How do I solve this problem? The trouble that I have is evaluating if 2^∞ or ∞³ is larger?

How Do I Solve This Problem? The Trouble That I Have Is Evaluating If 2^ Or Is Larger?

Answers

Answer 1

For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)

But if you've been introduced to L'Hopital's rule: we have

[tex]\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0[/tex]


Related Questions

Is "y = 0.860x + 3.302" a function? Explain why.

Answers

Answer:

Yes.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Any line that follows slope-intercept form will be a function.

If we graph this line, we can see that each x-value has its own y-value and it passes the vertical line test.

∴ y = 0.860x + 3.302 is indeed a function.

Sara has a rectangular garden in her backyard that measures 12 m by 15 m. She wants to put a rock walkway on the diagonal. How long will the walkway be? Round to the nearest tenth of a meter

Answers

Answer:

19.2 m

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

12^2 + 15^2 = c^2

144 + 225 = c^2

369 = c^2

Taking the square root of each side

sqrt(369) =sqrt(c^2)

19.20937271=c

To the nearest tenth

19.2 = c

Answer:

Diagonal of rectangle walk = 19.2 meter (Approx.)

Step-by-step explanation:

Given:

Length of rectangle = 12 meter

Width of rectangle = 15 meter

Find:

Diagonal of rectangle walk

Computation:

Diagonal of rectangle = √l² + b²

Diagonal of rectangle walk = √Length of rectangle² + Width of rectangle²

Diagonal of rectangle walk = √12² + 15²

Diagonal of rectangle walk = √144 + 225

Diagonal of rectangle walk = √369

Diagonal of rectangle walk = 19.2093

Diagonal of rectangle walk = 19.2 meter (Approx.)

Identify the equation of the circle that has its center at (9, 12) and passes through the origin.

Answers

Answer:

(x-9)^2 +(y-12)^2 = 225

Step-by-step explanation:

First find the length of the radius

If is the distance from the center to the point

d = sqrt( (x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (0-9)^2 + (0-12)^2)

   = sqrt ( 81+144)

  = sqrt(225)

  = 15

The equation for a circle is

( x-h) ^2+ (y-k)^2 = r^2

(x-9)^2 +(y-12)^2 = 15^2

(x-9)^2 +(y-12)^2 = 225

The+pie+chart+shows+the+age+distribution+in+a+village+of+120+a)+how+many+people+are+older+than+60+=+120+B)+What+percentage+of+the+villagers+are+under+25?+I+KNOW+A+I+NEED+TO+KNOW+B

Answers

Answer:

if the village is of 120 people and  120 people are over the age of 60 then 0 people are under the age of 25.

Step-by-step explanation:

Noelle has containers that each hold one gallon of liquid. She used these containers to dispose of waste from the chemistry laboratory. She collected 3 quarts 1 pint of liquid from the first table, 4 quarts from the second table, 2 quarts from the third table , and 3 quarts 1 pint from the fourth table. What is the least number of containers Alyssa needed to collect the waste ? ( 4 quarts = 1 gallon , 2 pints = 1 quart )

Answers

Answer:

4 containers.

Step-by-step explanation:

Since Noelle collected 3 quarts 1 pint of liquid from the first table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.

She also collected 4 quarts from the second table, 2 quarts from the third table.

Finally, she collected collected 3 quarts 1 pint of liquid from the fourth table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.

So, the total amount of liquid she collected in quarts is V = 3.5 quarts + 4 quarts + 2 quarts + 3.5 quarts = 7.5 quarts + 5.5 quarts = 13 quarts

We now convert this value to gallons to know the amount of containers Noelle needs since she has one gallon containers.

13 quarts = 13 × 1 quarts = 13 quarts × 1 gallon/4 quarts = 13/4 gallons = 3.25 gallons

Since the total amount of liquid is 3.25 gallons = 3 gallons + 0.25 gallons, Noelle would need 4 containers since 3 containers would contain the first 3 gallons and the fourth container would contain the remaining 0.25 gallons.

So, Alyssa would need 4 containers.

simplify m√p + n√p - √p

Answers

Answer:

[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]

(12) In a relay race, Mia ran 1.43 kilometers. Then she passed the baton to Gerald, who ran an
additional 2.7 kilometers. How many kilometers did they run in all?
a. 4.13 Kilometers
b. 3.36 kilometers
G. 3.50 Kilometers
d. 1.70 kilometers

Answers

Answer:

4.13

Step-by-step explanation:

To find out how many kilometres they ran in all you have to do 1.43+2.7 =4.13

Answer:

a

Step-by-step explanation:

Mai running=1•43km

Gerald=2•7km

Mai+Gerald=they run in all

1.43+2.7 = 4.13km

What number added to 23 equals 41?
Equation:
Solution:

Answers

Whatever 41-23 equals and that’s the answer

Answer:

1. x + 23 = 41

2. x = 18; solution is 18

Step-by-step explanation:

We can translate the question into an equation. Because the question is asking to find a specific number we don't know the value of, let that unknown number be a variable; x. We know, from the information given in the question, that x added to 23 is equal to 41. When we're adding a number to another number, we use the + symbol. So far, we have x + 23. Now, the last part says "equals 41". We can imply when something equals another thing, we use the = sign. Then, we're left with the equation: x + 23 = 41.

To solve for this equation:

x + 23 = 41

Subtract 23 from both sides:

x + 23 - 23 = 41 - 23

x = 18

Therefore, our solution is 18.

please help!! asap need 5 and 6

Answers

Answer:

both substitutions

Step-by-step explanation:

in 5. based on 3 BC is substituted by its equal counterpart AB.

and in 6. we use 1. to substitute AC by its associated absolute value.

PLEASE HELP!

Record the lengths of the sides of ΔABC and ΔADE.

I would appreciate it.

Answers

AB: 20

BC: 12

AC: 16

AD: 10

DE: 6

AE: 8

Please help 50 points! ​

Answers

d=10

Answer:

Solution given:

[tex]\sqrt{25+3x}=d+2x[/tex]

squaring both side

25+3x=(d+2x)²

when x=-3

25+3*-3=(d+2*-3)²

25-9=(d-6)²

16=(d-6)²

[tex]\sqrt{16}=d-6[/tex]

4=d-6

d=4-6

d=10

Answer:

d = 6

Step-by-step explanation:

[tex] \sqrt{25 + 3( - 3)} = d + 2( - 3) \\ 4 = d - 6 \\ d = 10[/tex]

hopefully this makes sense

:)

would appreciate the help please!

Answers

Answer:

I think SAS is the correct Ans

What is the sum of the polynomials? (6x+7+x^2)+(2x^2-3)
a.-x^2+6x+4
b.3x^2+6x+4
c.9x + 4
d.9x^2+4

Answers

Answer:

b.

[tex]{ \tt{(6x + 7 + {x}^{2})(2 {x}^{2} - 3) }} \\ = { \tt{(2 + 1) {x}^{2} + 6x + (7 - 3) }} \\ = { \tt{3 {x}^{2} + 6x + 4 }}[/tex]

Plz help out will give brainliest

Answers

Answer:

10 degrees = C

Step-by-step explanation:

Total internal angles add to 180 degrees.

Add all values of c and set equal to 180.

18c = 180.

c=10

Answer:

c = 10

Step-by-step explanation:

3c + 6c + 9c = 180 degrees. Every triangle has 180 degrees.

18c = 180                Combine the like terms. Divide by 18

18c/18 = 180/18

c = 10

Please Solve:
x^2-4x-5=0

Answers

The quadratic equation answer is: x^1 = -1; x^2=5 and the number of solutions are 2 real solutions. Hope this helps :)

asap help no wrong answers

Answers

the answer is in the picture

plzz help will mark brainliest

Answers

Answer:

Step-by-step explanation:

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

First put it into general form by setting the equation to zero  and moving all variables to one side.

x^2 + 11y + y^2 -3x + 11 = 5x +23 - y

       +y              -5x -11           -11

x^2 + y^2 - 8x + 12y = 12

Then solve by completing the square

x^2 - 8x         y^2 + 12y        = 12

(x -    )^2 + (y +   )^2 =

Half of 8 is 4

Then square 4 to get 16  

Therefore, we plug the 4 into the first parentheses

x^2 - 8x + 16 + y^2 + 12y      =12 +16

(x - 4)^2 + (y +  )^2 =

Half of 12 is 6

Squared, that would be 36

plug this into the second parentheses

x^2 - 8x + 16 + y^2 +12y + 36 = 12 + 16 + 36

(x - 4)^2 + (y + 6)^2 =

12 + 16 = 28 + 36 = 64

Therefore, the equation of the circle is: (x - 4)^2 + (y + 6)^2 = 64

Which is option D

What is the vertex of the function f(x) = -|x + 7| − 4?

A.
(-7,-4)
B.
(7,4)
C.
(-7,4)
D.
(7,-4)

Answers

Answer:

it would be

D.

(7,-4)

Mark me as brainliest pleases

Answer:

it would be A (-7,-4)

Step-by-step explanation:

Sue, Jane, and Alice share 213 paper clips equally among themselves. if Alice gives 24 paper clips to Sue, how many paper clips does Sue have altogether?

Answers

213/3 = 71
71 + 24 = 95 answer

In the same amount of time, James drove twice as far as Roger. Altogether, James and Roger drove 90km. Find the number of kilometres driven by each person.

Answers

Answer:

james drove 60 and roger drove 30

Step-by-step explanation:

90/3= 30= roger

90/3=30x2=60= james

james(60)+roger(30)= 90

Please help me with this (geometry)

Answers

Answer:

∠ 6 = 55°

Step-by-step explanation:

∠ 6 and 125° are same- side interior angles and sum to 180° , then

∠ 6 = 180° - 125° = 55°

The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and "colony-forming units (CFUs)" are counted after an incubation period. Here are data from two locations in a plant that processes 37,000 turkeys per day, taken on four days in the summer. The units are CFUs per cubic meter of air.

Day Day 2 Day 3 Day 4

Kill room 3175 2526 1763 1090

Processing 529 141 362 224

The spore count is clearly higher in the kill room. Give sample means and a 99% confidence interval to estimate how much higher the spore count is in the kill room?

Answers

Answer:

-611.031 < μd < 4260.031

Step-by-step explanation:

This is a matched pair design :

______Day1 Day 2 Day 3 Day 4

x1 Kill room 3175 2526 1763 1090

x2 Processing 529 141 362 224

First we obtain the difference, d ;

d = (x1 - x2)

d = 2646, 2385, 1401, 866

The mean difference, dbar = Σd/ n = 7298 / 4 = 1824.5

The standard deviation of difference,

Sd = √(Σx-dbar)²

Using calculator, Sd = 834.086

The 99% confidence interval :

Mean ± margin of error

dbar ± margin of error

Margin of Error = Tcritical * Sd/√n

Tcritical at 99%, df = n-1 ; df = 4-1 = 3

Tcritical = 5.84

Margin of Error = 5.84 * 834.086/√4 = 2435.53112

Confidence interval = 1824.5 ± 2435.53112

(-611.031 ; 4260.031)

Thank you guys for helping me !! Can you help me with this question ?

Answers

Answer:

(A). x² + y² - 4x + 6y - 3 = 0

Step-by-step explanation:

(x - 2)² + (y + 3)² = 4²

x² - 4x + 4 + y² + 6y + 9 - 16 = 0

x² + y² - 4x + 6y - 3 = 0

Which expression is equivalent to

Answers

Answer:

[tex]\frac{(x+2)}{(x-1)}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + x -2}{x^2 -2x+1}[/tex] =

[tex]\frac{(x+2)(x-1)}{(x-2)(x-1)}[/tex] =

[tex]\frac{(x+2)}{(x-1)}[/tex]

Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.​

Answers

Answer:

Consider the equation 3x + 2y = 12

Now, square both sides:

(3x + 2y)^2 = 122

=> 9x^2 + 12xy + 4y^2 = 144

=>9x^2 + 4y^2 = 144 – 12xy

From the questions, xy = 6

So,

9x^2 + 4y^2 = 144 – 72

Thus, the value of 9x^2 + 4y^2 = 72

Answered by GAUTHMATH

write the equation of the line that goes through points (2,-2) (4,-10)

Answers

Answer:

The slope-intercept form equation of the line that passes through (2, 4) and (4, 10) is y = 3x - 2.

Step-by-step explanation:

A particular strain of bacteria triples in population every 45 minutes Assuming you start with 50 bacteria in a Petri dish how many bacteria will there be in 4.5 hours

Answers

Answer:

4.5 hours in minutes = 270

Every 45 minutes, bacteria triples

You start with 50

Divide 270 (total time) by 45 (every time bacteria triples)

270/45 = 6

36,450 bacteria

HELP ASAP 10 POINTS BRAIN LIST THANKS AND 5 STAR BUT IF CORRECT

Answers

Answer:

3 cm^3

Step-by-step explanation:

The volume of a prism is given by

V = l*w*h

V = 1/2 * 3/2 * 4

V = 3 cm^3

Answer:

3 cm³

Step-by-step explanation:

V = L * W * H

V = (4 cm)(3/2 cm)(1/2 cm)

V = 12/2 * 1/2 cm³

V = 12/4 cm³

V = 3 cm³

Omg who can help me? Its due tomorrow

Answers

I could help ! But the light kinda makes some of the words hard to read

find the scale factor

Answers

Answer:

I think its 1.4

Step-by-step explanation:

if you divide 42 by 1.4 it makes 30 and if u multiply 30 by 1.4 it makes 42

Answer:

the scale factor is 7/5

Step-by-step explanation:

42/30=

42/30=

then you find a common factor between the two is 6, so you divide both sides of the fraction by 6 to get 7/5. and because they both are the same you know that they both have the same scale factor. Which is 7/5. I am not quite sure if you need to find the missing side length but in case you do multiply 40 by 7/5 so it looks like 40/1 x 7/5. 40 x 7 = 280. 280/5 = 56. so your side length is 56.

Other Questions
Please help me solve this question It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will be exactly 7.50 minutes in the record store find the missing length indicated. How many three digit numbers have a 2 as a tens digit?? A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shorts. Which inequality represents the maximum cost of each pair, s, the coach can buy? Why do the most successful students evaluate what they read and hear? 3) Write down the names of organs that participate in respiration I explain any two of of them. Since the rules cannot address all circumstances, the Code includes a conceptual framework approach for members to use to evaluate threats to compliance. Using this framework, Group of answer choices the first step is to discuss the threat with the client's management team. safeguards can be used to eliminate any threat. all threats must be completely eliminated. more than one safeguard may be necessary. there are 219 people at the science camp. 112 people are enrolled in the chemistry class, and 45 people are enrolled in the physics class. how many students are enrolled in both classes if 79 students are not enrolled in either of them? With Newtons mechanics came powerful machines, and eventually the steam engine, the motive force which reshaped the world by overturning agrarian society, spawning factories and stimulating commerce. . . .What is the meaning of the underlined term?individuals employed by Newtontools utilized by Newtonideas generated by Newtonengines built by Newton Por qu se eligi a Balboa para ser el cono de nuestra moneda nacional y no Pedrarias? 2(a)A car accelerates from 22ms^-1 to 43ms*-1 in 18.6 seconds.(a) Calculate the acceleration of the car.2(b)Find the distance covered by the car in 10 seconds.2(c) Find the velocity after 5 seconds. Compare and contrast a federalist system of government to a confederate system of government. Which one word can you use to replace liable to be called upon to account for his own actions Surgeons at Hospital A report that the mortality rate at the end of a one-year follow-up after a new coronary bypass procedure is 15%. At Hospital B, the surgeons report a one-year mortality rate of 8% for the same procedure. Before concluding that the surgeons at Hospital B have vastly superior skill, which of the following possible confounders would you examine?a. the severity (stage) of disease of the patients at the two hospitals at baselineb. the start of the one-year follow-up at both hospitals (after operation versus after discharge)c. differences in postoperative care at the two hospitalsd. equality of follow-up for mortalitye. all of the above if what happen dose not make us richer, we must welcom it if it .... When the length of each side of a square is increased by 5 cm, its area is increased by 895 cm2. Find the length of a side before the increase.The length of a side before the increase is... Which of the following observations constituted the strongest evidence against the existence of blending inheritance?a) Some characters are shaped by the environment (as well as heredity).b) Sometimes two parents have the same appearance, but they have one or more offspring with a different appearance.c) Characters acquired from the environment of the parents are often transmitted to the offspring.d) Individuals never have characters intermediate to their parents-- there is always complete "dominance" of one parent's character. Fiona is writing a paper about how to be successful in life. She has come across this text in the source "To Be Famous We Must Be Ambitious" by Rosetta Dunigan: The desire to be thought well of, to desire to be great in goodness, is in itself a noble quality of the mind. It is often termed ambition." Which sentence represents the best way Fiona can use this excerpt in her paper without plagiarizing? In a 100 metre race, the time of the winner was 10. 57 seconds and the time of the athel athlete who came third was 10. 64 seconds Write down a possible time for the athlete who came Second