity and the inflection points. (e) Use the information from parts (a)-(d) to sketch the graph of f. 1 1 37. f(x) = 1 + 38. f(x) 7 (x - 2)² x2 e 39. f(x) = x2 + 1 - x 20 . 40. f(x) 1- e = 42. f(x) = x - x? - Inx - 41. f(x) = e = - 43. f(x) = ln(1 – In x) 44. f(x) = ett
Answers
a) Vertical asymptotes can be found by equating the denominator to zero.
Horizontal asymptotes can be found using limits. 37. f(x) = 1 + 1/(x - 2)², we can see that the denominator of the rational expression is a perfect square that cannot be zero.
Therefore, there is no vertical asymptote. As x approaches infinity or negative infinity,
the expression approaches 1, so y = 1 is the horizontal asymptote.39.
f(x) = x² + 1 - x/20, as x approaches infinity,
the function approaches infinity.
Therefore, there is no horizontal asymptote.
The expression is in the form ax² + bx + c, with a = 1 which is positive, therefore, the function opens upwards and there is no vertical asymptote. As x approaches infinity, the function approaches infinity, so there is no horizontal asymptote.
c) The local maximum or minimum of a function can be found by using the first derivative of the function.37. f(x) = 1 + 1/(x - 2)²,
after calculating the first derivative we get that it is less than zero before x = 2 and greater than zero after x = 2, so x = 2 is the local minimum.39. f(x) = x² + 1 - x/20,
after calculating the first derivative,
we can see that it changes signs at x = 1/2, so we can say that x = 1/2 is the local maximum.
d) The concavity of a function can be found by using the second derivative of the function.
The inflection point is where the concavity of the function changes.37. f(x) = 1 + 1/(x - 2)²,
after calculating the second derivative we can see that the function is always concave up.
So, there is no inflection point.39.
f(x) = x² + 1 - x/20,
after calculating the second derivative we can see that the function changes concavity at x = 10/3,
therefore, this is the inflection point.
e) The graph of the function can be sketched using all the information we found before:
37. f(x) = 1 + 1/(x - 2)²,
there is a horizontal asymptote at y = 1.
There is a local minimum at x = 2.
There are no inflection points.39. f(x) = x² + 1 - x/20,
there is no horizontal asymptote.
There is a local maximum at x = 1/2. T
here is an inflection point at x = 10/3.
To know more about Vertical asymptotes visit:
https://brainly.com/question/32503997
#SPJ11
Related Questions
Select the real-world problem that could be solved using a proportion.
Answers
the answer is D
300/6 = x/10
once solved, it will be proportional
If R is the midpoint of QS, QR=8x-51 and RS=3x-6, find QS.
Answers
Correct answer get brainliest and 5 star
Answers
Answer:
B
Step-by-step explanation:
(Slant height)^2= (Radius)^2+(Height)^2
(20)^2= (12)^2+(Height)^2
Height=16
Answer:
B. pls mark me at brainliest and like my answer.
Step-by-step explanation:
⩥ɓeŋʝ⩤
Find the slope of the line.
Help?
Answers
Answer:
-1/2x
Step-by-step explanation:
We know point (-10, 0) and point (0,-5)
So, the slope would be -5/10 or simplified at -1/2
y= -1/2x
Answer: -1/2
Step-by-step explanation:
Use two points on the graph and plug it into the formula
y2-y1 divided by x2-x1
Events D and E are independent, with P(D)- 0.6 and P(D and E) - 0.18. Which of the following is true? A. P(E)- 0.12 B. P(E) = 0.4 C. P(D or E)-0.28 D. P(D or E) 0.72 E. P(D or E)-0.9
Answers
The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.
To determine the correct answer, let's analyze the given information.
We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.
Given:
P(D) = 0.6
P(D and E) = 0.18
Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:
P(D and E) = P(D) * P(E)
Substituting the given values:
0.18 = 0.6 * P(E)
To find the value of P(E), we can rearrange the equation:
P(E) = 0.18 / 0.6
P(E) = 0.3
Therefore, the correct answer is A. P(E) = 0.3.
Learn more about probability here: https://brainly.com/question/32117953
#SPJ11
An art teacher is pouring paint into containers that each hold 2/3 gallon. How many gallons of paint should they buy if they need to fill 8 containers?
Answers
Answer as a mixed number = 5 & 1/3 gallons
That rounds up to 6 full gallons assuming s/he cannot buy a fractional amount of a gallon.
=======================================
Explanation:
We multiply the two numbers given
8*(2/3) = 16/3
Then we can convert this to a mixed number if we wanted
16/3 = (15+1)/3 = 15/3 + 1/3 = 5 + 1/3 = 5 & 1/3
The teacher needs to buy 5 full gallons plus an additional 1/3 of a gallon of paint.
Assuming the teacher cannot buy a fractional amount of paint, s/he will need to bump that value to the nearest whole number. So the art teacher will need to buy 6 gallons of paint. He or she will have leftovers but it's better than coming up short.
If the triangle is a 60-90-30 triangle and has a hypothenuse of 16, how would I solve for the missing two sides?
Answers
Answer:
shorter leg = 8
longer leg = 8√3
Step-by-step explanation:
If the hypotenuse of the 60-90-30 triangle is 16, we can use the ratios of the sides to find the lengths of the other two sides. Here's how we can solve for the missing sides:
The length of the shorter leg (opposite the 60-degree angle) is half the length of the hypotenuse:
shorter leg = (1/2) * hypotenuse
= (1/2) * 16
= 8
The length of the longer leg (opposite the 30-degree angle) can be found using the ratio of the sides in a 30-60-90 triangle:
longer leg = shorter leg · √3
= 8√3
So, the missing side of the triangle are 8 and 8√3
If the following system has a solution, what is the
x − coordinate of the solution?
4x + 8y = 60
x + 8y = 30
a. 6
b. 10
c. 618
d. 730
e. the system has no solution
Answers
Find the circumference of the circle.
Answers
Answer:
11\(\pi\)
Step-by-step explanation:
To find the circumference of a circle, the formula is:
d * \(\pi\) = c
We already know the diameter, so we just plug that in:
11 * \(\pi\) = c
11\(\pi\) = c
Let me know if you have any questions.
Round each number to 4 significant digits a. 431,801 b. 10,235.0 c. 1.0348 d. 0.004384010 e. 0.00078100 f. 0.0098641
Answers
1) Rounding those number to 4 significant digits
a. 431,801 = 431,800
b. 10,235.0 = 10240
c. 1.0348 = 1.035
d. 0.004384010 = 0.0040
e. 0.00078100 =0.0008
f. 0.0098641 =0.009
The criteria are rounding up to those numbers greater than or equal to 5, and considering the how low is the number or how great it is.
If an experiment is a 2x2x3 fully-crossed factorial design, then which of the following are definitely true? It has 2 independent variables, 2 dependent variables, and 3 extraneous variables It has 3 dependent variables It has 3 independent variables One of the variables in the experiment has 2 levels, another has 2 levels, and the third has 3 levels The experiment has a total of 7 conditions The experiment has a total of 12 conditions
Answers
A 2x2x3 fully-crossed factorial design means that there are 3 independent variables, each with 2 levels, 2 levels, and 3 levels, respectively. Therefore, it is not true that the experiment has 2 independent variables or 3 dependent variables. It also does not have any extraneous variables because all variables are manipulated and measured.
The experiment has a total of 12 conditions, which is calculated by multiplying the levels of each independent variable together (2x2x3=12). This means that each participant in the experiment will be exposed to all 12 conditions, which can be time-consuming and may require a large sample size.
In summary, the only statement that is definitely true is that one of the variables in the experiment has 2 levels, another has 2 levels, and the third has 3 levels. The experiment has 3 independent variables, 12 conditions, and no extraneous variables.
To know more about fully-crossed factorial design visit:
https://brainly.com/question/25507319
#SPJ11
If value of a $100 stock drops 10% one year, then increases 10% the next year, what is the value of the stock after the increase?
Answers
Answer:
$99
Step-by-step explanation:
100 - (100 x .10) = 90
90 + (90 x .10) = 99
Find the perimeter of a rectangle with Area = x^2 + 8x + 12
Answers
Answer:
(x+6)*(x+2)
step-by-step explanation:
Please help (: Solve the equation.
n – 29 – 33 = –49
13
–111
–53
–13
Answers
Answer:
13
Step-by-step explanation:
Select the correct answer.
Given the following formula, solve for y.
I-
2.
2
A.
y = x – 2(w + z)
B.
y = 2w + z-
1
C.
y = 2(w + 2)
D.
y
(20 +
Answers
Answer:Objective: Solve systems of equations with three variables using addition/elimination.
Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down
to one with only one variable (by substitution or addition). With three variables
we will reduce the system down to one with two variables (usually by addition),
which we can then solve by either addition or substitution.
To reduce from three variables down to two it is very important to keep the work
organized. We will use addition with two equations to eliminate one variable.
This new equation we will call (A). Then we will use a different pair of equations
and use addition to eliminate the same variable. This second new equation we
will call (B). Once we have done this we will have two equations (A) and (B)
with the same two variables that we can solve u
Step-by-step explanation:
sorry my answer was wrong
A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. You draw the first marble, return it to the box and draw a second marble. What is P(both marbles are orange)?
Answers
Answer:
1/15
Step-by-step explanation:
1/5+3+2 all of the marbles
2/10 odds of drawing an orange marble(bc 2 orange marble)
3/9 because to get 3 green and 1 marble is removed and 9 is total marbles left
2/10*3/9=1/15 muliply odds because 2 draws of marbles
(b) Given the matrix D = k 0 0 3 k² k³ 0 kª k³ kº k k k 0 0 0 k¹⁰ Find all possible value(s) of k if det(D) = 1024."
Answers
To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.
Given matrix D:
D = | k 0 0 |
| 3 k² k³ |
| 0 kª k³ kº |
| k k k |
| 0 0 0 |
| k¹⁰ |
The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
- 0(det | 3 k² k³ |
| 0 kª k³ |
| k k k |)
+ 0(det | 3 k² k³ |
| k k k |
| k k k |)
Simplifying further, we have:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
Now, we can calculate the determinant of the 3x3 submatrix:
det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |
This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:
det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº
Now, we can set det(D) equal to 1024 and solve for k:
k⁴+kº = 1024
Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.
Learn more about matrix here
https://brainly.com/question/2456804
#SPJ11
Select the equivalent expression.
Answers
Answer:
The answer is B
Step-by-step explanation:
This is because when you distribute the -4 to 9^6 and 7^-24 you will get 9^-24 and 7^36. Then, you can move the 7^-24 to the denominator because of the negative exponent rule.
PS: ^ means to the power of
Please help will give brainliest
Answers
Answer: The answer is B.
Step-by-step explanation:
as you can see, all you need to do is divide 5 into getting 2 equal parts which is 2.23 and then the negative sign is added to that answer which is: -2.23
pleasseeee helppppppp
Answers
factor completely h^3+2h^2-9h-18
(please can someone explain to me the steps and not just the answer)
Answers
Step 1: Group this into two groups:
\(h^3 + 2h^2-9h-18=(h^3 + 2h^2)+(-9h-18)\)
When you do that, be sure to group the "–" into the group with the 9 and make sure there's "+" between the groups.
Step 2: Factor out the GCF from both individual groups:
\((h^3 + 2h^2)+(-9h-18) = h^2 (h+2) -9(h+2)\)
Step 3: Notice both groups have that (h+2)? That's a new GCF between the two groups, so factor that out:
\(h^2 (h+2) -9(h+2) = (h+2)(h^2-9)\)
Step 4: That \((h^2-9)\) piece can be factored further, since it's a difference of squares:
\((h+2)(h^2-9) = (h+2)(h+3)(h-3)\)
Now it's factored.
what is the critical value for 96 confidence interval for a sample size of 15
Answers
The critical t-value is approximately 1.753.
To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).
In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.
This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.
It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.
For such more questions on critical
https://brainly.com/question/30459381
#SPJ8
Using the information given, select the statement that can deduce the line segments to be parallel. If there are
then select none.
When m_1= m_D
O AB II DC
AD || BC
none
Answers
Answer:
it is AD l l DC so ots B
Step-by-step explanation:
Answer
If the line segment AB is parallel to the line segment DC then, m∠1=m∠D by corresponding angles.
What is corresponding angle?Congruence and similarity tests in geometry involve comparing corresponding sides and angles of polygons.
Each side and angle in one polygon is paired with a side or angle in the second polygon, with the order of adjacency preserved.
One is an exterior angle (beyond the parallel lines), while the other is an interior angle (inside the parallel lines).
Corresponding angles and transversal lines are defined. Corresponding angles are a subset of angle pairs. Angles on the opposite side of the transversal are referred to as alternate angles.
If line segment AB is parallel to line segment DC,
m∠1=m∠D, by corresponding angles
If line segment AD is parallel to line segment BC,
m∠3=m∠B, by corresponding angles
Thus, this can be concluded regarding the given scenario.
For more details regarding angles, visit:
https://brainly.com/question/28451077
#SPJ7
Thirty samples of size 4 of the customer waiting time at a call center for a health insurance company resulted in an overall mean of 10.4 minutes and average range of 0.9 minutes . Compute the control limits for x and r charts.
Answers
the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).
To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:
For the x-bar chart:
Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar
Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar
For the R chart:
Upper Control Limit (UCL) for R = D4 * R-bar
Lower Control Limit (LCL) for R = D3 * R-bar
Where:
x-double-bar = Overall mean of the sample means
R-bar = Overall mean of the sample ranges
A2 = Constant from the control chart constants table
D4 = Constant from the control chart constants table
D3 = Constant from the control chart constants table
For sample sizes of 4, the control chart constants are as follows:
A2 = 0.729
D4 = 2.281
D3 = 0
Given the information you provided:
Overall mean (x-double-bar) = 10.4 minutes
Average range (R-bar) = 0.9 minutes
Let's calculate the control limits:
For the x-bar chart:
UCL for x-bar = 10.4 + 0.729 * 0.9
= 10.4 + 0.6561
= 11.0561 minutes
LCL for x-bar = 10.4 - 0.729 * 0.9
= 10.4 - 0.6561
= 9.7439 minutes
For the R chart:
UCL for R = 2.281 * 0.9
= 2.0529 minutes
LCL for R = 0
To know more about limits visit:
brainly.com/question/12207539
#SPJ11
write a fraction to show the value of each 9 in the decimal 0.999. how is the value of the 9 on the left related to the value of the 9 on the right? how is the value of the 9 on the rigth related to the value of the 9in the middle?
Answers
The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.
How to write decimal number in fractionTo write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method
The digit 9 in the tenths place represents 9/10 or 0.9.
The digit 9 in the hundredths place represents 9/100 or 0.09.
The digit 9 in the thousandths place represents 9/1000 or 0.009.
Thus, the fractions are
0.9 = 9/10
0.09 = 9/100
0.009 = 9/1000
The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.
The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.
Learn more on fraction on https://brainly.com/question/17220365
#SPJ4
Nathan is a cat enthusiast! He currently cares for 4 different cats. He adopts 2
new cats every year. Write and graph an equation to represent how many
cats he will have after x amount of years.
Answers
y=4+2x
Explanation:
He starts with four. Every year he will gajn 2 cats. Multiply 2 by the number of years (x).
an unnormalized relation is a table that has more than one row.
Answers
An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.
Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.
In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.
To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.
In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.
To know more about unnormalized relation click this link -
brainly.com/question/30888382
#SPJ11
Fâ-statistics computed using maximum likelihoodâ estimators:
A.
can be used to test joint hypotheses.
B.
do not follow the standard F distribution.
C.
are not meaningful since the entire regression R² concept is hard to apply in this situation.
D.
cannot be used to test joint hypotheses.
Answers
A. can be used to test joint hypotheses.
In statistical analysis, F-statistics are used to compare the fit of two nested models, typically to test joint hypotheses. Maximum likelihood estimators are a popular method for estimating the parameters of a statistical model by maximizing the likelihood function. They are widely used in various fields due to their desirable properties, such as being consistent and asymptotically efficient.
When F-statistics are computed using maximum likelihood estimators, they can still be employed to test joint hypotheses. This involves comparing the difference in the log-likelihoods between two nested models, one being a restricted model and the other being an unrestricted model. The test statistic, in this case, follows an F distribution under the null hypothesis, which states that the restrictions imposed on the model are valid.
Learn more about non-linear models here: brainly.com/question/29470083
#SPJ11
Which function has a domain where x + 3 and a range where y2?
O fx)=
(x-5)
(x+3)
2(x+5)
O fx)=
(x+3)
O fx)=
2(x+5)
(x-3)
ORX)=(x-3)
(x+5)
Answers
Answer:
the second choice or B would be the answer
The function that has a domain where x ≠ 3 and a range where y ≠ 2 are:
f(x) = 2 (x + 5) / (x - 3)
f(x) = 2 (x + 5) / (x - 3)
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The domain of a function consists of all the possible values of x for which the function is defined, and the range of a function consists of all the possible values of y that the function can take.
Now,
f(x) = 2 (x + 5) / (x - 3)
The denominator x - 3 cannot be equal to zero, so x cannot be equal to 3.
Therefore,
The domain of the function is all real numbers except x = 3,
or (-∞, 3) U (3, ∞).
To find the range, we need to consider what values of y the function can take for different values of x.
As x approaches 3 from either side, the value of the function becomes increasingly large (positive infinity for x approaching 3 from the right, and negative infinity for x approaching 3 from the left).
This means that the function has a vertical asymptote at x = 3, and the range of the function is all real numbers except y = 2, or (-∞, 2) U (2, ∞).
And,
f(x) = 2 (x + 5) / (x - 3)
The only value of x that makes the denominator x - 3 equal to zero is x = 3. Therefore,
The domain of the function is all real numbers except x = 3, or
(-∞, 3) U (3, ∞).
To find the range, we again consider what values of y the function can take for different values of x.
As x approaches 3 from either side, the value of the function approaches positive or negative infinity (depending on the sign of x - 3).
This means that the function has a vertical asymptote at x = 3, and the range of the function is all real numbers except y = 2, or (-∞, 2) U (2, ∞).
Therefore,
Both functions have the same domain and range, and both satisfy the conditions of having a domain where x is not equal to 3 and a range where y is not equal to 2.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
the perimeter of a triangle is equal tot he sum of the lengths of sides a b c what is the formula
Answers
Answer:
a + b + c = P
Step-by-step explanation: