Mathematics College

Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for
a.

Answers

Answer 1
Looks like the sequence might be

[tex]a_{n+1}=\dfrac{a_n+\frac2{a_n}}2[/tex]

Assume that [tex]\displaystyle\lim_{n\to\infty}a_n=L[/tex]. Then taking the limit of both sides, we have

[tex]L=\dfrac{L+\frac2L}2\implies L=\pm\sqrt2[/tex]

But in order for the sequence to converge, only one of these values must be true. Since [tex]a(1)=2>0[/tex], each successive number will also be positive, so the limit must be [tex]L=\sqrt2[/tex].
Answer 2
Final answer:

The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).

Explanation:

This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).

To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).

By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.

Therefore, the limit of the sequence as n tends to infinity is 0.

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Related Questions

If sinø= 4/7, what is cosø?

Answers

If sine (theta) = 4/7 then theta is found by:
arc sine (4/7) = theta
theta = 34.85 Degrees
cosine (34.85) = 0.82065




If y varies inversely as the square of x, and y=7/4/ when x=1, find y when x=3

Answers

y varies inversely as the square of x. So we can write the relation between x and y as:

[tex]y= \frac{k}{ x^{2} } [/tex]

where k is a constant of proportionality. It is given that y = 7/4 when x = 1.
Using these values, we can write:

[tex] \frac{7}{4}= \frac{k}{1} \\ \\ k= \frac{7}{4}[/tex]

So, now the equation in terms of x and y can be written as:

[tex]y= \frac{7}{4 x^{2} } [/tex]

We are to find y when x = 3. So we can write:

[tex]y= \frac{7}{4(9)}=\frac{7}{36} [/tex]

Thus, for x= 3 value of y will be 7/36

Q # 15 find the volume of the sphere

Answers

C IS THE CORRECT ANSWER


[tex]4 \times 5 \times 5 \times 5 \times \pi \times \frac{1}{3} = \frac{500\pi}{3} \\ = \frac{1570}{ 3} = 523.33[/tex]


good luck
The volume of a is found by using the formula;

Area = (4/3)πr³
Where r ⇒ radius of the sphere
            π=3.14

Area = (4/3)× 3.14 ×5³
        =523.33333 in³

To the nearest cubic, the  answer is 523 in³

triangle abc and triangle bcd have vertices A(-6, -7), B(-6, 4), C(2, -7), D(8, 4) what is the area in square units of trapezoid ABCD which is formed by the two triangles?

Answers

Try this solution/explanation:
According to the attached graph AC||BD, AB⊥BD and AB⊥AC.
|BD|=14; |AB|=11; |AC|=8.
All the details are in the attachment.

answer: 121 (sq.units).

what is the factored form of a fourth degree polynomial function with coefficients that has -3,1and 1+5i

Answers

Complex factors are
  (x +3)(x -1)(x -1 -5i)(x -1 +5i)

If you want the complex factors combined to a real factor, the factorization is
  (x +3)(x -1)(x² -2x +26)

limit approaches infinity of 3^n / 3n+1

Answers

Consider, pls, the suggested solution (see the attachment).

You scored the following grades on your first three math tests: 71, 78, 81. You only have one test remaining. What is the highest possible test average you can get?

Answers

Assuming the highest score for a test is 100.

Highest possible total scores for 4 tests = 71 + 78 + 81 + 100 = 330

Highest possible average score for 4 tests = 330 ÷ 4 = 82.5

Answer: 82.5
The answer is 82.5 Hope this helps

Complete the inequality. 9% ___ 0.4

Answers

9% is less than 0.4. 0.4 is really 4/10 which is 40% 40 is greater than 9 therefore 9% is less than 0.4! So your answer is 9%<0.4! I hope this helped!

A bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles. If three marbles are pulled out find each of the probabilities. Find the probability of pulling three green marbles out with replacement

Answers

[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]

The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]

Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles

So, total marbles = 25 marbles

Number of favorable or green marbles = 5 marbles

Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]

The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile/12482564/8273204d?utm_source=registration

Answers

The park is a total of 3+3 = 6 miles east of the mall, and 4+5=9 miles north of it. The Pythagorean theorem tells you the straight-line distance in miles is
  √(6² +9²) = √117 ≈ 10.8

The service plan for edith's cell phone charges her $29.50 a month for 300 minutes and 10¢ a minute for each additional minute over the 300 minutes. if edith uses 400 minutes this month, how much money will she have to pay?

Answers

No matter how much or little she talks, she'll pay at least $29.50 a month. This is for 300 minutes, meaning she's 100 minutes over the maximum (400 - 300).  We then multiply this amount by 0.10 and add it to 29.50. To write this as an equation, it would be 29.50 + x0.10 where x is the number of minutes over 300. In this case 29.50 + (100)0.10 = 29.50 + 10 = $39.50

What is the equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]

Answer:

Step 1: Choose (x1, y1). (6,3)

Step 2: x2= -1 y2=2

Step 3: 1/7

Step 4: b= 15/7

What is the equation of the line in slope-intercept form?

B) y=1/7x+15/7

Step-by-step explanation:

The bold numbers are the answers.

( I need mo pts)

write parametric equations of the line 2x+3y=11

Answers

To solve this problem you must apply the proccedure shown below:

 1. You have the following equation of the line given in the problem above: 2x+3y=11.

 2. Therefore, you have:

 x=t

 3. When you substitute x=t into  2x+3y=11, you obtain:

  2t+3y=11

 4. Now, solve for y, as below:

 3y=11-2t
 y=(11/3)-(2t/3)

 Therefore, the answer is:

 x=t
 y=(11/3)-(2t/3)
 

Answer:

C

Step-by-step explanation:

If youre doing the test ;)

Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
2,000
1 + e3 − t
where P(t) is the total number of people infected after t hours. What does 2,000 represent in equation?
A) the rate at which the disease spreads
B) the number of the people in the school
C) the expected change in number of people infected
Eliminate
D) the total number of people infected after t hours

Answers

B. The number of people in the school, in an exponential function, the first number should always be the initial amount.

Please Help: 25 Points!

Jeremy constructed this solid by combining two rectangular prisms and a square pyramid. What is the surface area of this figure?

Answers

Triangle area:
 A1 = (1/2) * (6) * (7)
 A1 = 21
 Rectangle area of the base:
 A2 = (14) * (6)
 A2 = 84
 Area of the posterior rectangle:
 A3 = (5) * (6)
 A3 = 30
 Area of the frontal rectangle:
 A4 = (6) * (2)
 A4 = 12
 Area of the rectangle parallel to the base:
 A5 = (8) * (6)
 A5 = 48
 Rectangle area located between posterior and front rectangles:
 A6 = (3) * (6)
 A6 = 18
 Area of the side walls of the figure:
 A7 = (14) * (2) + (3) * (6)
 A7 = 28 + 18
 A7 = 46
 Superficial area:
 A = 4 * A1 + A2 + A3 + A4 + A5 + A6 + 2 * A7
 A = 4 * 21 + 84 + 30 + 12 + 48 + 18 + 2 * 46
 A = 368
 Answer:
 A = 368 m ^ 2

Answer:

368

Step-by-step explanation:

Trip bought an icecream cone that is 4 inches tall with a radius of 2 inches

Answers

check the picture below.

keeping in mind that in 1 US ounce there are 1.805 in³, then in 35 ounces there are 63.175 in³, and in 3 oz there are 5.415 in³.

so the volume of the cone content alone will be, the 63.175 in³ when filled up, minus the topping and minus the 5.415 in³ from the cookie shell.

[tex]\bf \stackrel{\stackrel{volume}{\textit{when filled up}}}{63.175}~~-~~\stackrel{\stackrel{volume}{\textit{of hemisphere}}}{\cfrac{2\pi r^3}{3}} ~~-~~\stackrel{\stackrel{volume}{\textit{of cookie shell}}}{5.415} \\\\\\ \stackrel{\stackrel{volume}{\textit{when filled up}}}{63.175}~~-~~\stackrel{\stackrel{volume}{\textit{of hemisphere}}}{\cfrac{2\pi (2)^3}{3}} ~~-~~\stackrel{\stackrel{volume}{\textit{of cookie shell}}}{5.415}\\\\\\ 63.175-\cfrac{16\pi }{3}-5.415[/tex]

if a plane leave the ski resort every hour. the first plane leaves at 10 and the second plane leaves at 4 how man planes leave each day

Answers

Asked and answered elsewhere.
https://brainly.com/question/9934382

Two positive numbers have a difference of four and a product of 96 what are the numbers

Answers

Answer:
The two positive numbers are 12 and 8. 

Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4

The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96

So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12

Now we plug each these pairs into the first equation to see if they satisfy the equation.

96 - 1 = 95               24 - 4 = 20
95 > 4                      20 > 4

48 - 2 = 46               16 - 6 = 10
46 > 4                       10 > 4

32 - 3 = 29               12 - 8 = 4
29 > 4                       4 = 4

Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.

78 million in scientific notation

Answers

[tex]=78\cdot1,000,000=78\cdot10^6=7,8\cdot10^7[/tex]

Answer:

[tex]78\ million=7.80\times 10^7[/tex]

Step-by-step explanation:

A number N can be written in scientific notation as :

[tex]N=p{\circ}0\times 10^q[/tex]

Where

p is the any real number

q is any integer

Here, the given number is 78 million. Firstly, we must know meaning of 1 million.

Since, [tex]1\ million=10^6[/tex]

[tex]78\ million=78.0\times 10^6[/tex]

To convert the above number in scientific notation, we can shift the decimal before 8 such that,

[tex]78\ million=7.80\times 10^7[/tex]

Hence, this is the required solution.

The formula for finding the horsepower of a vehicle is: Horsepower = weight × ( velocity 234 ) 3 Weight is the total weight of the vehicle, driver and any passengers. Velocity is determined by the speed at the end of a quarter mile run. The newest hybrid auto weighs 2200 pounds and the driver is 180 pounds. At the end of the quarter mile run, the speed is 98 miles per hour.
What is the horsepower of the car rounded to the nearest whole number?

161 hp
175 hp
209 hp
417 hp

Answers

The answer is option 2
 Power = 175 hp
 The correct formula to calculate the power is:
 Power = weight * (speed / 234) ³
 Where the weight is that of the vehicle plus the driver's
 Therefore the calculation is as follows:
 Power = (2200 + 180) * (98/234) ³
 Power = 174.8266 hp
 Rounding ...
 Power = 175 hp

A right rectangular prism is shown. What shape best describes the cross section cut perpendicular to the base of a right rectangular prism? Parallelogram Trapezoid Rectangle Square

Answers

Since the cross section is constrained to be perpendicular to the base, the shape of it is constrained to be a ...
  Rectangle

_____
That rectangle may be a square, but is not required to be.

The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.

A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.

This is because a rectangular prism has six faces, and the base of the prism is one of those faces.

When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.

Since the base is a rectangle, the cross-section will also be a rectangle.

In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.

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John plays a game in which he throws a baseball java questions

Answers

Which statement correctly describes these electric field lines?

The expression 5(F-32) divided by 9 yes the Celsius temperature for a Fahrenheit temperature of F degrees C noon Fahrenheit temperature in Centerville was 86° what was the temperature in degrees Celsius

Answers

Substitute the given information into the formula and do the arithmetic.
  5(86 -32)/9 = 5(54/9) = 5(6) = 30

The temperature was 30 °C.

Answer:

30°C

Step-by-step explanation:

The following expression can be used to convert Farenheit degrees (°F) to Celsius degrees (°C).

°C = 5 . (°F - 32) / 9

If the temperature in Centerville is 86°F, we can replace this value in the previous expression to find its value in the Celsius scale.

°C = 5 . (°F - 32) / 9

°C = 5 . (86 - 32) / 9

°C = 5 . (54) / 9

°C = 270 / 9

°C = 30°C

stella received a package in the shape of rectangular prism. the box has a length of 21/2 feet, a width of 11/2 feet, and a height of 4 feet. stella wants to cover the box with wrapping paper. how much paper will sge need?

Answers

To get the amount of paper required to cover the box, we find the area of the box. 
The dimensions of the box are as follows:
length=21/2 ft
width=11/2 ft
height=4 ft

Area of the box is given by the formula:
SA=2lw+2lh+2hw
SA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)
SA=2(231/4)+2(42)+2(11/2×4)
SA=115.5+84+44
SA=243.5  ft²
Stella will need 243.5 ft²

Answer:

Step-by-step explanation:

To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²

Please please help me with this

Answers

n=1→an=a1 (first term)=16 (on the graph for n=1)→First term = 16
n=2→an=a2 (second term) = 4 (on the graph for n=2)→Second term = 4

ratio=(Second term)/(First term)=a2/a1=4/16
Simplifying the fraction dividing the numerator (4) by 4 and the denominator (16) by 4:
ratio=(4/4)/(16/4)→ratio=1/4

Answer: Option A. First term = 16, ratio = 1/4

3x < 12 what is this in the interval notation

Answers

Divide by 3 to find the solution.
  x < 4

Interval notation uses parentheses around the lower and upper limit of the interval. Here, the lower limit is -∞ and the upper limit is 4. The parentheses are round ( ) if the limits are NOT included as part of the interval. They are square brackets [ ] if the limits are included in the interval.

Here, since -∞ is not an actual number, we use the round bracket on that end of the interval. Since the solution space does not include 4, we use the round bracket on that end of the interval as well.

The solution to your inequality is ...
  (-∞, 4)

Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese. He learned an average of 130 words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words write a system of equations to represent this situation. Use x to represent Portugal, and y to represent Brazil.

Answers

Number of months that Lance lived in Portugal: x
Number of months that Lance lived in Brazil: y

Lance lived in Portugal and Brazil for a total of 14 months to learn Portuguese:
(1) x+y=14

He learned an average of 130 words per month when he lived in Portugal:
Number of words that Lance learned in Portugal: 130x

and an average of 150 new words per month when he lived in Brazil:
Number of words that Lance learned in Brazil: 150y

In total, he learned 1920 new words:
(2) 130x+150y=1920

Write a system of equations to represent this situation:
(1) x+y=14
(2) 130x+150y=1920

43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin

Answers

Set up
Let the dimes = d
Let the pennies = p
Let the quarters = q

Equations
You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters. 

p + d + p = 43          (1)
p = d                        (2)
p +10d +25q = 451  (3)

Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.

Put the results of 2 into 1.
2p  + q = 43                   (4)  
You need to modify equation 3 as well.
p + 10p + 25q = 451
11p + 25q  = 451           (5)

Solve the new equations
2p +  q = 43               (4)
11p + 25q = 451        (5)

Multiply 4 by 25
25(2p- + q = 43)
50p + 25q = 1075     (6)  Subtract (5) from (6)
11p + 25q = 451
39p = 624                        Divide by 39
p = 624 / 39
p = 16

Since the pennies and dimes are equal there are 16 dimes
p + d + q = 43
16 + 16 + q = 43
32 + q = 43
q = 11

Check
16 + 10*16 + 11*25 = ?
16 + 160 + 275  = ?
451 = ?

Nice problem. Thanks for posting.

which of the following best describes the English expression the product of two and a number minus eleven

Answers

That expression would usually be interpreted to mean
  2n -11

_____
It is somewhat ambiguous, so could also be interpreted to mean
  2(n -11)

Wording could be changed to remove the ambiguity, if one were interested in doing that.

Which number is not in scientific notation?

A: 1.10 ⋅ 103
B: 4.0 ⋅ 1016
C: 7.03 ⋅ 10−2
D: 350 ⋅ 102

Answers

the anser would be c fo it to be in scientific notation you have to have an exponet

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