Let f(x) = 8x^3-3x^2Then f(x) has a relative minimum atx= __a relative maximum atx=___and infection point atx=___
Answers
Answer:
\(\begin{gathered} f\mleft(x\mright)\text{ has a relative minimum at x=1/4} \\ f\mleft(x\mright)\text{ has a relative maximum at x=0} \\ f\mleft(x\mright)\text{ has an inflection point at x=1/8} \end{gathered}\)Step-by-step explanation:
To find the relative minimum and maximum, find the first derivate of the following function:
\(f\mleft(x\mright)=8x^3-3x^2\)Derivating, using the derivative of a sum is equal to the sum of the derivatives. f'(x)=g'(x)+h'(x)
\(f^{\prime}\left(x\right)=24x^2-6x\)A relative maximum point is a point where the function changes direction from increasing to decreasing. Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing.
Equalize the first derivable to 0.
\(\begin{gathered} 24x^2-6x=0 \\ 6x\left(4x-1\right)=0 \\ 6x_1=0 \\ x_1=0 \\ \\ 4x_2-1=0 \\ x_2=\frac{1}{4} \end{gathered}\)Then, the x-coordinate of the relative minimum is x=1/4, and the x-coordinate of the relative maximum is x=0.
The inflection point is a point of a curve at which a change in the direction of curvature occurs. To find the inflection points, find the second derivate and solve for equals 0:
\(\begin{gathered} f^{^{\prime}^{\prime}}\left(x\right)=48x-6 \\ Equalize\text{ to 0:} \\ 48x-6=0 \\ x=\frac{6}{48} \\ x=\frac{1}{8} \end{gathered}\)Related Questions
raph of y = f(x) is graphed below. What is the end behavior of f(2)?
Answers
By observing the graph we have got the following :
The graph is going down after the point (-7,0)
After the point (x,f(x)) =(-7,0) ,as x decreasing, the function f(x) is decreasing
\(as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty\)The graph is going up after the point (4,0).
After the point (x,f(x)) =(4,0), as x increasing, the function f(x) is increasing
\(as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty\)Hence we get
\(as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty\text{ and }as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty\)
Hence the first option is correct.
Consider the following.
The variable r is directly proportional to the square of t, and
r = 324
when
t = 108.
Write the equation that expresses the relationship between the variables. (Let k represent the variation constant.)
r =
Using the given data, solve for the variation constant k.
k =
Answers
Answer:
you just have to subtract
A teacher purchased a fish tank for her classroom. The dimensions of the tank are 32 inches by 50 inches by 48 inches. What is the maximum amount of water that the tank can hold?
A: 2,400 in3
B: 38,400 in3
C: 76,800 in3
D: 153,600 in3
PLEASE ANSWER THIS I'VE BEEN STUCK ON THIS QUIZ FOR 6 HOURS
Answers
Answer:
The maximum amount of water that the tank can hold is C: 76,800 in3.
To find the volume of the tank, we need to multiply its length, width, and height. In this case, the volume of the tank is 32 inches * 50 inches * 48 inches = 76,800 in3.
The maximum amount of water the tank can hold is V = 76,800 inches³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular tank be V
To find the maximum amount of water that the tank can hold, we need to calculate the volume of the tank.
The volume of a rectangular prism (like a fish tank) is found by multiplying its length, width, and height.
Therefore, the volume of this fish tank is:
32 inches x 50 inches x 48 inches = 76,800 inches³
Hence , the fish tank can hold a maximum of 76,800 inches³ of water.
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50 points for 3 questions. solve and explain please.
Answers
(1) The value of x is determined as 16.8.
(2) The measure of length VX is calculated as 4.1.
(3) The measure of angle UWV is 69.5⁰.
What is the value of the missing lengths of the triangle?
The value of the missing lengths of the triangle is calculated by applying the following formula;
(1) For the two similar triangles, the value of x is calculated as follows;
20 / (28 - x) = 30 / x
20x = 30 (28 - x )
20x = 840 - 30x
20x + 30x = 840
50x = 840
x = 840 / 50
x = 16.8
(2) The measure of length VX is calculated by applying trig ratios.
tan 63 = 8 / VX
VX = 8 / tan 63
VX = 4.1
(3) The measure of angle UWV is calculated as follows;
angle T = 360 - (94 + 127) = 139
angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)
angle UWV = 69.5⁰
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how?
does anyone know how to give people brainiest? someone said to wait because it comes after awhile so i went to a question of mine that someone answered 18 hours ago, and there was still no crown beside the heart. do i have to wait a full day? or is it a brainly plan i have to pay for? please answer.
Answers
Step-by-step explanation:
You can wait some time like 3 days but as a rule of thumb, there has to be 2 people to give 1 of them brainliest
f(x) = -x -5, solve for x when f(x) = -6
Answers
Answer:
x = 1
Step-by-step explanation:
Unions, intersections, and complements involving 2 sets
Sets B and C are subsets of the universal set U.
These sets are defined as follows.
U={f, k, m, s, x, y, z)
B={k, s, y}'
C={s,z}
(a) B'UC' = 1
(b) B'nc =
Answers
Intersection of B'∩C = {k, y}
To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.
1. Complement of set B (B'):
The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.
2. Intersection between B' and C:
Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.
The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.
So, the answer to (b) is B'∩C = {k, y}.
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What percent of the front page is taken up by the
prom story, including the prom photograph?
A. 20%
B. 22%
C. 25%
D. 45%
E. 60%
Answers
The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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I need it done very quick pls help
Answers
Enter the correct answer in the box.
What standard form polynomial expression represents the perimeter of this quadrilateral?
3x2 - 4x + 3
4x + 2x
x3 - 2x
x2 + 6x - 11
image not to scale
Answers
None of the choices on the list is correct.
.....Top side: 0x³ + 3x² - 4x + 3
...Right side: 1x³ + 0x² - 2x + 0
Bottom side: 0x³ + 1x² + 6x - 11
......Left side: 4x³ + 2x² + 0x + 0
----------------------------------------------
..Addum up: 5x³ + 6x² + 0x - 8 <== answer
But BLM tho right?24.114.88.15
Answers
PLEASE HELP!! ASAP NOWWWW Two races that a student runs every year are the 1492-mile race in his hometown and the -meter race in his college town. Complete parts (a) through (d) below.
Answers
Answer:
College town race is 31% of the home town race.
Step-by-step explanation:
Length of hometown race = 3 miles
Length of college town race = 1492 meters
Since 1 meter = 0.0006214 miles
Therefore, 1492 = 0.93 miles
Percentage of college town race to the hometown race,
= \(\frac{\text{College town race}}{\text{Home town race}}\times 100\)
= \(\frac{0.93}{3}\times 100\)
= 31%
Therefore, the college town race is 31% of the home town race.
On Monday, 198 students went on a trip to the zoo. A 4
buses were filed and 6 students had to travel in cars How many students were
in each bus?
Answers
Students who travelled by bus= 198-6 = 192
Assuming that each bus had an equal amount of students we can see that:
192/4 = 48 students in each of the 4 busses
Determina el cuadrado de 111 111 111, calculando primero los cuadrados de 1;11;111...
Answers
Answer:
12345678987654321
Step-by-step explanation:
1*1=1
11*11=121
111*111=12321
...
111111111 * 111111111 = 12345678987654321
there are three numbers for the combination to the store safe the first number is 17 the other two numbers can be multiplied together to give a product of 24 what are all of the possibilities for other two number write your answers as multiplication equations and then write all the possible combination to the safe
Answers
1 x 24, 2 x 12, 3 x 8, and 4 x 6
17-1-24
17-2-12
17-3-8
17-4-6
13 People fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2.7-mile section of a parade route.
Answers
The size of the crowd that is 5 feet deep on both sides of the street along a 2.7 -mile section of a parade route is 74,131 people.
How to calculate the crowd?The number of people that can fit comfortably in a 5 feet by 5 feet area = 13.
Therefore;
The ratio of the number of people per unit area = 13/(5 × 5) = 13/25
The area A occupied by the crowd = 5 feet × 2.7 mile × 2
2.7 miles = 14,256 feet
∴ A = 5 feet × 14,256 feet × 2 = 1,42,560ft²
We then have:
\(\frac{number\ of\ people}{1,42,560} = \frac{13}{25}\)
∴Number of people = 13/25 × 1,42,560 = 74,131.2 ≈ 74,131 people
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What is the equation of the line that passes through the point (2,−2) and has a slope of 1/2
Answers
Answer:
y = 1/2x - 3Step-by-step explanation:
Given:
Line passing through the point (2, -2)The slope is m = 1/2The equation of a line:
y = mx + b, where m is a slope, b is a y-interceptUse the coordinates of the point and find the value of b:
-2 = 1/2*2 + b-2 = 1 + bb = -2 - 1b = -3The line is:
y = 1/2x - 3Answer:
y = ½x - 3
Step-by-step explanation:
x = 2
y = - 2
a = ½
y = ax + b
- 2 = ½(2) + b
- 2 = 1 + b
b = - 2 - 1
b = - 3
y = ax + b
y = ½x + (-3)
y = ½x - 3
Is the following a reflection,
rotation or translation?
Answers
A man's gross income is R500 000. He worked at different places throughout the year
and a total of 17% of his earnings was deducted by his employers as PAYE throughout
the tax year. He qualifies for a rebate of R13 257. Calculate how much tax he still
owes. Information taken from the tax table shows that, for a taxable income between
R393 201 and R550 100, R93 135 + 36% above R393 200 needs to be paid.
O R101 678
O R71 774
O R33 326
O R25 191
<
Previou
Next >
Answers
The man still owes R87,726 in taxes.
To calculate the tax amount the man still owes, we need to determine his taxable income first.
Gross income: R500,000
Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000
Taxable income: R500,000 - R85,000 = R415,000
Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.
Tax owed: R93,135 + 36% of (taxable income - R393,200)
Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)
Tax owed: R93,135 + 0.36 * R21,800
Tax owed: R93,135 + R7,848
Tax owed: R100,983
Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.
Tax owed - Rebate: R100,983 - R13,257 = R87,726
Therefore, the man still owes R87,726 in taxes.
The correct option is not provided among the given answer choices.
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During an election for city council, you hear a candidate say that 68% of children in the city live in poverty. A
typical school in this city has about 1,200 students.
Based on the candidate statement about how many children in a typical school live in poverty
Answers
It can be estimated that about 816 children in the typical school are living in poverty.
Percentage calculationBased on the candidate's statement, approximately 816 children in a typical school in this city live in poverty.This is calculated from the 68% of children in the city that live in poverty, multiplied by the 1,200 students in a typical school. This rate of poverty among children is a concerning statistic, and one that needs to be addressed. It highlights the need for effective solutions to help children in this city out of poverty.These solutions could include initiatives such as providing better access to education and employment opportunities, increasing access to healthcare, or providing more social services and supports. Given that poverty has a long-term, negative effect on the health, wellbeing and life chances of children, this is a pressing issue that needs to be addressed.It is important that city council candidates have a plan in place to tackle this issue and help improve the lives of children in this city.To learn more about percentage calculation refer to:
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PLEASE HELP !!!!
Question 3(Multiple Choice Worth 4 points)
(04.01)
The graph of a function is shown:
Which of the following correctly identifies the set of outputs?
{(5,-2), (1, -1), (2, 2), (2,5)}
{(-2,5), (-1, 1), (2,-2), (5,2)}
{-2, -1, 2,5}
{-2, 1, 2, 5)
Answers
Answer:
{(-2, 5), (1, -1), (2, -2), (5, 2)}
What is the answer to this combination lock
Answers
Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
How do I write “3 is less than a number”?
Answers
Answer:
3 - x
Step-by-step explanation:
Just think in order in bits.
3
So, write 3.
Less than = subtraction
So, write a subtraction symbol.
A number = a variable, such as x.
So, write a variable.
That will give you: 3 - x
Enter the exact values of the trigonometric ratios in the boxes.
sin 45°
cos 30
tan 60
=
Answers
The required value of trigonometric ratios is,
sin 45° = 1/\(\sqrt{2}\)
cos 30 = \(\sqrt{3}\)/2
tan 60 = 1/ √3
We know that,
Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Therefore,
sin 45° = 1/\(\sqrt{2}\)
cos 30 = \(\sqrt{3}\)/2
tan 60 = 1/ √3
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Want Brainliest? Please help! :(
Find the circumference and the area of a circle with diameter 6 m.
Use the value 3.14 for pi, and do not round your answers. Be sure to include the correct units in your answers.
Answers
Answer:
Circumference=18.84 m
Area = 28.26 \(m^{2}\)
Step-by-step explanation:
Circumference = 2πr
= 2 x 3.14 x 3 (radius = 6/2 = 3)
= 18.84 m
Area = π\(r^{2}\)
= 3.14 x \(3^{2}\)
= 28.26 \(m^{2}\)
Answer:
Circumference=18.84 m
Area = 28.26
Step-by-step explanation:
if q^2-1 is divisible by 8 if q is _____
Answers
Answer:
if q is odd
Step-by-step explanation:
Hello,
Either q is odd or is even.
Case 1 - we can find k integer so that q = 2k
Then, in the case
\(q^2-1=4k^2-1\)
This is not divisible by 8, for instance, q = 6
\(q^2-1=36-1=35=7*5\)
Case 2 - we can find k integer so that q = 2k+1
\(q^2-1=(2k+1)^2-1=4k^2+4k+1-1=4k(k+1)\)
k(k+1) is divisible by 2 so the initial number is divisible by 8
Conclusion, the answer is q is odd.
Thanks
#9 Consider the expression 9x - 4b + 3. Select all of the statements below
that are true.*
There are 2 variables in the expression.
9 is the only coefficient in the expression
There are 2 terms in the expression.
3 is the constant in the expression
There are 3 terms in the expression
I need help plz
Answers
Answer:
Step-by-step explanation:
True:
- There are two variables
- 3 is the constant
- There are 3 terms in the expression
Desmond is 5 inches taller than Niki.
If we let
represent Niki's height in inches, write an algebraic expression for Desmond's height.
Answers
If the area of the triangles is 32 square centimeters, how long are the base and height?
Answers
Answer:
i think is 8 and 8
Step-by-step explanation:
A little girl has learned how to write digits. So far, she knows only: one, two,
three and four. She took a piece of paper and wrote five of each digit to make a huge
number. She came to her Daddy and said, “When I will grow up, I'll buy as many
chocolate bars as this number tells and we'll split them among you, Mommy, and
me!" But her Daddy answered, “It will not work; there will be a remainder.” What is
the remainder?
Answers
Answer:
it's what will be left when it's divided