iff(x)=13x3−4x2 12x−5 and the domain is the set of all x such that 0≤x≤9 , then the absolute maximum value of the function f occurs when x is
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Given that the function is f(x) = 13x^3 - 4x^2 + 12x - 5 and the domain is the set of all x such that 0 ≤ x ≤ 9, we need to determine the absolute maximum value of the function f occurs when x is: First, we need to find the critical points of the function f(x) in the domain [0, 9].
Critical points of the function are given as:f'(x) = 39x^2 - 8x + 12 = 0Solving the above equation, we get:x = (-(-8) ± √((-8)^2 - 4(39)(12))) / 2(39)x = (8 ± √400) / 78x = 1/3, 4/13
We check the value of f(0), f(1/3), f(4/13), f(9).f(0) = -5f(1/3) = 1.88889f(4/13) = 2.6022f(9) = 10588
Absolute maximum value of the function is the maximum value among f(0), f(1/3), f(4/13), and f(9).
Hence, the absolute maximum value of the function f occurs when x is 9. Therefore, option D is the correct answer.
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Related Questions
An item is priced at $13.46. If the sales tax is 6%, what does the item cost including sales tax?
Answers
.80 + 13.46 =14.46.
Answer: $14.46
Solve the problem. Find \( k \) such that the line \( -k x+21 y=4 \) is parallel to the line through \( (5,-8) \) and \( (2,4) \). \[ \begin{array}{l} k=-84 \\ k=-86 \\ k=-83 \\ k=-83.5 \end{array} \]
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The slope of the given line \(-kx + 21y = 4\) can be determined by rearranging it into the slope-intercept form \(y = mx + b\), where \(m\) represents the slope. We can rewrite the equation as:
\[21y = kx + 4 \Rightarrow y = \frac{k}{21}x + \frac{4}{21}\]
From this form, we can see that the slope of the given line is \(m = \frac{k}{21}\).
Now, let's find the slope of the line passing through \((5, -8)\) and \((2, 4)\). The slope of a line can be calculated using the formula:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
Substituting the coordinates, we have:
\[m = \frac{{4 - (-8)}}{{2 - 5}} = \frac{{12}}{{-3}} = -4\]
Since the given line is parallel to the line passing through the given points, the slopes of both lines should be equal. Therefore, we can set \(\frac{k}{21} = -4\) and solve for \(k\).
\[\frac{k}{21} = -4 \Rightarrow k = -4 \times 21 = -84\]
Therefore, the value of \(k\) that satisfies the condition is \(k = -84\).
what is the volume of each cylinder with a radius of 2.7 cm and a height of 5 cm
Answers
Answer:
114.51
Step-by-step explanation:
I'm not to sure what you meant by 'each' so I solved it like there was only one cylinder. hope this helped
19% of 43 estimated answer
Answers
Answer:
19% of 43 = 8.17
Answer: 8.6
Step-by-step explanation: we can estimate 19% to 20% and do .2 times 43 and get 8.6
which of these is not an outcome? a.) drawing a king of diamonds from a standard deck of cards b.) rolling a 4 on a die c.) flipping heads on a coin d.) rolling an even number that is less than 2 on a die
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d) Rolling an even number that is less than 2 is not a valid outcome when rolling a die.therefore, option d) is correct.
The outcome that is not possible is (d) rolling an even number that is less than 2 on a die.
A standard die has six sides numbered from 1 to 6, and all the even numbers on a standard die are 2, 4, and 6.
The statement "rolling an even number that is less than 2" contradicts the fact that the lowest even number on a die is 2.
Thus, it is not possible to roll an even number that is less than 2 on a standard die, making it an invalid outcome.
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A polynomial is a single term or the sum of two or more terms containing variables with exponents that are
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whole numbers and coefficients that can be constants or variables. The exponents in a polynomial must be non-negative integers (whole numbers).
The polynomial terms can be added or subtracted, but the exponents of the variables must still be whole numbers.
For example, the following are polynomials:
1. 3x^2 + 5x - 2
2. 2y^3 + 4y^2 - 7y + 1
3. x^4 + 2x^3 - x^2 + 3x - 1
In these examples, the exponents are all whole numbers (2, 3, and 4), and the coefficients (the numbers multiplied by the variables) can be constants or variables themselves.
However, expressions like 2x^(1/2) or 3x^(-2) are not considered polynomials because the exponents in these cases are not whole numbers.
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Please help me it takes do long to do this please
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Answer:
I really don't know , I am in 7th grade
Answer:
x = 121°
Step-by-step explanation:
The lower left vertex and 115 are adjacent and supplementary, thus
left vertex = 180° - 115° = 65°
The angle round a point = 360°, so the top vertex is
360° - 304° = 56°
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle, thus
x = 65° + 56° = 121°
Help lssshjwejjwkwkwwkk
Answers
61 matchsticks need to make 20 squares.
Given,
From the figure,
Matchsticks are used to make the pattern.
To make these 4 squares, you need 13 matchsticks.
To find the how many matchsticks do you need to make 20 squares?
Now, According to the question:
Let the need matchsticks be 'n'
The number of the squares to make 1 square , you need 4 matchsticks,
and when you need to add one square, you need three more matchsticks .
So , we have to make n no. of squares you need
4 + 3(n - 1) matchsticks (n \(\geq\) )
= 4 + 3n - 3
= 1 + 3n
When, n = 20
1 + 3 x 20
= 61
Hence, 61 matchsticks need to make 20 squares.
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Mukesh can walks 8 1/3 km in one hour. How much distance will he covers in 2 2/5 hours?
pls answer it quickly
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Answer.
20 km.
Hope that helps...
Identify the slope of the line
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The slope of the line that passes through the points, (3, 4) and (-4, -5) is: A. 9/7.
How to Determine the Slope of a Line?The slope of a line can be calculated by using the slope formula, which is given as:
Slope (m) = change in y / change in x or rise / run.
Given that the following points lie on a line:
(3, 4)(-4, -5)The slope of the line would be solved using the slope formula as explained below:
Slope (m) = change in y / change in x = (-5 - 4) / (-4 - 3)
m = -9 / -7
Slope (m) = 9/7.
Therefore, the slope is identified as:
a. 9/7.
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The figure below is a net for a triangular pyramid. If all the triangles are equilateral, what is the surface area of the pyramid, in square centimeters? ASAP thanks.
Answers
The Surface area of the pyramid is 68 square cm
The total surface area of the pyramidThe total surface area is the area of all the triangles
Area of a triangle = 0.5bh
b is the base
h is the height
Given te followin
b = 6cm
h = 5.2cm
Surface area of the pyramid = 5(0.5 * 6 * 5.2)
Surface area of the pyramid = 78 square cm
Hence the Surface area of the pyramid is 68 square cm
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Suppose the difference between actual and predicted weekly sales of a company follows a uniform distribution between $2800 and $2800. Determine the following: a. The probability that the actual sale is under predicted by at least $1200? b. The probability that the actual sale is within $1300 of the predicted sale?
Answers
The probability distribution for the difference between actual and predicted weekly sales of the company is a uniform distribution between $2800 and $2800. Actualsale of under predicted is 4/7 and with in predicted sale is 13/14
(a) To find the probability that the actual sale is under predicted by at least $1200, we need to determine the area under the PDF to the left of $1200. Since the PDF is constant within the range, the probability is equal to the ratio of the difference between $1200 and $2800 to the total range of $2800. Therefore, the probability is (2800 - 1200) / 2800 = 1600 / 2800 = 4/7, or approximately 0.5714.
(b) To find the probability that the actual sale is within $1300 of the predicted sale, we need to determine the area under the PDF between $-1300 and $1300. Again, since the PDF is constant within the range, the probability is equal to the ratio of the difference between $1300 and $-1300 to the total range of $2800. Therefore, the probability is (1300 - (-1300)) / 2800 = 2600 / 2800 = 13/14, or approximately 0.9286.
In summary, the probability that the actual sale is under predicted by at least $1200 is 4/7, and the probability that the actual sale is within $1300 of the predicted sale is 13/14.
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find the values of a and b that make f continuous everywhere
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It is possible to choose a and b such that the value of function(x) at any given point is equal to the limit of f(x) as x approaches any value. This guarantees that f is continuous throughout.
A function's limit as x approaches any value must match the value of f(x) at that moment in order for the function to be continuous everywhere. In order to ensure that this need is satisfied, the values of a and b that make up f(x), whether it be a linear equation, polynomial, or another sort of equation, must be chosen. Since the behaviour of the function varies smoothly as x approaches any value, this ensures that the function is continuous throughout. In other words, a and b values must be selected in a way that the function is continuous, i.e., defined and devoid of breaks or discontinuities.
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The complete question is
Find the values of a and b that make f continuous everywhere that f is continuous throughout.
Find the measure of x.
Answers
Answer:
139.5
Step-by-step explanation:
cos(angle) = adjacent/hypotenuse
cos(55) = 80/x
x*cos(55) = 80
x = 80/cos(55)
x = 139.4757
x = 139.5 (rounded)
Answer:
Step-by-step explanation:
90 + 55 + a = 180
145 + a = 180
a = 180 -145
a = 35
secQ = B/H
1.3 = 80 / x
x = 80/1.3
x = 61.6
Can someone please help me really struggling
Answers
And I don’t know about point slope form, it wasn’t in my standards, I’m sorry.
Answer:
your y-intercept is 5 and your slope is 1 hope this helps with translating into the form you want
Step-by-step explanation:
order
22
100
2.2
2
10
0.002
200%
0.02
220
10
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The order of these values from smallest to largest would be 0.002, 0.02, 2, 2.2, 10, 22, 100, 200, and 220.
What is organize?Organization is a way of classifying specific objects according to a pre-established order so that they are easier to identify.
In this case they were different numbers and the organization given to them was in ascending order, that is, from smallest to largest. So they were in the following order:
0.0020.0222.21022100200220Learn more about numbers in: https://brainly.com/question/17429689
39.98× 0.5 is approximately equal to
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Answer:
20
Step-by-step explanation:
it equals 19.99 but if you round it equals to 20
Find the perimeter of the figure.
this makes absolutely no sense at all
Answers
Answer:
50
Step-by-step explanation:
5+10+22+14= 15 thats all the sides! Hope this helps
Answer:
51 m²
Step-by-step explanation:
5 + 5 + 7 + (11+5) + 7 + 11 = 51
Need some assistance yall look at picture :) Algebra 2 type vibe
Answers
Answer:
It is C.
III is saying that the two functions are inverse functions. If two functions, f(x) and g(x) are inverse, then f(g(x)) = x and g(f(x)) = x. Therefore, we see that if III is true, then I and II should also be true. Now, all we have to prove is that f(x) and g(x) are inverse functions. As we said before, if two functions are inverse, then f(g(x)) = x and g(f(x)) = x.
f(g(x)) = 3(\(\sqrt[3]{\frac{x-2}{3} }\))^3 + 2
f(g(x)) = 3[(x-2)/3]+2
f(g(x)) = x-2 + 2
f(g(x)) = x
Therefore, we have proved that f(g(x)) = x, and so f(x) and g(x) are inverse functions, and so all of I, II, and III are true. Thus, the answer is C.
fyi, we didn't have to do g(f(x)) because if f(g(x)) = x, then so will g(f(x)).
What is the graph of the function rule? y=|3x|+2
Options below!
Answers
Answer: the 4th/last option
Step-by-step explanation:
Y goes up when x goes down or up. When x = 0, y = 2
Step-by-step explanation: I like to have the 3 on the
outside and we can just write it as y = 3|x| + 2.
Now, we know that this is the form y = a|x - h| + k where
(h, k) represents the vertex of the function.
Notice that there is no value of h so we say that h = 0.
In addition, we know that k = 2 so our vertex is (0, 2).
This eliminates the first graph and the third graph.
Since a is positive, our function opens upward.
So graph 4 matches with our equation.
What is an equation of the line that passes through the points (2, -7)(2,−7) and (2, -2)(2,−2)
Answers
Answer:
X = 2
Step-by-step explanation:
Slope: (- 7 - -2)/(2 - 2) = -5/0 = 0
The line is vertical (undefined
What is 12x12 inch Square and 3/4 inch pixels?
Answers
What is the asymptote of f(x)=2x-5
Answers
Answer:
No asymptote
Step-by-step explanation:
This equation is linear, so it will not have an astmptote.
there are 3 consecutive even integers .if twice the first integer added to the third is 268,228, find all three integers
Answers
At a movie theater tickets cost $9 for children and $12 for adults. A group of people bought tickets for a movie and bought 4 adult tickets and paid a total of $102 how many children’s tickets did they buy. Write an equation and solve the word problem.
I know they buy 6 children’s tickets but idk how to write the equation. URGENT HELP!!!!!!!!
Answers
Answer:
102-(12•4)÷9 hope this helps
Answer:
102= 6x+b
Step-by-step explanation:
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is ________ .a. urinaryb. bladderc. fissured. supravesical
Answers
The correct option of the given question is option (c) fissure.
When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.
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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.
In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.
The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.
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4. An urn contains four blue balls and six green balls of the same size so that they are undistinguishable bytouch. Two balls are selected without replacement. Find the following probabilities.(a) The second ball is blue given that the first is green(b) The second ball is blue given that the first ball is blue(c) A blue and a green ball are selected(d) Two blue balls are selected
Answers
Answer:
Explanation:
From the information given,
number of blue balls = 4
number of green balls = 6
Total number of balls = 4 + 6 = 10
Probability = number of favorable outcomes/number of total outcomes
Probability of selecting a blue ball = 4/10 = 2/5
Probability of selecting a green ball = 6/10 = 3/5
Since there is no replacement,
Probability of selecting a green ball and blue ball = 6/10 x 4/9 = 4/15
a) This is a conditional probability
The probability that the second ball is blue given that the first is green = (4/15)/(3/5) = 4/15 x 5/3 = 4/9
The probability that the second ball is blue given that the first is green = 4/9
b) This is a conditional probability
The probability of selecting a blue ball and another blue ball = 4/10 x 3/9 = 2/15
The probability that the second ball is blue given that the first is blue = (2/15)/(2/5) = 2/15 x 5/2
The probability that the second ball is blue given that the first is blue = 1/3
c) Probability of selecting a blue and a green ball = 4/10 x 6/9
Probability of selecting a blue and a green ball = 4/15
d) Probability of selecting two blue balls = 4/10 x 3/9
Probability of selecting two blue balls = 2/15
The sum of two numbers is 33. One number is 17 less than the other. Find the numbers. the smaller number is ? The larger number is ?
Answers
Answer:
8 and 25
Step-by-step explanation:
We can set up an equation to help solve this problem.
Let x represent the smaller number
x+(x+17)=33
2x+17=33
2x=16
x=8
The smaller number is 8
Add 17 to 8
The larger number is 25
Answer:
Smaller number:8 larger number:25
Step-by-step explanation:
25-8=17
25+8=33
You can also set up an equation to help things be easier.
How many Real Solutions
Answers
Answer:
D.0
Step-by-step explanation:
Our system of equations is
y= x²+1y=xthen we can conclude that
x²+1 = xx²+1-x = 0x²-x+1 = 0This is a quadratic equation so we will use the dicriminant method:
Let Δ be our dicriminant
a= 1b= -1c= 1Δ = (-1)²-4*1*1 = 1-4 = -3 < 0The dicriminant is negative so this equation has no real solutions
the the system has no real solutions
a small college has 500 freshmen, 400 sophomores, 350 juniors, and 300 seniors. administrators wish to conduct a survey of their students, and they find a simple random sample of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. the overall sample is:
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The overall sample for the survey consists of 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors, totaling 155 students.
To create an overall sample for the survey, the administrators selected a certain number of students from each class level. They randomly sampled 50 freshmen, 40 sophomores, 35 juniors, and 30 seniors. By combining these individual samples from each class, the administrators obtained an overall sample size of 50 + 40 + 35 + 30 = 155 students. This overall sample represents a portion of the student population from each class level and allows for a representation of students from different academic years in the survey.
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