For real numbers $x,$ what is the largest possible value of \[ 5 - (x-3)^2 ?\].

Answers

Answer 1

The largest possible value of f(x) will be -∞.

Limit

For solving this question, you can calculate the limit of f(x) for x→∞.  Since the definition of limit is: the limit of  f(x), as x approaches b , equals L. See:  [tex]\lim _{x\to \ b \:}f(x))=L[/tex]

Therefore:

[tex]\lim _{x\to \infty \:}\left(5-\left(x-3\right)^2\right)\\ \\ \lim _{x\to \infty \:}\left(5\right)-\lim _{x\to \infty \:}\left(\left(x-3\right)^2\right)[/tex]

Applying the Constant Law -   The limit of a constant is the constant itself: [tex]\lim _{x\to \infty \:}\left(5\right)=5[/tex]

Applying the Difference Law -  The limit of a difference is the difference of the limits: [tex]\lim _{x\to \infty \:}\left(\left(x-3\right)^2\right)=\infty[/tex]

Thus,

[tex]\lim _{x\to \infty \:}\left(5-\left(x-3\right)^2\right)= \lim _{x\to \infty \:}\left(5\right)-\lim _{x\to \infty \:}\left(\left(x-3\right)^2\right)= 5- \infty=- \infty[/tex]

The largest possible value of f(x) will be -∞.

The result is consistent since it is possible to note that [tex](x-3)^2[/tex]positive number. Also, see that there is a difference between 5 and  [tex](x-3)^2[/tex]-∞.

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Related Questions

Kendra sells gourmet boxes of cookies. One box of cookies costs kendra $6. 75 to produce. She sells her boxes of cookies for $10. What is kendra's return on investment (roi)?.

Answers

Answer:48%

Explanation:

I took the test

If the circle shown is rotated and traced 360° along the dotted path, the resulting three-dimensional figure would look like a picture of a.

Answers

Answer:

It would be a donut

Explanation:

I took the test

220 v is applied to two different conductors made of the same material. One conductor is twice as long and twice the diameter of the second.

Answers

Answer:

so then what is the main question here

Write a program that takes a date as input and outputs the date's season in the northern hemisphere. The input is a string to represent the month and an int to represent the day.

Answers

A program that takes a date as input and outputs the date's season in the northern hemisphere is; done using input as a string to represent the month and an int to represent the day.

How to Program in Python

The seasons in the northern hemisphere are Spring, Summer, Autumn and Winter.

Now, the dates for each of these seasons are;

Spring: March 20 - June 20

Summer: June 21 - September 21

Autumn: September 22 - December 20

Winter: December 21 - March 19

Using the given information of input as a string to represent the month and an int to represent the day and combining with the seasons above, we can write the program in python as;

input_month = input()

input_day = int(input())

months= ('January', 'February','March', 'April' , 'May' , 'June' , 'July' , 'August' , 'September' , "October" , "November" , "December")

if not(input_month in months):

   print("Invalid")

elif input_month == 'March':

   if not(1<=input_day<=31):

       print ("Invalid")

   elif input_day<=19:

       print("Winter")

   else:

       print ("Spring")

elif input_month == 'April' :

   if not(1<=input_day<=30):

       print("Invalid")

   else:

       print("Spring")

elif input_month == 'May':

   if not(1<=input_day<=31):

       print("Invalid")

   else:

       print("Spring")

elif input_month == 'June':

   if not(1<=input_day<=30):

       print("Invalid")

   elif input_day<=20:

       print ("Spring")

   else:

       print("Summer")

elif input_month == 'July' or input_month == 'August':

   if not(1<=input_day<=31):

       print("Invalid")

   else:

       print("Summer")

elif input_month == 'September':

   if not(1<=input_day<=30):

       print("Invalid")

   elif input_day<=21:

       print ("Summer")

   else:

       print ("Autumn")

elif input_month == "October":

   if not(1<=input_day<=31):

       print("Invalid")

   else:

       print("Autumn")

elif input_month == "November":

   if not(1<=input_day<=30):

       print("Invalid")

   else:

       print ("Autumn")

elif input_month == "December":

   if not(1<=input_day<=31):

       print("Invalid")

   elif input_day <=20:

       print ("Autumn")

   else:

       print ("Winter")

elif input_month == 'January':

   if not(1<=input_day<=31):

       print("Invalid")

   else:

       print("Winter")

elif input_month == "February":

   if not(1<=input_day<=29):

       print("Invalid")

   else:

       print ("Winter")

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James wants to carpet the room shown in the diagram. If he uses 12 ft wide carpet strips, how many linear feet will he need to buy?.

Answers

Answer:

11

Explanation:

The room is rectangular. The required carpet can be measured by dividing the area of the room by 12. 60 linear feet of carpet is required. Therefore, option D is correct.

What is the area of a rectangle?

A rectangle is a four-sided polygon with four right angles (90-degree angles). It is a type of quadrilateral, which means it has four sides. Opposite sides of a rectangle are parallel and congruent (equal in length). The two pairs of opposite sides of a rectangle are also equal to each other.

The formula for calculating the area of a rectangle is: Area = Length x Width

Given information,

Width of the carpet = 12 feet

Now,

The area = (40 x 24) - (20 x 12)

Area = 960 - 240 = 720 square feet

The required linear feet of the carpet is:

720 / 12 = 60

Therefore, option D is correct.

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#SPJ2

Your question is incomplete, most probably the full question is this:

James wants to carpet the room shown in the diagram. If he uses 12 ft wide carpet strips, how many linear feet will he need to buy?

A) 11

B) 12

C) 20

D) 60

What do the people in the philippines tell us about the fragility of genetics?.

Answers

8. Filipinos are genetically similar in that 99.9% of their DNA is identical.

9. Climate and heredity can have an impact on physical traits. Living in a certain environment has natural consequences for man's development and evolution, including his physical traits.

11. As a result of their country's successive colonizations and trade with many nations. This provided an opportunity for some Filipinos to marry foreigners. This had an impact on their sons and daughters' physical characteristics, as well as their family line.

22. Queens is a neighborhood in New York City that is thought to be the most varied metropolitan area in the world, with nearly half of the population being immigrants.

8. Filipinos are genetically similar in that 99.9% of their DNA is identical.

9. Physical traits can be modified by a variety of factors.

How much heat is produced by burning 4. 00 moles of acetylene under standard state conditions?.

Answers

Hadithi Fupi ni aina ya kazi andishi ambayo huwa fupi; na huangazia wazo moja kwa kurejelea kisa kimoja. Hadithi huwa na wahusika wachache na huchukua muda mfupi. Aghalabu hadithi fupi huchapishwa katika mkusanyiko wa hadithi nyingine fupi.

Answer:

-5198

Explanation: One mole of acetylene produces -1299.5 kj of heat. Therefore, we would need to multiply -1299.5 by the 4.00 moles to get our answer

One of the physicians concludes that intermountain healthcare isn’t really serious about improving teamwork. The physician asks mark allen if it is really important to change teamwork behaviors. Mark reemphasizes the importance of teamwork and professionalism in the organizations.

Answers

The skills needed to focus on improving active listening skills include:

Give speakers clear nonverbal evidence that you are listening attentively, including leaning toward the speaker, maintaining eye contact, and not fidgeting.Show the speaker respect by not interrupting and by using an inclusive, friendly, and sharing tone.Follow up on unusual or inconsistent communication cues from the speaker, such as changes in tone, vocabulary, and body language to determine the real message the speaker is trying to send.

What is active listening?

Active listening means the practice of preparing to listen, the observation of the verbal and non-verbal messages that are being sent, and then giving appropriate feedback.

From the complete question, Mark Allen, is the Clinical Information Systems Manager at Intermountain Healthcare and he is working with a team of physicians, nurses, administrators, and other healthcare providers in order to improve the quality of healthcare at Intermountain Healthcare.

Since he wants to implement a skill development program on active listening skills, it is important to focus on improving active listening skills.

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If the measure of total measure of the angle is 65° and m∠1 = 35°. What is the measure of ∠2?.

Answers

The measure of m∠2 is 30°

Angles

Angles are formed when two lines intersect at a point. The measure of the opening between this two lines are called the angles.

Therefore, the total measure of the angle is 65 degrees.

m∠1 = 35°

m∠2 = ?

Therefore,

m∠2 = total angle - m∠1

m∠2 = 65° - 35°

m∠2 = 30°

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Some disadvantages of relying solely on financial measures include that: (check all that apply. ).

Answers

Answer:

Credit cards

Loans

Buying cars

Buying houses

shopping

Explanation:

Block a rests on top of block b as shown in (figure 1). The table is frictionless but there is friction (a horizontal force) between blocks a and b. Block b has mass 6. 00 kg and block a has mass 2. 00 kg. If the horizontal pull applied to block b equals 12. 0 n, then block b has an acceleration of 1. 80 m/s2.

Answers

The acceleration of block A is 0.6 m/s².

Net force on the blocks

The net force on the blocks is determined by applying Newton's second law of motion.

∑F = ma

Acceleration of bock A

The acceleration of block A is calculated by applying Newton's second law of motion as follows;

[tex]F_a + F_b = F\\\\F_a = F-F_b\\\\m_a a_a = F- m_ba_b\\\\a_a = \frac{F- m_ba_b}{m_a}[/tex]

Where;

Mb is mass of block B = 6 kgMa is mass of block A = 2 kg[tex]a_b[/tex] is acceleration of block B = 1.8 m/s²[tex]a_a[/tex] is the acceleration of block A = ?

[tex]a_a = \frac{12\ - \ 6 \times 1.8}{2} \\\\a_a = 0.6 \ m/s^2[/tex]

Thus, the acceleration of block A is 0.6 m/s².

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Why is it advisable to start a research introduction with the problem​

Answers

Answer:

A vague, disorganized, or error-filled introduction will create a negative impression, whereas, a concise, engaging, and well-written introduction will lead your readers to think highly of your analytical skills, your writing style, and your research approach.

Explanation:

Please mark me as brainliest

Taigas, tundras, and tropical rainforests share what common abiotic component.

Answers

Explanation:

The closer the spacing of isobars, the stronger is the pressure gra- dient force. The stronger the pressure gradient force, the stronger is the wind. Thus, closely spaced isobars mean strong winds; widely spaced isobars mean lighter wind.

What is the value of δg at which a reaction becomes spontaneous? express your answer numerically.

Answers

A  spontaneous reaction must have a negative change in free energy.

Change in Free energy

The change in free energy can be used to decide the spontaneity of a chemical reaction. We must recall that a spontaneous reaction must have a negative change in free energy. A reaction at equilibrium has a change in free energy value of zero. A reaction that is not spontaneous have a positive change in free energy.

Since the numerical values are missing in the question, we can not compute the numerical change in free energy.

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Making Sentences(not least than eight words)

1.dignity-

2.revelry-

3.acknowledged-

4.fortune-​

Answers

Answer:

1. A man Is expected to lead a life of dignity.

2. The tired students went back home after a long day of revelry.

3.An acknowledged expert was invited to tour our campus.

4. The woman was blessed by health and good fortune.

A clone has _____________ of chromosomes as its parents.

Answers

Answer:

A clone has ....The same exact..... of chromosomes as its parents.

Choose the best answer. Where might you find a lot of sea life? el mar el teatro el estadio el monumento.

Answers

Answer:

A :el mar

Explanation:

trust me, i took the test. it means "the sea"

Answer: A. El mar.

Explanation: On Edge!

What is the kinetic energy of a 1. 0-kg billiard ball that moves at 5. 0 m/s?.

Answers

Answer:

12.5 J

Explanation:

The formula for a kinetic energy (KE) is

KE = 0.5*m*v²

Given m = 1.0 kg, v = 5.0 m/s, so

KE = 0.5*1.0*(5.0)² = 12.5 J

How many moles are 98. 3 grams of aluminum hydroxide al(oh)3.

Answers

Answer:

1.260 mol

Explanation:

What are the opposing arguments for gender equality brainly.

Answers

The opposing arguments for gender equality is that females are more vulnerable in the society.

What is Gender equality?

Gender equality is a situation in which people of all genders have equal rights, responsibilities and opportunities.

The opposing arguments for this is that females are more vulnerable to incidences such as violence, hate speech etc. This therefore are the opposing arguments on why gender equality isn't practised in all countries.

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A swim team ordered 36 jackets that each cost the same amount. The total cost of the order was $1,116. Let c be the cost of each jacket. How much did each jacket cost? choose the equation that represents this problem.

Answers

Answer:

$31

Explanation:

To find the cost per jacket, divide:

$1,116 ÷ 36

Each jacket costs $31.

A student pushes a 51. 5 kilogram bookshelf across a smooth floor with a net force of 67 n.

Answers

Assuming a student pushes a 51. 5 kilogram bookshelf across a smooth floor with a net force of 67 n the acceleration is 1.30m/s².

Acceleration

Using this formula

Acceleration= Net force/Mass of bookshelf

Where:

Mass of bookshelf =51.5 kilogram

Net force =67 Newton

Let plug in the formula

Acceleration=67n/51.5 kilogram

Acceleration=1.30 m/s²

Inconclusion the acceleration is 1.30m/s².

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A problem associated with path-goal theory is that.

Answers

Answer:

A. it has received less research support than other contingency leadership models.

Explanation:

Leo just moved from a job where he dealt with the consumer market to working as a salesperson in the b2b market. As he considers his new responsibilities, it's likely that leo will.

Answers

As Leo considers his new responsibilities, it's likely that he will learn that B2B buyers require more personal service than buyers in the consumer market.

What is B2B?

B2B is an acronym for business-to-business and it can be defined as a type of market in which a business (producer) sells its products directly to other businesses such as:

WholesalersRetailers

What is B2C?

B2B is an acronym for business-to-consumer and it can be defined as a type of market that involves businesses selling their goods and services directly to the consumers or end users for personal use rather than the wholesalers or retailers.

In this scenario, Leo is likely to learn that B2B buyers require more personal service than buyers in the consumer market.

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In what way can you show a sense of adaptability to the diverse philippines literary history.

Answers

By studying Philippines' diverse history, appreciating the significance of history is critical to understanding adaptability, acceptance of life's numerous challenges, and adjustment of expectations. Furthermore by understanding the importance of history not only as a school subject but also as a means of discovering one's past is essential. Today's input is necessary for a better future. Knowledge of history helps one to determine the future.

You roll a six-sided die twice. What is the probability of rolling a 2 and then a 6?.

Answers

Answer:

1/6x1/6=2.777 per cent

Explanation:

Which statement best explains the working principle of an electric motor.

Answers

Answer:

The principle of an electric motor is based on the current-carrying conductor which produces magnetic field around it. A current-carrying conductor is placed perpendicular to the magnetic field so that it experiences a force.

Explanation:

In this exercise we have to use the knowledge of electric motors and explain that they work through a closed circuit and a source.

What are electric motors?

Electric motors are electrical machines that transform electrical energy into mechanical energy. There are many types of electric motors, and we can basically separate them into three large groups which are direct current motors, alternating current motors and universal motors.

In a simpler way, we can say that they are motors that use a closed system that has a source and an electric current.

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Based on the diagram of von thünen’s model of agricultural land use, which statement best explains the connection between land value and agricultural production regions?.

Answers

The statement that best explains the connection between land value and agricultural production regions is that;

Grain crops needs extensive acreage and are said to to be grown on land that is little costly and farther away from the market than on other agricultural land uses.

What is the Von Thunen model of agricultural land use?

The man Von Thunen was said to have given the idea of a land-use model in the urban and rural landscapes that are said to surround a city

His idea is one that shows how economic rent lowers from the center of a city to its other parts. His theory on the system of land use around a city is one that there is no trade alliance with any other kind of country.

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Canis familiaris (dogs) and canis lupus (wolves) are a different(1 point) brainly.

Answers

Canis familiaris (dogs) and canis lupus (wolves) are a different subspecies.

What are subspecies?

It is a group of individuals of a species that, in addition to its own characteristics, have in common other morphological characteristics that distinguish them from other subspecies.

Characteristics of subspecies

It is the only taxonomic rank below species (infraspecific).

Canis lupus is the species, which includes both subspecies dogs and wolves.

The dog is a domestic subspecies of the wolf, according to the comparison of the genetic maps of both they belong to the same species.

Therefore, we can conclude that the subspecies is a taxonomic category that, based on its name, is understood to be below the species.

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Answer:

Species

Explanation:

Hope this helps

One way to lessen the u. S. Government budget deficit is to.

Answers

Explanation: In simple words, budget deficit can be defined as the amount by which the expenditure of the Govt. is exceeding its revenue in a particular period.
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