The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is (4 points)
-1
39
35
71
A function assigns the values. The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To find the point at which the function has the maximum value we need to differentiate the function. Therefore, the function can be written as,
[tex]f(x) = 2x^3 - 18x^2 + 48x - 1 \\\\\dfrac{d}{dx}f(x) = \dfrac{d}{dx}(2x^3 - 18x^2 + 48x - 1)\\\\f' = 6x^2-36x+48[/tex]
Equate the function with zero to know at what value of x the function returns a maximum value.
6x² - 36x + 48 = 0
x² - 6x + 8 = 0
x² -2x -4x +8 = 0
(x-2)(x-4)=0
Since we want to the value in the interval of 0 to 3, therefore, 2 is the value at which the function will have its maximum value.
f(2) = 2(2)³ - 18(2)² + 48(2) - 1
f(2) = 39
Hence, The maximum value of f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3] is 39. thus, the correct option is B.
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To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], locate the critical points and evaluate the function at the critical points and endpoints. The maximum value is 71.
Explanation:To find the maximum value of the function f(x) = 2x^3 - 18x^2 + 48x - 1 on the interval [0, 3], we need to locate the critical points and the endpoints of the interval. First, find the derivative of the function: f'(x) = 6x^2 - 36x + 48. Set the derivative equal to zero and solve for x to find the critical points. Then evaluate the function at the critical points and the endpoints to find the maximum value.
The critical points are x = 1 and x = 4. Evaluating the function at these points: f(1) = -7 and f(4) = 71. Evaluating the function at the endpoints of the interval: f(0) = -1 and f(3) = 35. The largest value is 71, so the maximum value of f(x) on the interval [0, 3] is 71.
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Which of the following equations correctly expresses the relation between vectors A⃗ ,
B⃗ , and C⃗ shown in the figure?
A) A⃗ +B⃗ +C⃗ =0
B) A⃗ =B⃗ +C⃗
C) B⃗ =A⃗ +C⃗
D) C⃗ =A⃗ +B⃗
Factor the polynomial. 54c 3d 4 + 9c 4d 2 A. 9c 3d 2(d 2 + 6c) B. 9c 3d 2(6d 2 + c) C. 9c 4d 2(d 2 + 6) D. 9c 4d 2(6d 2 + 1)
TRUE or FALSE. 6 1/3 percent is equal in fraction to 4/75
Nathan cut 3 pieces of rope. Each was between 1.1 m and 1.2 m. Write down how long each piece might be.
The minute hand of a clock is 9.5cm long. how far will the tip of the hand travel in one day
convert to an improper fraction, type your answer with the negative in the numerator.
-8 3/4
The mixed number -8 3/4 can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, resulting in -29/4.
Explanation:The mixed number given is -8 3/4. An improper fraction is one where the numerator (top number) is greater than the denominator (bottom number). To convert a mixed number to an improper fraction, we should multiply the whole number by the denominator of the fraction and then add the numerator. Here, this would look like (-8*4)+3 = -32 + 3 = -29. The denominator stays the same. So, -8 3/4 is equal to -29/4 in improper fraction form.
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Mikel traded Australian dollars for Thai baht at an exchange rate of 1 Australian dollar = 29.3225 Thai baht. He gave the exchanger a total of $1900 and was charged a flat fee of $40. Approximately how many Thai baht does Mikel have?
Answer:
The answer is 54539.85 Thai baht.
Step-by-step explanation:
1 Australian dollar = 29.3225 Thai baht.
Mikel gave the exchanger a total of $1900 and was charged a flat fee of $40.
As he was charged a fee so we will subtract it from the original amount.
[tex]1900-40=1860[/tex] Australian dollars
So, this amount in Thai baht becomes:
[tex]1860\times29.3225=54539.85[/tex] Thai baht.
The answer is 54539.85 Thai baht.
In Jaden’s garden, there is a triangular patch of grass. He wants to plant a geranium in the patch at a point equidistant from all its vertices. Where should Jaden plant the geranium?
in the center of the inscribed circle of the triangle
in the center of the circumscribed circle of the triangle
at the point of intersection of the angle bisectors of the triangle
at the point of intersection of an angle bisector and a perpendicular bisector of the triangle
Answer:
In the center of the circumscribed circle of the triangle
Step-by-step explanation:
This implies that he wish to plant a geranium in such a way that its position would be of equal distance to the vertices of the triangle.
To circumscribe a circle to the triangle means to construct or draw a circle outside the triangle. And the circle would touch the three vertices of the triangle externally. Thus, the center of the circle is equidistant to the vertices.
For Jade to plant a geranium in the patch at a point equidistant from all vertices of the triangle, he should plant it in the center of the circumscribed circle of the triangle.
*NEED HELP??!!!
In one study it was found that the correlation coefficient between two variables is -0.93
Which statements is true?
There is a weak association between the variables
There is a weak association between the variables
There is a strong association between the variables
There is a strong association between the variables
Answer: There is a strong association between the variables
Step-by-step explanation:
The correlation is a term use inn statistics to define the relationship between any two or more than two variable.
When the value of correlation coefficient lies between -1 to -0.5 or 0.5 to 1, then it means that there is strong association between the variables.When the value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5, then it means that there is moderate association between the variables.When the value of correlation coefficient lies between -0.3 to -0.1 or 0.1 to 3, then it means that there is weak association between the variables.Given : In one study it was found that the correlation coefficient between two variables is -0.93.
Since -1<-0.93< -0.5
It means, that There is a strong association between the variables
Inverse function y = x2 − 18x.
The question is about finding the inverse of the quadratic function y = x^2 - 18x. To find the inverse, swap x and y then solve for y, considering the function's restricted domain to ensure it's a function. Understanding transformations like scaling, reflecting, and translating is also crucial for interpreting and graphing functions.
Explanation:The student is asking about how to find the inverse function of a given quadratic function y = x2
- 18x. To find the inverse, we need to swap the x and y variables and solve for y. The steps involve setting x = y2 - 18y and then applying the quadratic formula or completing the square to solve for y. It is important to note that not all functions have inverses that are also functions without restricting the domain, especially quadratics, which are not one-to-one. However, if we consider only the increasing or decreasing intervals separately, we can find a suitable inverse restricted to that part of the domain.
The critical points like x and y intercepts can help us to verify if we have found the correct inverse function. Additionally, understanding the effects of various transformations on the function can be useful in graphing and interpreting the inverse.
Regarding transformations of functions, the operations may include scaling, reflecting, and translating the graph. For instance, the function f(x) = 2x - 2 features a y-intercept at (0, 2) and would be transformed as follows for different operations:
f(2x) which shrinks the graph horizontally by a factor of half.f(-2x) which reflects the graph across the y-axis.f(-2(x+1)) which results in a horizontal shift to the left by one unit by adding 1 to the independent variable x.Which of the following points lie in the solution set to the following system of inequalities?
y > −3x + 3
y > x + 2
(2, −5)
(−2, 5)
(2, 5)
(−2, −5)
Answer:
Hi!
The correct answer is (2,5).
Step-by-step explanation:
To find which ordered pair is in the solution set of the system of inequalities:
y > −3x + 3 y > x + 2you have to replace the values into the system and both results have to be true.
For ordered pair (2,5) where x=2, and y=5.
y > −3x + 3 5 > -3(2) + 3 // replace the values5 > -6 + 35 > -3 is TRUE.AND
y > x + 2 5 > 2 + 25 > 4 is TRUE.Correct answer: (2,5)
The length of a rectangle is 3 inches more than the width. the perimeter is 42 inches. find the length and width.
Which pair or pairs of polygons are congruent?
3 and 4
1 and 3
1, 3 and 4
2, 3 and 4
1, 2, 3 and 4
Answer: 1 and 3
Pair 1 is the mirror image of one another and it is shifted 1 unit up. so they are congruent
Pair 2 : the size of green image is increased when compared to the size of red image.
Pair 3: The red image is shifted up and right to get the green image. The size of the image are same. so they are congruent.
Pair 4: The size of the image differs.So they are not congruent.
You roll two dice, what is the probability of rolling two even numbers?
Robert buys 4 pounds of cauliflower at $0.85 a pound. He also buys 4 pounds of brussels sprouts. If he spends $6.40 on the vegetables, how much did the brussels sprouts cost per pound? A. $0.80 B. $0.75 C. $0.85 D. $0.76
Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride. Which function can be used to determine how much money he has left over after x rides?
A) f(x) = 1.25x + 64
B) f(x) = -16x + $80
C) f(x) = -1.25x + 64
D) f(x) = -1.25x - 64
Alexander has 418 song on his mp3 player. he divides the songs into 11 equal groups. about how many songs are in each group
how do i find what x equals for 7x-5=-5
Sales on credit are immediately counted as cash receipts?
The correct answer to this open question is the following.
Sales on credit are not immediately counted as cash receipts.
When a good is sold and people pay for it with cash, that is counted as cash receipts. Other methods don't. If the product is sold on credit, the store is not receiving any cash at all. It is receiving a promise of pay that has to be payable by the credit institution or the bank.
Find all solutions in the interval [0, 2π).
7 tan^3x - 21 tan x = 0
A) pi/3, 2pi/3, 4pi/3, 5pi/3
B) 0, pi/5, π, 6pi/5
C) 0, pi/3, 2pi/3, π, 4pi/3, 5pi/3
D) 0, pi/3, π, 4pi/3
simplify the expression 3x^2(x^2-4x-2)+(5x^3+7x^2+2x+11)
Given the conditional statement "If it is January, then it is winter in the United States," which is true?
A) The Converse Of The Conditional
B) The Inverse Of The Conditional
C)The Contropositive Of The Conditional
D) Not Here ...?
Given the conditional statement, 'If it is January, then it is winter in the United States.' The convese and inverse aren't always true, but the contrapositive is, therefore, the correct answer is C) The Contrapositive of the Conditional.
Explanation:The given statement is 'If it is January, then it is winter in the United States.' In logic, this statement is termed as a conditional statement. Let's analyze the options provided:
The Converse of the Conditional: This would reverse the statement to 'If it is winter in the United States, then it is January.' This is not always true since winter lasts for three months: December, January, and February.The Inverse of the Conditional: This would negate both the original statement's hypothesis and conclusion, resulting in 'If it is not January, then it is not winter in the United States,' which is also not always true.The Contrapositive of the Conditional: This reverses and negates the statement, turning it into 'If it is not winter in the US, then it is not January.' This statement is true. If it's not winter (meaning it's spring, summer, or fall), it cannot be January.Learn more about Conditional Logic here:https://brainly.com/question/2114683
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An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007, causing extensive damage. Earlier that year, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania. How many times more intense was the Japanese earthquake than the Pennsylvania earthquake? (Round your answer to the nearest whole number.)
Final answer:
The 6.4 magnitude earthquake in Japan was approximately 1995 times more intense than the 3.1 magnitude earthquake in Pennsylvania, when calculated using the logarithmic Richter scale.
Explanation:
To determine how many times more intense the Japanese earthquake was than the Pennsylvania earthquake, we need to understand how the Richter scale measures the intensity of earthquakes. The Richter scale is logarithmic, and an increase of one unit corresponds to a tenfold increase in the amount of energy released by an earthquake. To calculate the intensity difference, we need to use the formula:
Intensity ratio = 10(magnitude of larger earthquake - magnitude of smaller earthquake)
For the earthquakes in question:
Magnitude of Japanese earthquake = 6.4
Magnitude of Pennsylvania earthquake = 3.1
Thus, the intensity ratio is:
Intensity ratio = 10(6.4 - 3.1)
Intensity ratio = 103.3
Calculating this with a calculator gives us an intensity ratio of approximately 1995.26. Rounded to the nearest whole number, the Japanese earthquake was about 1995 times more intense than the Pennsylvania earthquake.
Your class is learning how to tie knots.each student needs a peace of rope thatis 3/8 yards. how much do we need for 16 stdents
use a finite sum to estimate the average value of f on the given interval by partitioning the interval into four subintervals of equal length and evaluating the f at the subinterval midpoints.
f(x)=x^4 on [0,2]
A function is a relationship between inputs where each input is related to exactly one output.
The average value of the function f(x) on [0, 2] is 3.03515625.
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(x) = [tex]x^{4}[/tex] on [0, 2]
Partitioning the interval into four subintervals of equal length.
= 2-0 / 4 = 2/4 = 1/2 = 0.5
This means the four subintervals are:
[0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].
Midpoints of each partitioned interval.
[0, 0.5] = 0.25
[0.5, 1] = 0.75
[1, 1.5] = 1.25
[1.5, 2] = 1.75
Now,
f(0.25) = [tex]0.25^{4}[/tex]
f(0.75) = [tex]0.75^{4}[/tex]
f(1.25) = [tex]1.25^{4}[/tex]
f(1.75) = [tex]1.75^{4}[/tex]
Now,
The average value of f(x) = [tex]x^{4}[/tex] on [0, 2].
= 1/2 [ ([tex]0.25^{4}[/tex] + [tex]0.75^{4}[/tex] + [tex]1.25^{4}[/tex] + [tex]1.75^{4}[/tex])/(2 - 0)]
= 0.5 [ ([tex]0.25^{4}[/tex] + [tex]0.75^{4}[/tex] + [tex]1.25^{4}[/tex] + [tex]1.75^{4}[/tex])/2 ]
= 3.03515625
Thus,
The average value of the function f(x) on [0, 2] is 3.03515625.
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The Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 9 authors in all. Would you be surprised if none of the names f these authors were among the 10 most common? (Assume that authors' names are independent and follow the same probability distribution as the names of all residents.)
The probability suggests a 28.7% chance that none of the 9 authors have names among the 10 most common.
In a probability context, the likelihood of encountering one of the 10 most common names among the authors of your textbooks can be estimated based on the fact that these names account for 9.6% of all U.S. residents. However, the probability distribution of authors' names may not precisely mirror that of the general population, as authorship is influenced by factors beyond name popularity.
Given that there are 9 authors, each with an independent chance of having a name among the top 10, the probability that none of them have a common name is [tex]0.904^{9}[/tex], assuming an even distribution. This is because
0.904 represents the proportion of names that are not in the top 10.
Calculating this probability results in approximately 0.287, or 28.7%. So, there is about a 28.7% chance that none of the authors have a name among the 10 most common.
In a brief summary, it wouldn't be overly surprising if none of the authors' names matched the 10 most common names given the probability, but it's not an unexpected outcome. Probability alone doesn't guarantee specific outcomes in small samples.
Which of the following are equal to the expression below?
square root of 40/2
A. square root of 10
B. 20
C. square root of 20
D. square root of 40/4
Write all classifications that apply to the real number 2/3.
use benchmarks to estimate 2.81+3.73