Let f be a continuous function and let c be in the domain of f. Suppose that f"(x) > 0 when x < c and that f"(x) < 0 when x > c. Then c is [Select] Chossen : - point of inflection - critical point - concavity point - convexity point - concaver upper-downer
Answers
The point where the concavity of the function changes is called the point of inflection.
What is a point of inflection?Given that,Let f be a continuous function and let c be in the domain of f.Suppose that f"(x) > 0 when x < c and that f"(x) < 0 when x > c.Then c is a point of inflection.
Hence, the correct answer is point of inflection.
The point where the concavity of the function changes is called the point of inflection. A continuous function has an inflection point where its concavity changes, and the tangent at that point is still continuous.
A point of inflection may occur as a result of a change in concavity, or it may occur as a result of a change in concavity from a down-facing parabola to an up-facing parabola or vice versa.
The basic theorem for the second derivative test of the stationary point is as follows:If f ''(c) > 0, then f has a relative minimum at c.
If f ''(c) < 0, then f has a relative maximum at c. If f ''(c) = 0, then the test fails and we must use another approach.
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Related Questions
Evaluate each function: 1. p(a) = 3a-2; find p(-5) 2. h(t) = 4t+2; find h(-4) 3. f(a) = 3a-4; find f(1) 4. g(x) = 3x+ 1; find g(-9) 5. k(x) = x-1; find k(5) 6. f(x) = x+1; find f(7) 7. h(t) = 4t+2; find h(-8) 8. g(x) = 2x=1; find g(2) 9. w(a) = a+4; find w(9) 10. g(n) = 4n+2; find g(-9)
Answers
There are three landmarks, P, O and R. It is known that R is 8.7 km from P and 9.3 km from Q, and that decimal place.
Answers
Landmark R is located 8.7 km from landmark P and 9.3 km from landmark Q, with distances given to one decimal place.
We have three landmarks: P, O, and R. The given information states that R is located 8.7 km from P and 9.3 km from Q, with the distances provided to one decimal place.
From this information, we can conclude that R is positioned between P and Q, closer to Q since the distance from R to Q is smaller than the distance from R to P.
However, the exact positions of P, O, and Q are not known, as their coordinates or angles of separation are not provided. Without additional information or a specific coordinate system, it is not possible to determine the precise locations of P, O, and Q or to visualize their spatial arrangement.
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Complete Question:
Rithish went from place P to place Q and from there to place R. P is 8.7 km
from Q and Q is 13.8 km from R. Mithun went from place P to place S and from
there to place R. P is 7.9 km from S and S is 14.1 km from place R. Who travelled
more distance and by how much?
in the equation Y = 8x+ 5 the name for y are
Answers
Answer:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Step-by-step explanation:
Slope intercept of (-2,2) (0,-2)
Answers
Answer:
-4/2
Step-by-step explanation:
HELP ASAP
A picture is 7 inches wide and 9 inches long. A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long. What scale factor was used to enlarge the picture?
9/7
7/9
31.5/7
7/31.5
Answers
By simply taking the width after it was enlarged and dividing it by the width before it was enlarged we can find the scale factor that was used. In this case it would be 31.5 (width after)/ 7 (width before) which gives us a scale factor of 31.5/7. Simplifying would yield a scale factor of 4.5 times.
The Scale factor was used to enlarge the picture is 7/ 31.5.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
A picture is 7 inches wide and 9 inches long.
A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.
So, scale factor is
= Original dimension / Enlarged dimension
= 9/ 40.5
= 90/ 405
= 10/45
= 2/9
Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.
= 7/ 3.15
= 70/31.5
= 2/9
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Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
The sides of a triangle are 4,8, and 10. If the longest side of a similar triangle measures 30, find the shortest side.
Answers
Answer:
12?
Step-by-step explanation:
PLEASE CAN I HAVE HELP
Answers
Answer:
1.28
is the answer :) since the number after 7 is 5 you round up
Answer: 1.28
The 7 is in the hundredth's place, and since there is a 5 after it, we round up.
Jay and Kevin are shoveling the snow off a driveway. Working together, they can clear the driveway of snow in 14 minutes. Working alone, itwould take Kevin 21 minutes longer to clear the driveway of snow than it would take Jay working alone. When j is the number of minutes it wouldtake Jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation:How long would it take jay to clear the driveway of snow working alone?
Answers
The Solution:
The correct answer is j = 21 [option B]
Given:
\(\frac{1}{j}+\frac{1}{j+21}=\frac{1}{14}\)We are required to solve for j.
\(\begin{gathered} \frac{1}{j}+\frac{1}{j+21}=\frac{1}{14} \\ \\ \frac{j+21+j}{j(j+21)}=\frac{1}{14} \end{gathered}\)\(\frac{2j+21}{j(j+21)}=\frac{1}{14}\)Cross multiply:
\(\begin{gathered} j(j+21)=14(2j+21) \\ j^2+21j=28j+294 \\ j^2+21j-28j-294=0 \end{gathered}\)\(undefined\)Answer:
see photo #12
Step-by-step explanation:
plz help i give brainlist !!!!!!!!!1 help now please
Answers
Answer:
option 3
Step-by-step explanation:
What is the GCF of 36x^2y and 18xy ^2?
Please i really need the answers
Answers
You accept a job that pays out $15,000 your first year. You are given the option of either earning an additional $500 each year you work or 2% of your current salary. Your plan is to stay with this job for 4 years. Which option do you choose and how much will you make? 2% or $500? $
Answers
To compare the two options, we need to calculate the total earnings for each option over the 4-year period.
Option 1: Earning an additional $500 each year
The total earnings for this option will be:
Year 1: $15,000
Year 2: $15,500 ($15,000 + $500)
Year 3: $16,000 ($15,500 + $500)
Year 4: $16,500 ($16,000 + $500)
Total earnings over 4 years = $15,000 + $15,500 + $16,000 + $16,500 = $63,000
Option 2: Earning 2% of current salary
To calculate the earnings for this option, we need to find the salary for each year using the formula:
salary = $15,000 + 2% × (previous year's salary)
Year 1: salary = $15,000
Year 2: salary = $15,300 ($15,000 + 2% × $15,000)
Year 3: salary = $15,606 ($15,300 + 2% × $15,300)
Year 4: salary = $15,924.12 ($15,606 + 2% × $15,606)
Total earnings over 4 years = $15,000 + $15,300 + $15,606 + $15,924.12 = $61,830.12
Therefore, the first option of earning an additional $500 each year results in higher total earnings of $63,000 over 4 years, compared to earning 2% of the current salary, which results in total earnings of $61,830.12. Hence, the first option of earning an additional $500 each year is the better choice.
what is the term for the value that occurs most often in a series of numbers?
Answers
The term for the value that occurs most often in a series of numbers is called the mode.
The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.
To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.
The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.
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polynomials math question
Answers
Answer:
C. Trinomial
Step-by-step explanation:
It has three, -9x^2, 8x, & 5.
can you give me an answer i don't know how to do this
Answers
Answer:
It should be ≈ 6,6
calculated the angle <CAB and both are 90°. But that would mean BC is wrong
HELP ASAP!!! HELP FAST PLEEASE!!!
Answers
Answer:
3yz^3 + 1
Step-by-step explanation:
t(5x^3yz^2) = 15x^3y^2z^5 + 5x^3yz^2
t = [5x^3yz^2(3yz^3 + 1)]/5x^3yz^2
t = 3yz^3 + 1
what's the pattern of 4 , 10 , 20 , 34 , 52 , 74 , 100
hurry plzzzz
Answers
Answer:
The pattern is 6,10,14,18,22,26
If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q→p?
O the original conditional statement
O the inverse of the original conditional statement
O the converse of the original conditional statement
O the contrapositive of the original conditional statement
Answers
Answer:
(c) the converse of the original conditional statement
Step-by-step explanation:
If a conditional statement is described by p→q, you want to know what is represented by q→p.
Conditional variationsFor the conditional p→q, the variations are ...
converse: q→pinverse: p'→q'contrapositive: q'→p'As you can see from this list, ...
the converse of the original conditional statement is represented by q→p, matching choice C.
__
Additional comment
If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.
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Hareem takes a medicine to control his blood pressure. he takes a 25 mg pill in the morning. suppose that 60% of the medicine is processed by hareem's body by the time he takes a second 25 mg pill in the evening. what is the recursive definition for the amount of the blood pressure medicine in hareem bloodstream after n hours?
a. a1=25, an= 0.40an-1 + 25
b. a1=25, an = 0.60n-1 +25
c. a1=40, an=0.60n-1 +25
d. a1 = 0.60, an = 0.40an-1
Answers
The recursive definition for the amount of the blood pressure medicine in Hareem's bloodstream after n hours can be defined as :
a. a1=25, an= 0.40an-1 + 25
Base Case:
The initial amount of medicine in Hareem's bloodstream after 0 hours is 25 mg.
Recursive Step:
The amount of medicine in Hareem's bloodstream after n hours can be calculated by taking 60% of the amount of medicine in his bloodstream after (n-1) hours, and then adding 25 mg.
To write this recursive definition in mathematical notation:
M(n) = 25 mg, if n = 1
M(n) = 40 mg, if n = 6
M(n) = M(n-1) + (60% * M(n-1)), if n > 6
This recursive definition represents the amount of the blood pressure medicine in Hareem's bloodstream after n hours. The base case sets the initial amount of medicine, and the recursive step calculates the amount of medicine at each hour by taking 60% of the previous amount and adding 25 mg.
The correct option is a. a1=25, an= 0.40an-1 + 25
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assume you purchased 500 shares of xyz common stock on margin at $40 per share from your broker. if the initial margin is 60%, the amount you borrowed from the broker is _________.
Answers
Common stock on margin amount borrowed from the broker=8000
In the world of finance, the common stock margin is the security that a trader or exchange requires an investor to place with them in order to cover the credit risk the investor's position entails for them. If an investor borrows money from their broker to purchase financial instruments, borrows money to sell those same instruments for a loss, or enters into a derivative contract, credit risk is created. An investor who purchases an asset on margin does so by taking out a broker loan for the remaining amount. When an investor purchases an asset on margin, they make a smaller initial payment to the broker and put up collateral in the form of marginable assets in their brokerage account.The margin, in a broad commercial context, is the distinction between the selling price of a good or service and the
amount borrowed from the broker = 500 x 40 x (1- 0.6)
amount borrowed from the broker=8000
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Use the given diagram for questions 8-10.
Jerry is designing a boardwalk. His blueprints are shown.
8. What shapes can be used to find the area of the shaded region?
9. Divide the shaded area into smaller shapes on the graph.
10. What is the area of the shaded region?
Answers
Using the trapezium area formula, we can see that the expression you supplied may be reduced to 97 cm².
What is area?Area is a mathematical term that refers to the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters, square feet, or square inches, depending on the system of measurement used. The area of a shape is determined by multiplying its length and width, or by using a specific formula depending on the shape of the object. Knowing the area of an object can be useful in many fields, including architecture, engineering, and mathematics.
Here,
a. The shapes that are present in the diagram are: rectangle and trapezium.
b. divide the shaded part using horizontal lines and vertical lines.
c. area of shaded part:
=4*2+(4+2)*3/2+(2+6)*5/2+(2+5)*2/2+(4+6)*2/2+6*3+(4+6)*5/2
=97 cm²
Using the formula for the area of a trapezium, we can see that the expression you provided can be simplified to 97 cm².
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Total cost 44083 sales tax 4% what is the original price
Answers
Answer:45846.32
Step-by-step explanation:
to get the total price first we will do 44083 times 4/100 which give us the amount of 1763.32 which will be added to 44083 as it the sales tax which will give us total answer of 45846.32 and the currency
Answer:
45846.32
Explain how you got your answer:
I need help asap help
Answers
Answer:
$1.75
Step-by-step explanation:
0 myopenmath.com Chapter 1 Quiz Score: 0/300 3/30 answered Progress saved Submit and End (El 15' 0
Question 12 v < > B 10 pts '0 1 (D Details For the function f(:(:) = 69: + 2, evaluate and simplify the
difference quotient. [: Check Answer
Answers
The difference quotient for the function f(x) = 69x + 2 is a constant value of 69. This means that the average rate of change of the function over any interval is always 69.
To evaluate and simplify the difference quotient for the function f(x) = 69x + 2, we first need to understand what the difference quotient represents. The difference quotient is a mathematical expression that measures the average rate of change of a function over a given interval. It is defined as:
[f(x + h) - f(x)] / h,
where h represents a small change in the x-values.
Let's proceed with calculating the difference quotient for the given function:
[f(x + h) - f(x)] / h
= [(69(x + h) + 2) - (69x + 2)] / h
= [69x + 69h + 2 - 69x - 2] / h
= (69h) / h
= 69.
To simplify the expression, we used the distributive property to expand the function f(x + h). Then, we simplified the numerator by combining like terms. The constant terms 2 and -2 canceled each other out. The h term in the numerator can be factored out, which allows us to cancel it out with the h term in the denominator. Finally, we are left with the simplified expression of 69.
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An instructor wants to determine if a longer lesson would improve student test scores. Which variable would be theexplanatory variable?A. The quality of the lessonB. The length of the lessonC. Student test scoresD. The number of students in the class
Answers
The explanatory variable in this scenario would be B. The length of the lesson.
An explanatory variable is one that is used to explain or predict the outcome of a dependent variable.
In this case, the instructor wants to determine if a longer lesson would improve student test scores.
Therefore, the length of the lesson is the explanatory variable because it is being used to predict or explain the outcome of the dependent variable, which is the student test scores.
The other options, the quality of the lesson, the number of students in the class, and the student test scores, are not being used to explain or predict the outcome of the dependent variable, so they are not the explanatory variable.
Hence, the correct answer is, option B: The length of the lesson.
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In a test, +3 marks are given for every correct answer and -1 mark are given for every
incorrect answer. Sona attempted all the questions and scored +20 marks, though she
got 10 correct answers.(i) How many incorrect answers has she attempted?
(ii) How many questions were given in the test?
Answers
Let’s say Sona attempted x incorrect answers. Since she got 10 correct answers, she scored 10 * 3 = 30 marks from the correct answers. From the incorrect answers, she lost x * 1 = x marks. So her total score is 30 - x. We know that her total score is +20, so we can set up the equation: 30 - x = 20. Solving for x, we get x = 10.
So, Sona attempted 10 incorrect answers.
The total number of questions in the test would be the sum of the correct and incorrect answers, which is 10 + 10 = 20 questions.
MARKING BRAINLIEST
PLS HELP
Answers
Answer:
25
Step-by-step explanation:
Moving it down does not change the length.
Use the remainder theorem to find P (3) for P(x) = -x+3x² - 2x-5.Specifically, give the quotient and the remainder for the associated division and the value of P(3).믐Quotient =Х5 ?Remainder = 0p(3) = 0
Answers
We are given the function
\(P(x)=-x^3+3x^2-2x-5\)we are to use remainders theorem to find p(3)
Therefore
Given p(3) then x = 3
Hence
\(\begin{gathered} P(3)=-3^3+3(3)^2_{}-2(3)-5 \\ P(3)=-27+27-6-5 \\ P(3)\text{ = -11} \end{gathered}\)Hence, p(3) = - 11
Therefore, the Remainder is - 11
Finding the quotient
Given
\(\begin{gathered} p(x)\text{ = 3 }\Rightarrow\text{ x = 3} \\ \text{therefore} \\ x\text{ -3 is a factor} \end{gathered}\)Therefore to find the quotient we will use long division method
\(x-3\sqrt[]{-x^3+3x^{^2}-2x-5}\)This gives
\(\begin{gathered} \text{ -x}^2\text{ -2} \\ x-3\sqrt[]{-x^3+3x^2-2x-5} \\ \text{ (-) -}x^3+3x^2 \\ ----------------------- \\ \text{ -2x - 5 } \\ \text{ ( - ) -2x}^{}\text{ + 6} \\ -------------------- \\ \text{ - 11} \end{gathered}\)Therefore, The quotient is
\(-x^2-2\)From the solution above
P(3) = - 11
PLEASE HELP IMMEDIATELY!!!!
Select all of the zeroes of the function.
Answers
Answer: A C and D
Step-by-step explanation:
Answer: A B
Step-by-step explanation: because I sadly had to figure it out, anyways hope this helps y'all
For safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 5 systems detects theft with a probability of 0.88 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 5 systems will detect it. What is the probability that when a theft occurs, at least oneof the 5 systems will detect it? Your answer should be rounded to 5 decimal places.
Answers
The probability that at least one of the 5 systems will detect the theft when it occurs is what the bank is interested in. To find this probability, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
Let A be the event that at least one of the 5 alarm systems detects the theft. The complement of A is the event that none of the 5 systems detects the theft, which we will denote by A'.Since each system detects the theft with a probability of 0.88, the probability that any one system does not detect the theft is 1 - 0.88 = 0.12.
Therefore, the probability that none of the 5 systems detect the theft is: P(A') = (0.12)⁵ = 0.00005376Using the complement rule, we can find the probability that at least one of the 5 systems will detect the theft: P(A) = 1 - P(A') = 1 - 0.00005376 = 0.99994624Therefore, the probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.99995 when rounded to 5 decimal places.
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