If you are examining a function over an interval ( a , b ) , for a and b finite, is it possible not to have an absolute maximum or absolute minimum?

Answers

Answer 1

Yes, it is not possible to have an absolute maximum or absolute minimum.

Here,

We are examining a function over an interval ( a , b ) , for a and b finite,

We have to find,  is it possible not to have an absolute maximum or absolute minimum.

What theorem indicates the existence of absolute maxima or absolute minima of a function?

If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].

Now,

The function is define over an interval (a, b).

Hence, the function is define on open interval.

So, it is not possible to have an absolute maximum or absolute minimum.

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Related Questions

-8(1-a)=-8(a-7) solve the equation

Answers

Answer:

a=4

Step-by-step explanation:

answer: a=4

-8(1-a)=-8(a-7)

8a-8=-8(a-7)

The function f is defined by the following rule
f(x)=2x-1
Complete the function table

Answers

The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.

What is the value of the expression?

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The function is given below.

f(x) = 2x - 1

The value of the function at x = - 3 will be

f(-3) = 2(-3) - 1

f(-3) = - 6 - 1

f(-3) = - 7

The value of the function at x = - 2 will be

f(-2) = 2(-2) - 1

f(-2) = - 4 - 1

f(-2) = - 5

The value of the function at x = 0 will be

f(0) = 2(0) - 1

f(0) = 0 - 1

f(0) = - 1

The value of the function at x = 1 will be

f(1) = 2(1) - 1

f(1) = 2 - 1

f(1) = 1

The value of the function at x = 5 will be

f(5) = 2(5) - 1

f(5) = 10 - 1

f(5) = 9

The value of the function at x = -3, -2, 0, 1, and 5 will be -7, -5, -1, 1, and 9, respectively.

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Help? Anyone pls. I'd give brainliest

Answers

Answer:

3/2

Step-by-step explanation:

xy= -2 X -3

= 6

z = 4

so xy/z is 6/4 which is 3/2.

PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING

Answers

Answer:

1/3

Step-by-step explanation:

Find the length of a picture frame whose width is 3 inches and whose proportions are the same as a 9-inch wide by 15-inch long picture frame.

Answers

Answer:

The length is 5.

Step-by-step explanation:

Since the proportions are the same, 3 is 3 times less than 9. The same applies to 15, which 3 times less would be 5. It has a ratio of 3:5.

can someone answer this please, thank you​

Answers

Answer:

9x

Step-by-step explanation:

EF = 3x

 FG is three times longer ....then FG =    three * EF     = 3 * 3x = 9x

A sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat. what is the percent of fat in this hamburger sample?

Answers

The percentage of fat in this hamburger sample is 15 %.

What is percentage ?

Percentage is the value per hundredth.

According to the given question a sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat.

To find what percentage of the hamburger contains fat we put amount of fat in the numerator and total amount on the denominator and multiply this fraction by 100 to obtain the result in terms of percentage.

∴ (30/200) × 100

= 3000/200

= 30/2

= 15 %.

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You arrive in Tokyo with $320. How many yen can you buy ?

Answers

Answer:

You can buy 31788.8 with $320.

Step-by-step explanation:

To calculate this, we know that yen is 0.01007 dollars per foreign. We also know that 1 dollar = 99.34 So, therefore you will multiply 320 * 99.34 and you will get 31788.8 Yen.

I hope this helps and have a good day! :D

To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment?

The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.

Answers

well, first off, let's see how much each one costs per month.

so, hmmm if she goes with the Bank loan at 9% for 3 years

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &3 \end{cases} \\\\\\ A=9000[1+(0.09)(3)] \implies \boxed{A = 11430}[/tex]

now, that's for 36 months, so she'd be owing the Bank per month [tex]\cfrac{\stackrel{total}{11430}}{\underset{months}{36}}~~ = ~~\text{\LARGE 317.5}[/tex]

now let's take a look at the Credit Card's loan at 18% for 7 years

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9000\\ r=rate\to 18\%\to \frac{18}{100}\dotfill &0.18\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases} \\\\\\ A=9000\left(1+\frac{0.18}{12}\right)^{12\cdot 7} \implies A \approx \boxed{31433.31}[/tex]

now, in 7 years there are 84 months, thus  [tex]\cfrac{\stackrel{total}{31433.31}}{\underset{months}{84}}\approx \text{\LARGE 374.21}[/tex]

so, the Bank will give her a better deal per month, and to be honest altogether.

The plan with simple interest will give the lowest monthly repayment.

The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.

Option C is the correct answer.

What are simple interest and compound interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Compound interest is the interest that is made from the principal and the interest as well in consecutive years.

We have,

Simple interest:

Principal = $9000

Rate = 9%

Time = 3 years

Simple interest:

= P x R x T / 100

= 9000 x 9 x 3 / 100

= 2430

Amount = simles interest + principal

A = 9000 + 2430 = $11430

3 years = 36 months

Monthly  payment = 11430 / 36 = $317.5

Compound interest:

Principal = $9000

Rate = 18%

Time = 7 years

A = P [tex](1 + \frac{18}{100}) ^{7}[/tex]

A = 9000 [tex](1 + 0.18) ^{7}[/tex]

A = 9000 x3.19

Amount = $28,710

7 years = 84 months

Monthly payment = 28710 / 84 = $341.78

Thus,

The plan with simple interest will give the lowest monthly repayment.

The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.

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how do put this 7+2x=11+5x

Answers

7 + 2x = 11 + 5x

collect like terms
2x - 5x = 11 - 7

- 3x = 4
divide both sides

x = - 4/3

In alternative form: x = - 1 1/3
In decimal form: -1.333


Simplify the following expression.

(13x + 9y) + (38x + 33y)
-----------------------------------
22x + 42y (A)

22x + 46y (B)

51x + 42y (C)

51x + 46y (D.)

Answers

Answer:

C: 51X+42Y

13x + 38x + 9y + 33y

adding,

51x + 42y so option C

1) take away the brackets and distribute the plus:
13x + 9y + 38x + 33y

2) add the like terms
13x + 38x + 9y + 33y
= 51x + 42y

what is the value of a?

A.-16
B.-3
C.3
D.16​

Answers

Answer:

Which equation do I refer to?

Step-by-step explanation:

10.) The height of a tree trunk is 20 meters, and the base has a diameter of 1 meter. If the tree has the mass
420, what is the density of the tree?

Answers

26.27 kgm⁻³

Density is the ratio of  mass to volume

Density = Mass / Volume

Let us assume tree is a cylinder,

d= 1

r = d/2 = 0.5 m

h= 20 m

m= 420kg

Volume = π r²h

              = 22/7 x o.25 x 20

Density = mass / volume

              = 420 / 22/7 x o.25 x 20

              = 26.27 kgm⁻³

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A tank truck fills the gas stations reservoir at the rate of 10 1/4 gallons per minute.if the reservoir was empty and it is now 41 gallons full how long has the tanker been filling the reservoir

Answers

The tanker has been filling the reservoir for 4 minutes given that it fills at a rate of 10 1/4 gallons per minute.

Rate refers to the relationship of two quantities of different units. Usually, it is a measure or quantity of something per unit time.

rate = amount / time

If a tank truck fills the gas station's reservoir at the rate of 10 1/4 gallons per minute, and if the reservoir is empty at the start and become 41 gallons full, we can determine how long the tanker has been filling the reservoir by dividing the final amount by the rate.

time = amount / rate

where amount = 41 gallons

rate = 10 1/4 gallons per minute

time = 41 gallons / 10 1/4 gallons per minute

time = 4 minutes

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Please help me!!! I need help asap on this question Whoever is correct will get brainly!

Answers

Answer:

I am not 100% sure more like 12% sure that it is c

Step-by-step explanation:

True/False: Negative numbers closed under subtraction.
Provide an example if false.

Answers

The statement is false .

let ; n=-5

     m=-6

n - m= -5 -( -6 )

       = -5 + 6

       = 1

which is not a negative real number .

therefore it shows that negative real number are not closed under substrsction.

the process or skill of taking one number or amount away from another.

Example: 7-5=2

7 is a minuend

5 is a subtrahend

and 2 is a differenceSubtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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1 of 6
01:52 / 08:00
When this expression is simplified, what is my final answers
-5(2x - 5)
O 10x + 25
O 52x - 25
O-7x + 25
O-10x + 25

Answers

Answer:

-10x + 25

Step-by-step explanation:

We will distribute the - 5 in to 2x which is - 10x

Then distribute - 5 to - 5 which is 25

A hardware store sells planks of wood. the lengths, in centimetres, of the planks are normally distributed with mean 210 and standard deviation 7. two planks are selected at random. find the probability that they differ in length by more than 10 cm.

Answers

The required probability that they differ in length by more than 10 cm is 1.

Given that,
A hardware store sells planks of wood. the lengths, in centimeters, of the planks are normally distributed with a mean of 210 and a standard deviation of 7. two planks are selected at random. find the probability that they differ in length by more than 10 cm is to be determined.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

The
P(x > 10) = p(z = (x - μ)/σ)
P(x > 10) = p(z = (10 - 210)/7)
P(x > 10) = p(z = -28.57143)
P(x > 10) = 1

Thus, the required probability that they differ in length by more than 10 cm is 1.

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i need this done help i need all the work shown

Answers

The answer would be 22 because I added them all
rectangle: 8*4=32
square: 3^2=9
triangle:3*5=15 15/2=7.5

32+9+7.5=48.5

How long will it take you to bike 225 miles at
a
speed of 15 miles per hour?

Am I supposed to divide

Answers

Answer:

15

Step-by-step explanation:

225/15

2) How many distinguishable letter arrangements can be made from the letters in:
a) FLUKE?
b) PROPOSE?

Answers

Answer:

for "FLUKE" its 5! = 120

and "PROPOSE" its 7! /2!×2! = 1260

Step-by-step explanation:

"FLUKE" has no repeating letters.

"PROPOSE" has two repeating letters.

we divide by the repeating letters like I did on "PROPOSE" .

THANK YOU.

what is the difference between 25 and 21.2?

Answers

Answer: 3.8

Step-by-step explanation:

25.0

-

21.2

--------------

3.8

Adding -6 is the same as:

Answers

Answer:

It is the same as subtracting 6.

Step-by-step explanation:

1 + (-6) = 5

1 - 6 = 5

(c) Solve the equation 7x³ +28x² = 0

Answers

Answer:

x = - 4 , x = 0

Step-by-step explanation:

7x³ + 28x² = 0 ← factor out 7x² from each term on the left side

7x²(x + 4) = 0

equate each factor to zero and solve for x

7x² = 0 ⇒ x² = 0 ⇒ x = 0

x + 4 = 0 ⇒ x = - 4

first х=0 second х=-4

5/6 - 1/9 = ?/? - ?/? = ?/?
please help 20 points
i need to know what each ( ?/? ) is

Answers

5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is

5/6 -1/9 =15 /18 -2/18 =13 /18.

As given,

5/ 6 - 1/9 =?/? -?/? =?/?

Convert the given terms into like terms

Least common multiple of (6,9)=18

Value of each ( ?/?)

(5/6 ) × ( 3/3) -(1/9) × (2/2)

= 15 /18 - 2/18

= 13 /18

Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to

5/6 -1/9 = 15 /18 -2/18 = 13/18.

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What is 1+1 answer please despite

Answers

Answer:

2...?

Step-by-step explanation:

can someone help me solve this problem?

Answers

Answer:

no

Step-by-step explanation:

x=5

5(5+2)=35

8(5)-3=37

37 does not equal 35

[tex]Answer: Q\ is\ not\ midpoint\ of\ \overline {PR}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\overline {PQ}+\overline {QR}=\overline {PR}\\5(x+2)+(8x-3)=72[/tex]

Expand the parentheses on the left side of the equation:

x(5)+2*(5)+8x-3=72

5x+10+8x-3=72

13x+7=72

13x+7-7=72-7

13x=65

Divide both parts of the equation by 13:

x=5

Hence,

5(5+2)=

5(5)+2(5)=

25+10=

35

8(5)-3=

40-3=

37

35≠37

Peter is 10 years old and is 5 years younger than half his dad's age. If his dad is Z years old, what is Z?

Answers

Answer:

Z = 30

Step-by-step explanation:

trust me bro

fhfhfhfhhffh

Answer:

Please give brainliest if you think it applies

30

Step-by-step explanation:

Z/2 -5 = 10

Add 5 to both sides

Z/2 = 15

Multiply both sides by 2

Z = 30

|−5| − (−9) I need help asap!!!

Answers

Answer:

14

Step-by-step explanation:

the absolute value function always gives a positive result , that is

| - a | = | a | = a

- (- ) = + given

| - 5 | - (- 9)

= 5 + 9

= 14

Answer:

14

Step-by-step explanation:

Be extremely careful with absolute values, parentheses, and subtraction.

[tex]\left|-5\right|-\left(-9\right)=\left|-5\right|+9\\\left|-5\right|+9\\\left|-5\right|=5\\5+9\\=14[/tex]

√a² + b² = a + b

is this true or false? i think its true but i cant explain it right ​

Answers

Answer:

False

Step-by-step explanation:

Consider a=3 and b=4. The left hand side is 5 but the right hand side is 7.

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