c) Determine the location and values of the absolute maximum and absolute
minimum for the given function:
f(x) = (-x + 2)4, where 0 <x<3​

Answers

Answer 1

Answer:

The absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.

Step-by-step explanation:

f(x) = (-x + 2)⁴

to find the absolute maximum and minimum values, we differentiate f(x) with respect to x.

So df(x)/dx = f'(x) = 4(-x + 2)³

The maximum and minimum values are obtained when f'(x) = 0

So,  4(-x + 2)³ = 0

⇒  (-x + 2)³ = 0

⇒ -x + 2 = 0

-x = -2

x = 2

Now, f(2) = (-2 + 2)⁴ = 0⁴ = 0

So, the absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.


Related Questions

BEDMASS or PADMASS solve this pls

Answers

Answer:

Step-by-step explanation:

376389546535150-540111-107525

Given that f(x) = x2 – 3x – 28 and g(x) = x - 7, find
(f - g)(x) and express the result in standard form.

Answers

Answer:

[tex](f-g)(x)=x^2-4x-21[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=x^2-3x-28\text{ and } g(x)=x-7[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

Substitute:

[tex]=(x^2-3x-28)-(x-7)[/tex]

Distribute:

[tex]=x^2-3x-28-x+7[/tex]

Rearrange:

[tex]=(x^2)+(-3x-x)+(-28+7)[/tex]

Hence:

[tex](f-g)(x)=x^2-4x-21[/tex]

Get brainiest if right!!

3 hours after starting a trip, a driver increased his speed by 10
mph and arrived at his destination 11 hours after starting his
journey. If the distance traveled was 894 miles, find the original
speed of the driver.

Answers

299 miles I think I’m so sorry if it’s wrong

A nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?

Answers

Answer:

225cc

Step-by-step explanation:

the solution is attached to the picture.

The amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Functions and percentages

Let the amount of 10% solution she should use be x.

If a nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution, the equivalent equation will be:

90(0.45) + 0.1x = 0.2(90+x)

Simplify the resulting equation for "x"

40.5 + 0.1x = 18 + 0.2x
0.1x = 40.5 - 18
0.1x = 22.5
x = 225cc

Hence the amount of the 10% solution should he use if the nurse mixes 90 cc of a 45% saline solution with a 10% saline solution is 225cc

Learn more on proportion here: https://brainly.com/question/19994681

HELP ME PLZ WILL MARK U AS BRAINLIEST

Answers

Answer:

Step-by-step explanation:

a)

The mean for ground floor is 20.67

The mean for balcony is 15.8

b)

the difference between the means is ground floor - balcony

20.67 - 15.8 = 4.87

You can talk about it yourself for part c

: A pack of crayon was shared between two friend Shantel and Carl in the ratio 3:5. If Shantel received 27 crayons, how many crayons were in the pack? *

Answers

Answer:

72 crayons

Step-by-step explanation:

8/3 × 27 = 72 crayons

Does anyone know the answer?

Answers

Answer:

lx-3l

Step-by-step explanation:

negative in the abs means moving to the right

Answer:  |x-3|

=========================================================

Explanation:

We start with the parent function y = |x|

Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.

The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.

The graph doesn't shift up or down, so k = 0

The value of 'a' stays the same at a = 1.

In the past year, Latoya watched 33 movies that she thought were very good. She watched 60 movies over the whole year. Of the movies she watched, what
percentage did she think were very good?

Answers

Answer:

55%

Step-by-step explanation:

Just do 33/60 and multiply by 100

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______
a) sec sqr Theta
b) Cot theta
c) cot (pie/2-Theta)
d) csc sqr theta

Answers

Answer:

[tex](a)\ \sec^2(\theta) = 82[/tex]

[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]

[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]

[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = 9[/tex]

Required

Solve (a) to (d)

Using tan formula, we have:

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

This gives:

[tex]\frac{Opposite}{Adjacent} = 9[/tex]

Rewrite as:

[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]

Using a unit ratio;

[tex]Opposite = 9; Adjacent = 1[/tex]

Using Pythagoras theorem, we have:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]

[tex]Hypotenuse^2 = 81 + 1[/tex]

[tex]Hypotenuse^2 = 82[/tex]

Take square roots of both sides

[tex]Hypotenuse =\sqrt{82}[/tex]

So, we have:

[tex]Opposite = 9; Adjacent = 1[/tex]

[tex]Hypotenuse =\sqrt{82}[/tex]

Solving (a):

[tex]\sec^2(\theta)[/tex]

This is calculated as:

[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

Where:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]

So:

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]

[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]

[tex]\sec^2(\theta) = 82[/tex]

Solving (b):

[tex]\cot(\theta)[/tex]

This is calculated as:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

Where:

[tex]\tan(\theta) = 9[/tex] ---- given

So:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

[tex]\cot(\theta) = \frac{1}{9}[/tex]

Solving (c):

[tex]\cot(\frac{\pi}{2} - \theta)[/tex]

In trigonometry:

[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]

Hence:

[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]

Solving (d):

[tex]\csc^2(\theta)[/tex]

This is calculated as:

[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]

[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]

Where:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]

So:

[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]

[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]

[tex]\csc^2(\theta) = \frac{82}{81}[/tex]

what is the slope of the line that contains the points (-1,2) and (3,3)

Answers

Answer:

B

Step-by-step explanation:

Hi there!

We are given the points (-1,2) and (3,3) and we need to find the slope.

The formula for slope calculated from two points is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

since we have two points, we can substitute them into the formula, but let's label their values to avoid any confusion

[tex]x_{1}[/tex]=-1

[tex]y_{1}[/tex]=2

[tex]x_{2}[/tex]=3

[tex]y_{2}[/tex]=3

now substitute into the formula (m is the slope); remember: we have a negative number in this, so we'll be subtracting a negative.

m=[tex]\frac{3-2}{3--1}[/tex]

simplify

m=[tex]\frac{3-2}{3+1}[/tex]

m=[tex]\frac{1}{4}[/tex]

so B is your answer

Hope this helps! :)

This is the fourth one !

Answers

Answer and Step-by-step explanation:

Angle B' is congruent to Angle B.

The measure of an angle stays the same when dilating, translating, and other transformations.

#teamtrees #PAW (Plant And Water)

What's the Error? Explain the error. Find the correct solution.
42-(-6)=-7

Answers

Answer: 42 -(-6)= 48

Step-by-step explanation:

a negative - a negative will always equal a positive

:)

The length of a rectangle is 6 cm less than twice its width, and the area is 108cm2. Write an equation to solve for the dimensions.


x = (2x + 6) = 108
x = (2x - 6) = 108
2x = (x - 6) = 108
x = (x - 6) = 108

Answers

Answer:

4

Step-by-step explanation:

i think thats not my answer

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.

Answers

Answer:

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Step-by-step explanation:

First we have to find the sample mean and the sample standard deviation.

We have 15 measurements. Using a calculator, the mean is [tex]\overline{x} = 3.79[/tex] and the standard deviation is of [tex]s = 0.97[/tex].

Now, we have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{0.97}{\sqrt{15}} = 0.54[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3.79 - 0.54 = 3.25 hours

The upper end of the interval is the sample mean added to M. So it is 3.79 + 0.54 = 4.33 hours

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

football team consists of 20 each freshman and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that.
a. All 4 are seniors.
b. There is 1 each: freshman, sophomore, junior, and senior.
c. There are 2 sophomores and 2 freshmen.
d. At least 1 of the students is a senior.

Answers

Answer:c

Step-by-step explanation:

c

the number of apples in a basket varies directly as the number of oranges. if a basket had 35 apples with 7 oranges, how many apples are there in a basket with 30 oranges?

Answers

Answer:

150

Step-by-step explanation:

35÷7=5 therefore each 5 apples is equal to 1 orange

Answer:

150

Step-by-step explanation:

we're gonna compare ratios. if the initial ratio is 35/7, then we will need to make a similar one for this question. with apples on top, we'll write 'x/30' and cross multiply and solve to get 150

please answer both thanks​

Answers

Answer:

Question 4 is B and Question 5 is C

Step-by-step explanation:

Question 4 is B because the DIFFERENCE between the two terms is 15 therefore when you subtract the terms it must equal 15 so B could no be an answer. Also since they both equal 24 they both add up to 24

What is the answer? The question is on the picture

Answers

9514 1404 393

Answer:

  D.  32 square units

Step-by-step explanation:

At 40% scale, the length is ...

  (20 units)×40% = 8 units

and the width is ...

  (10 units)×40% = 4 units

The area is the product of length and width, so is ...

  A = (8 units)(4 units) = 32 square units

a purchasing agent for kelly bread company wants to estimate the mean daily usage of rye flour. she takes a sample for 50 straight days and finds that the sample mean is 180 pounds with a sample standard deviation of 38.5 pounds. State the 90% confidence interval for the mean

Answers

Answer:

The 90% confidence interval for the mean is (170.87 , 189.13)

Step-by-step explanation:

Using the calculator we can easily calculate   the 90% confidence interval for the mean, the given values are:

mean=180

sx : 38.5

n : 50

c - Level : 0.90

Then the output will be [170.87 , 189.13]

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval

Answers

Answer:

Average rate of change = 5

Step-by-step explanation:

Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,

Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]

From the table,

f(5) = 10

f(4) = 5

Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]

                                                                                    = 5

Answer:

=5

Step-by-step explanation:

A container holds 3.01 grams of
calcium powder for dogs. What is its
weight in centigrams?
Conv
3,010 cg
301 og
30.1 cg
0.0301 og
What is its weight in centigrams

Answers

Answer:

ur dog water kid *take the L dance

Step-by-step explanation:

cheese

3.01 grams = 301 centigrams

Need help with this please!

Answers

do you know you could download photo math and u just gotta scan it and it will tell you it

Write an equation of the line containing the point (3,5) and perpendicular to the line 4x-3y=5
The equation of the line is ___

Answers

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

[tex]-3y=-4x+5[/tex] and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and

[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and

[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so

[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5

Answers

t-3.2 ≤ 7.5

"at most" means less than or equal to

A tank contains 36,864 L of water. At the end of each subsequent day, half of the water is removed and not replaced. How much water is left in the tank after 11 days
There is approximately L of water left in the tank.
(Round to the nearest whole number as needed.)

Answers

Answer:

18 L

Step-by-step explanation:

a = 36,864 * (1/2)^(11)

a = 18

36 L of water will be left after 11 days

What is an Geometric Progression(AP)?

GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number .

Constituting an GP according to the question

36,864 , 18432 , 9216 , ...........

In order to find nth term  of an GP, formula used will be :

a(n) = a (r^(n-1))

considering above GP ,

a(n) = ? water left after 11 days

a = 36864

r= 18432 /36864 = 1/2

n = 11

a(n) = 36864 ((1/2)^(11-1))

  a(n) =   36

Hence 36 L of water will be left after 11 days

Learn more about GP:

https://brainly.com/question/4853032?referrer=searchResults

#SPJ2

A total of 416 tickets were sold for a school play they were either tickets for adults tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold

Answers

Answer:

let the number of adult tickets = x

Then the number of student tickets = 3x

Total tickets x+3x = 416

 

4x = 416

x = 416/4

x = 104

Therefore the number of adult tickets sold is 104

Step-by-step explanation:

Which of the following is true about the US federal government’s ability to borrow money

Answers

It to blurry barely could send it

Help pls it’s urgent. If your able to solve it than I’d really would appreciate you.

Answers

Answer:

Step-by-step explanation:

If the radius of the circle is equal to

[tex]\sqrt{\frac{A}{3} }[/tex] and the area is given as 45, then

[tex]r=\sqrt{\frac{45}{3} }[/tex] which simplifies to

[tex]r=\sqrt{15}[/tex] and to the nearest tenth,

r = 3.9

Please help!
An 80% confidence interval is found to be (200,240). What is the margin of error? O A. 32 O B. 20 O C. 40 O D. 16 SUBMIT​

Answers

Answer:

The margin of error is of 20, option B.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction between the bounds, divided by 2.

In this question:

Lower bound: 200

Upper bound: 240

Margin of error:

(240 - 200)/2 = 40/2 = 20

The margin of error is of 20, option B.

Given the statement “If a line is horizontal, then it has slope equal to zero,” what is its contrapositive?

Answers

Answer:

"If the line has a slope that is not 0, then the the line is not horizontal".

Step-by-step explanation:

The contrapositive of "If p then q" is "If not q then not p".

p=a line is horizontal

not p= a line that is not horizontal

q=the line has a slope equal to zero

not q=the line has a slope that is not zero

The equivalent statement in contrapositive form is therefore:

"If the line has a slope that is not 0, then the the line is not horizontal".

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Complete with singular they/them/their What made attractions like amusement parks and sportsevents accessible to a large number of people? Which of these can lead to the extinction of a species?Plz help Joshua is interested in running a half-marathon and seeks help from a personal trainer. During the first week of training, Joshua is asked to walk 5 miles every day. The following week, the trainer instructs him to walk a mile and then run a mile until he completes 5 miles. Each week, the training regimen gets harder. By the end of the month, Joshua is running 5 miles without stopping. By the end of the second month, Joshua is running the distance of a half-marathon (approx. 13 miles). After each training session, the trainer meets with Joshua to give him reinforcing feedback and to motivate him to continue training. This situation is an example of: JRE2 Inc. entered into a contract to install a pipeline for a fixed price of $2,245,000. JRE2 recognizes revenue upon contract completion. Cost incurred Estimated Cost to Complete2020 $ 256,000 $ 1,580,000 2021 1,630,000 533,000 2022 480,000 0 In 2022, JRE2 would report gross profit (loss) of: PLEASE HURRY!!!!!!!What tactics did the Democratic Party use to win the state elections of 1898? Check all that apply.violenceelectoral fraudintimidationproperty destructionsupport for the banksracist propaganda In the following lever system, what is the clockwise torque? A. 6 Nm B. 300 Nm C.1,200 Nm D. 1,800 Nm H2C=CH2 + H2 ? The legislature enacted __________ to impede African Americans ability to vote.A.voting feesB.literacy testsC.registration feesD.writing tests las chicas fastasman son ? libro rompecabezas ayuda When evaluated, which expression has a result that is a rational number? Written like this Someones mother has four sons North,West and South.What is the name of the fourth son. I see here it says the answer is Someone but what is the name of the son. Is a statement it has a period not a question mark and as far as the someones mother has four sons you could say Sherry is someones mother without the childs name being someone so some people think the answer as the it is written would be That the forth sons name is What . Which makes sense to me so does the answer change depending on if it ends with a period or a question mark What is the difference between gene mutations and chromosome mutations?A. Gene mutations are preventable and chromosome mutations are notB. Gene mutations can happen easily and chromosome mutations are more difficultC. Gene mutations only affect one gene while chromosome mutations affect many genes which of these molecules is nonpolar? Help please!!! I dont understand What should the Latin relative pronoun "quo" be translated as in this sentence:"Baucis et Philemon deis omnem cibum quo vixerunt (they lived) donaverunt" What is the purpose of the paean?O to honor the godsO to entertain the audienceO to create conflictO to provide exposition thesis for juvenile delinquency HELP? Robin saved money during the months of July and August can some one help me Which of the following activities should one practice when doing a close reading?Select all that apply.Read a passage multiple times.Underline words and phrases that seem important or that you don't understand.Draw lines to connect ideas, actions, or other elements to one another.Highlight most of the passage as you read through it.Avoid pauses or stopping to reflect on what you're reading.