The figure above shows the graph of f', the derivative of a function f. The domain of f is the set of all real numbers x such that -3 < x < 5. a. For what values of x does f have a relative maxlmum? Why? b. On what intervals is the graph of concave upward? Use ' to justify your answer. C. Suppose that f(1) = 0. In the xy-plane provided, draw a sketch that shows the general shape of the graph of the function f on the open interval 0 < x < 2. у X O 2
Answers
a) For value of x=-2 given function have a relative maximum.
b) The graph is concave upward in the interval of (-1,1) and (3,5)
c)
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What is Differentiation?Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
solution of above questions are:
a)Function 'f' has relative maximum at x=-2 because f'(x)=0 and f' is changing from +ve to -ve
b) (-1,1 ) and (3,5) are intervals of graph that is concave upward because f' is increasing and f'' is +ve.
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Related Questions
Find the rate change
Answers
If a+b=5 and a-b=4 then b^2-a^2 =
Answers
Answer:
\(a + b = 5 \\ a \: = 5 - b \\ a - b = 4 \\ 5 - b - b = 4 \\ 5 - 2b = 4 \\ 5 - 4 = 2b \\ 1 = 2b \\ \frac{1}{2} = \frac{2b}{2} \\0.5 = b \\ b = 0.5 \\ a = 5 - b \\ = 5 - 0.5 \\ = 4.5 \\ {a \: }^{2} - {b}^{2} = ( {4.5}^{2}) - ( {0.5}^{2} ) \\ = 20.25 - 0.25 \\ = 20 \\ {a}^{2} - {b}^{2} = 20\)
Step-by-step explanation:
HOPE THAT THIS IS HELPFUL.
HAVE A GREAT DAY.
The histogram shows the number of laps completed by swimmers on a team during practice.
A. which interval contains the most values?
B. How many swimmers are on the team?
C. What percent of the swimmers swam more than 14 laps? Round o the nearest tenth of a percent.
Explain.
Answers
Answer:
A) 10-14
B) 45
C) 6.7%
Step-by-step explanation:
A) The interval that contain the most values can be gotten by looking at the histogram and selecting the interval with the highest frequency. Hence the interval 10-14 contains the most values because it has a frequency of 20.
B)The total number of swimmers is gotten by summing all the frequency of each individual lap. Hence:
Total swimmers on team = 10 + 12 + 20 + 0 + 3 = 45 swimmers
C) The percentage of swimmers who swam more than 14 laps = (number of swimmers that swam more than 14 laps/total swimmers) * 100%
The percentage of swimmers who swam more than 14 laps = [(0 + 3)/45] * 100% = (3/45) * 100% = 6.7%
Draw the line 4x+3y =12 for valuesof x from -3 to 3
Answers
The line passes through the points \((-3, 8), (-2, 6.67), (-1, 5.33), (0, 4), (1, 2.67), (2, 1.33), and (3, 0).\)
What lines are related to slope-intercept?To draw the line \(4x + 3y = 12\) for values of x from -3 to 3, we can first rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
\(4x + 3y = 12\)
\(3y = -4x + 12\)
\(y = (-4/3)x + 4\)
Now we can use the slope-intercept form to find the y-values for different x-values within the range of -3 to 3.
When \(x = -3\) :
y = (-4/3)(-3) + 4 = 8
When x = -2:
\(y = (-4/3)(-2) + 4 = 6.67\)
When \(x = -1\) :
\(y = (-4/3)(-1) + 4 = 5.33\)
When \(x = 0\) :
\(y = (-4/3)(0) + 4 = 4\)
When x = 1:
\(y = (-4/3)(1) + 4 = 2.67\)
When \(x = 2\) :
\(y = (-4/3)(2) + 4 = 1.33\)
When \(x = 3\) :
\(y = (-4/3)(3) + 4 = 0\)
Now we can plot these points on a coordinate plane and draw a line through them to represent the equation \(4x + 3y = 12\) .
|
8 | ●
| ●
6 | ●
| ●
4 |●
|
2 |
|
0 |----------------
-3 -2 -1 0 1 2 3
Therefore, The line passes through the points (-3, 8), (-2, 6.67), (-1, 5.33), (0, 4), (1, 2.67), (2, 1.33), and (3, 0).
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nineteen students named lacrosse as there favorite sport. explain how to use the circle graph for the total number of students? 20% chosr swimming 42% chose volleyball and 38% chose laccrosse
Answers
The total number of students is 50
The number of students that named lacrosse as their favorite sport is given as:
\(Lacrosse = 19\)
From the circle graph, 38% chose lacrosse.
So, the proportion of students that represent lacrosse is:
\(Lacrosse = 38\% \times Students\)
Substitute 19 for lacrosse
\(19= 38\% \times Students\)
Multiply both sides by 100
\(1900 = 38 \times Students\)
Divide both sides by 38
\(50 = Students\)
Rewrite as:
\(Students = 50\)
Hence, the total number of students is 50
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using the exponential smoothing model for forecasting, the smoothing constant alpha determines the level of smoothing and what?
Answers
Answer:
Step-by-step explanation: The speed of reaction to differences between forecasts and actual results. is the answer i think
Select all points that are on the graph of f if we know that f(2)=−4 and f(5)=3.4.
Answers
The points that can be on the graph are (0, -8.9), (2, -4), (3, -1.6), and
(5, 3.4).
What is a function?A function is a relationship between inputs where each input is related to exactly one 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,
f(2) = -4
(2, -4)
f(5) = 3.4
(5, 3.4)
The equation of the line on the graph can be y = mx + c.
m = (3.4 + 4) / (5 - 2)
m = 7.4/3
(2, -4) = (x, y)
-4 = 7.4/3 x 2 + c
-4 - 4.9 = c
c = -8.9
Now,
The equation of the line is y = 2.47x - 8.9
For x = 2, y = 2.47 x 2 - 8.9 = = -4
(2, -4)
For x = 5, y = 2.47 x 5 - 8.9 = 3.4
(5, 3.4)
For x = 1, y = 2.47 x 1 - 8.9 = -6.4
(1, -6.4)
For x = 3, y = 2.47 x 3 - 8.9 = -1.6
(3, -1.6)
For x = 0, y = -8.9
(0, -8.9)
Thus,
The points are (0, -8.9), (2, -4), (3, -1.6), and (5, 3.4).
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I need someone to explain
Answers
Answer:
x= 26/5= 5 1/5= 5.2y= 17/5= 3 2/5= 3.4Step-by-step explanation:
explain what ? what is the question here ?
to find the intersecting point of both lines ?
if that is the case, then please consider that an intersection point is a point, where both equations deliver the same coordinates. it is the same point for both of them.
in other words, the question is for what pair of (x, y) are both equations true (their left and right sides are equal).
we do this by finding a way to express one variable by an expression in the other variable, and then use that identity in one of the equations to solve for the remaining variable. and then we use that in the other equation to solve for the first variable.
line b gives us such an identity right away.
y = (-1/2)x + 6
we can use that in the line a equation :
2x - ((-1/2)x + 6) = 7
2x + (1/2)x - 6 = 7
2x + (1/2)x = 13
(4/2 + 1/2)x = 13
(5/2)x = 13
5x = 26
x = 26/5 = 5.2
y = (-1/2)×5.2 + 6 = -2.6 + 6 = 3.4
PLEASE, I NEED THE ANSWER FAST
Answers
9514 1404 393
Answer:
x = 25
F = 82
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary.
(4x -2)° +(3x +7)° = 180°
7x = 175 . . . . . . . . . . . . . . . divide by °, subtract 5, collect terms
x = 25 . . . . . . . . divide by 7
The far right angle is then ...
(3x +7)° = (3(25) +7)° = 82°
The opposite angle in the parallelogram has the same measure, as does the vertical angle to it, angle f.
∠f = 82°
Evaluate the expression for the given value(s) of the variable(s). 6.5 – n; n = 1.8
Answers
Answer:
4.7
Step-by-step explanation:
Substitute value
6,5 - 1.8
=4.7
You are considering enrolling in an BAMA course. You could get a job with a BA that pays $50,000 per year, The BAMA costs $10,000 in tuition and books. The BAMA adds one year to your schooling You expect that after you finish you could get a job that pays STo,000 per year. Show your two options in the form of a graph.
Answers
The two options, pursuing a BA and pursuing a BAMA course, can be represented in the form of a graph depicting the financial outcomes over time.
To compare the two options, we can create a graph with two lines representing the total earnings for each choice over time.
1. Option 1: BA Degree Only
- The BA degree takes four years to complete.
- During these four years, there are no earnings from a job.
- After completing the BA degree, you can start working and earn a salary of $50,000 per year.
2. Option 2: BAMA Degree
- The BAMA degree takes five years to complete (including one additional year).
- During these five years, there are no earnings from a job.
- After completing the BAMA degree, you can start working and earn a salary of $100,000 per year.
On the graph, we can plot the years on the x-axis and the total earnings on the y-axis. The two lines representing the options will have different slopes to reflect the difference in earnings.
For the BA option, the line will start at $0 for the first four years and then increase sharply to $50,000 per year.
For the BAMA option, the line will start at $0 for the first five years and then increase more gradually to $100,000 per year.
By comparing the two lines on the graph, you can visually see the point at which the BAMA option surpasses the BA option in terms of total earnings. This point represents the break-even point where the investment in the additional year of education pays off.
It is important to consider not only the financial aspects but also other factors such as career prospects, personal interests, and long-term goals when making decisions about further education.
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Data set 2 is symmetric The prices for six books are given below. If all the prices are reduced by 50%, what is the new median price? $12.75, $14.80, $19.99 $9.95 $16.00, $17.95 (A) $7.40 (B) $7.70 (C) $15.24 (D) $15.40
Answers
After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)
To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.
Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.
To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.
Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.
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solve The Following Using The Distributive Property
(-75) x173+173x(-25)
Answers
you start by multiplying (-75) by 173 and you get -12975. you then multiplying 173 by (-25) and you get -4325
the overall answer is -17300
Answer:
Step-by-step explanation:
(-75) x173+173x(-25)
173(-75-25)
173(-100)
-17300
If 20 is subtracted from a number, the result is less than 7.
a) State the inequality in symbols.
b) Solve the inequality for x
Answers
Step-by-step explanation:
We have x - 20 < 7, so
x < 27.
A pizza will be plit among 3 friend. What amount of pizza will each
friend receive?
Answers
Each friend would receive 1/3 of the pizza. If the pizza is split evenly among three people, each person will receive an equal share of the pizza, which is 1/3 of the total amount.
Let's say the pizza is of size X. Then, each friend will receive X/3 of the pizza. This means that if the pizza is divided into three equal parts, each friend will get one of those parts.
It's important to note that the size of the pizza can vary, and the amount each friend will receive will depend on the size of the pizza. But if the pizza is divided equally among three friends, each friend will receive 1/3 of the pizza.
Additionally, if the pizza is not divided perfectly into three equal parts, the amount each friend receives may be slightly different. In that case, one friend may receive a slightly larger piece while another may receive a slightly smaller piece.
However, it is common practice in such situations to divide the pizza as fairly as possible to ensure that each friend gets an equal share of the pizza. This can be done by using a knife or a pizza cutter to divide the pizza into three equal sections based on the size and shape of the pizza.
It is also possible to agree on a different arrangement, such as one friend taking two pieces while the other two friends each take one piece. In the end, the goal is to make sure that everyone is satisfied with their share of the pizza.
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Consider the predicate "enrol_mark >= 50", what row(s) will be selected for this predicate by the dbms?
Answers
The rows selected for the predicate "enrol_mark >= 50" by the DBMS will include all rows where the value of the column "enrol_mark" is greater than or equal to 50.
In a DBMS (Database Management System), a predicate is a condition or criteria used to filter and select specific rows from a database table. In this case, the predicate "enrol_mark >= 50" indicates that we are interested in selecting rows where the value of the "enrol_mark" column is greater than or equal to 50.
When the DBMS evaluates this predicate, it will scan the table and compare the value of the "enrol_mark" column for each row. If the value is greater than or equal to 50, the row will be selected and included in the result set. Rows with "enrol_mark" values less than 50 will not be included in the result set.
It's important to note that the actual rows selected by the DBMS will depend on the specific data in the table. If there are rows where the "enrol_mark" column has values greater than or equal to 50, those rows will be selected. If there are no such rows, then the result set will be empty.
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how to find the area of a triangle without a given base
Answers
Answer:
Step-by-step explanation:
is there a height? Is the triangle with a 90 degrees angle? Is there any other conditions that are given?
The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed
through a busy intersection.
4.
8 12 16 20 24 28 32 36 40 44 48
Answers
Answer:
Median is 28
Step-by-step explanation:
Median is 28 smallest value is 8
Using integration on y-axis set up the integral(s) (do not solve) that gives the area of the region bounded by the graphs of the equations: y=x 2 −1,y=−x+2,x=0,x=1. The graph of the curves y=x 2 −1,y=−x+2 is given in Figure 1 . Figure 1: 2. (5 points) Consider the region that you identify in Question 1. Using the Washer/Disk method set up the integral(s) (do not solve it(them)) that allow you to compute the volume of the solid generated by revolving
Answers
Answer:
Here, given
Step-by-step explanation:
The radius of a circle is 6 centimeters.
Enter the area of the circle, in square centimeters.
Round your answer to the nearest hundredth.
Answers
Answer:
113.04
Step-by-step explanation:
Enter the area of the circle, in square centimeters. Round your answer to the nearest hundredth. 1.
find the measure of ADB
Answers
Answer:
it is 30
12344555667890
A right rectangular prism is 3 in by 4.25 in by 18.25 in. What is the total surface area of the prism?
145.0625 in2
180.625 in2
264.625 in2
290.125 in2
Answers
Identical at both ends, a prism is a three-dimensional solid object 145.0625 in2.
What is meant by surface?the outer face, outside, or exterior limit of a thing; topmost or uppermost layer or area. the six surfaces of a cube; any face of a body or entity.
Surface area; the size or area of the outside of the face. the outside, especially in contrast to the inside nature: to investigate something more deeply. surface, a group of points arranged in two dimensions (flat surface), a group of points arranged in three dimensions (curved surface), or the perimeter of any three-dimensional object.
In general, a surface is a continuous barrier that separates two areas of a three-dimensional space.
There are small cracks all over the surface of the picture. There are tiny cracks all over the surface of the picture. The surface of the bowl is gleaming.
145.0625 in2
180.625 in2
264.625 in2
290.125 in2
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50 POINTSSS PLEASE HELP
Create a list of steps, in order, that will solve the following equation
2(x+3) – 5 = 123
Solution steps:
Add 2 to both sides
Add 5 to both sides
Divide both sides by 2
Multiply both sides by 2
Subtract 5 from both sides
Subtract – from both sides
Square both sides
Take the square root of both sides
Answers
A list of steps, in order, that will solve the following equation include the following:
Add 5 to both sidesDivide both sides by 2.Subtract 3 from both sidesHow to create a list of steps and determine the solution to the equation?In order to create a list of steps and determine the solution to the equation, we would have to add 5 to both sides and divide both sides by 2 in order to open the parenthesis as follows;
2(x + 3) – 5 = 123
2(x + 3) – 5 + 5 = 123 + 5
2(x + 3) = 128
By dividing both sides of the equation by 2, we have the following:
2(x + 3)/2 = 128/2
x + 3 = 64
By subtracting 3 from both sides of the equation, we have the following:
x + 3 - 3 = 64 - 3
x = 61
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Niko found 12 diamonds in a video game.
Those 12 diamonds represented 48% of the
total for the level he was on. How many total
diamonds were on that level?
Answers
Answer:
25
Step-by-step explanation:
There’s a button for the pic
Answers
which value is the solution to the equation below? 4(-3x + 8) = -16
Answers
Divide both sides by 4.
−3x + 8 = -16/4Divide −16 by 4 to get −4.
−3x + 8 = −4Subtract 8 from both sides.
−3x = −4 −8Subtract 8 from −4 to get −12.
−3x = −12Divide both sides by −3.
x = -12/-3Divide −12 by −3 to get 4.
x = 4SkandarAnswer:
\(x=4\)
Step-by-step explanation:
Given equation:
\(4(-3x+8)=-16\)
Apply the Distributive Property of Addition:
\(\implies -12x+32=-16\)
Apply the Subtraction Property of Equality by subtracting 32 from both sides:
\(\implies -12x+32-32=-16-32\)
\(\implies -12x=-48\)
Apply the Division Property of Equality by dividing both sides by -12:
\(\implies \dfrac{-12x}{-12}=\dfrac{-48}{-12}\)
\(\implies x=4\)
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NEED THIS SOLVED NOW PLEASE HELP WILL GIVE BRAINLYEST
A new Community Sports complex is being built in safe harbor the perimeter of the rectangular playing field is 452 yards. The length of the field is 2 yards less than the width. What are the dimensions of the playing field?
Find the Width and the Length
Answers
Answer:
Let w = the width
Let 4w - 9 = the length
P = 2l + 2w
582 = 2(4w - 9) + 2w
582 = 8w - 18 + 2w
582 = 10w - 18
600 = 10w
60 yards = w
4w - 9 = 4(60) - 9 = 231 yards
Step-by-step explanation:
yes
A rectangular prism is 4 inches long, 3 inches wide, and 8 inches tall. Eli packs the prism with unit cubes to find the volume. Abby uses a formula to find the volume.
Answers
Answer
try asking siri
Step-by-step explanation:
this is simple knowledge
Please help! Giving out brainiest.
Answers
Answer:
x - 1
Step-by-step explanation:
3(3x + 3) - 2(5 + 4x)
9x + 9 -10 - 8x
x - 1
hope this helps!
In the figure pq is parallel to rs. The length of pt is 3 cm the length of pq is 5 cm, the length of rs is 15 cm what is the length of rt
Answers
Using the properties of parallel lines, it can be concluded that the corresponding sides of the triangles formed by the transversal are proportional. Thus, using the ratio of the corresponding sides, the length of rt is 9 cm.
Since pq is parallel to rs, we can use the property of similar triangles, which states that the corresponding sides of similar triangles are in proportion.
Therefore, we can set up the following proportion
pt/pq = rt/rs
Substituting the given values, we get
3/5 = rt/15
Cross-multiplying, we get
5rt = 45
Dividing both sides by 5, we get
rt = 9
Therefore, the length of rt is 9 cm.
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--The given question is incomplete, the complete question is given
" In the figure pq is parallel to rs. The length of pt is 3 cm the length of pq is 5 cm, the length of rs is 15 cm what is the length of rt "--
