Find the rational approximation of √15.

Answers

Answer 1

9514 1404 393

Answer:

  1921/496

Step-by-step explanation:

There are many rational approximations to √15, some better than others.

A linear approximation is often used:

  √15 ≈ 3 +(15-3^2)/(4^2-3^2) = 3 6/7 = 27/7

That can be refined by one iteration of the Babylonian method of determining the root:

  √15 ≈ (27/7 +15/(27/7))/2 = (3 6/7 +3 8/9)/2 = 3 55/63 = 244/63

This value is equivalent to the root rounded to 4 decimal places.

__

Another iteration of the Babylonian method gives the approximation ...

  √15 ≈ 119071/30744, equivalent to the root rounded to 9 decimal places.

__

The approximation 1921/496 is the best approximation that has a denominator under 1000.

_____

Additional comment

Successive rational convergents of the continued fraction approximation of √15 can be found as ...

  a'/b' = (3a +15b)/(a +3b)

This method adds approximately one more good decimal place per iteration.

__

Successive rational approximations can be found using the Babylonian method (Newton's method iteration) as ...

  a'/b' = (a² +15b²)/(2ab)

This method has "quadratic" convergence. It approximately doubles the number of good decimal places with each iteration.

You can use 3/1, 4/1, or 27/7 to begin either of these iterations.


Related Questions

Please anyone help please I’m stuck with this question please help please ASAP show work Too

Answers

This is the flip side of the previous one I answered. The range is the set of all y-values or outputs. Since you can only spend increments of $1.25, you cannot have all the numbers from 12 to 0 in your range.

The range is 12 dollars minus all possible increments of 1.25, until you can’t buy any more candy.

12
12-1.25 = 10.75
10.75-1.25 = 9.50
And so on.

The answer is D.

Which best describes a compass tool?
a. a plastic straightedge with equidistant units in inches or centimeters
b. a long wooden tool with a ruler on one side and a sliding holder on the other
c. a metal instrument with two legs-one with a point and one for a pencil
d. a curved plastic tool in the shape of the letter D with markings on the face

Answers

Answer:

I believe its c

Step-by-step explanation:

just for reference I can't guarantee

The best described compass tool is a metal instrument with two legs-one with a point and one for a pencil option (c) a metal instrument with two legs-one with a point and one for a pencil.

What is a magnetic field?

The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.

It is given that:

A tool is a compass tool which is an indicating the north direction.

As we know,

The magnetic field is defined as the field the magnetic materials generate.

A metal object with two legs, one for a pencil and one with a tip.

Thus, the best describes compass tool is a metal instrument with two legs-one with a point and one for a pencil option (c) a metal instrument with two legs-one with a point and one for a pencil.

Learn more about the magnetic field here:

brainly.com/question/14848188

#SPJ2

What is the expanded form of the number 34.576?

3 x 10 + 4 x 1 + 5 x 0.1 + 7 x 0.01 + 6 x 0.001
3 x 10 + 5 x 1 + 4 x 0.1 + 6 x 0.01 + 7 x 0.001
4 x 10 + 3 x 1 + 7 x 0.1 + 5 x 0.01 + 6 x 0.001
5 x 10 + 4 x 1 + 3 x 0.1 + 7 x 0.01 + 6 x 0.001

Answers

Answer:

its the first one I think

Help ASAP I'm in school need help​

Answers

Answer:

B

Step-by-step explanation:

this is the answer to this question

Help due tomorrow…..

Answers

Answer:

So the answer is H

Step-by-step explanation:

They could be situated as

x y z

in which case xy 5 and yz = 3

The total would be 8.

if they are situated like this

x z y

then xy = 5 and yz = 3 but its going the opposite way.

5 - 3 = 2

Helllllllllllppppppppp

Answers

-1/2 because slope is the rise over the run. If you count on the grid from one point on the line to another you go up one and 2 to the left meaning the slope is 1/2, buttttt when the line decreases going to the right, it has a negative slope so you just add a - sign in front

Squere root of 23 is between which two consecutive integers ?

Answers

Answer:

4 and 5

Step-by-step explanation:

4^2 = 16

5^2 = 25

i need helpppp Blake and josh are both saving money for a new bike, the ratio of blake saving 3:1 if they have saved 400$ how much has each boy saved

Answers

Answer:

Blake = $300

Josh = $100

Step-by-step explanation:

3:1

3(00) / 1(00)

300   /   100

Chow,...!

Hey guys answer for points!
Question: 7 = x + 2x - 5 - 5x
Please include your steps and make sure it is accurate! Brainiest for correct answer/good answer!

Answers

Answer:

please mark me brainliest

Step-by-step explanation:

7=3x-5-5x

7=3x-5x-5

7=-2x-5

7+5=-2x

12=-2x

x=12/-2

×=-6

Answer:

-6 = x

Step-by-step explanation:

7 = x + 2x - 5 - 5x

~Combine like terms

7 = -2x - 5

~Add 5 to both sides

12 = -2x

~Divide -2 to both sides

-6 = x

Best of Luck!

What is the opposite of 8.5?

Answers

Answer:

-8.5

Step-by-step explanation:

If I'm not mistaken this is true because the opposite of a whole number (That isn't 0) is always the negative

2(x-1)(x+2)[tex]2(x-1)(x+2)[/tex]

Answers

[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]

I assume the following equation is the question you asked.

[tex] \rightarrow \sf \: 2(x - 1)(x + 2)[/tex]

If yes, these are the following are the steps to reach your answer :-

[tex]\sf \: 2(x - 1)(x + 2)[/tex]

Use the distributive property to multiply 2 by x - 1.

[tex] \sf \: \left(2x-2\right)\left(x+2\right) [/tex]

Apply the distributive property by multiplying each term of 2x - 2 by each term of x + 2.

[tex] \sf \: 2x^{2}+4x-2x-4 [/tex]

Combine 4x and - 2x to get 2x.

[tex] \boxed{ \bf \: 2x^{2}+2x-4 }[/tex]

=> The answer will be 2x² + 2x - 4.

_________

Hope it helps.

▄▀▄▀▄ RainbowSalt2222 ▄▀▄▀▄

Rotate ΔCAR if C(-1,-4), A(2,3), R(-3,-2) 180° about the origin

Answers

Answer:

C(1,4) , A(-2,-3), R (3,2)

Step-by-step explanation:

the formula thing for rotating 180° about the origin is (x,y) -> (-x,-y)

this doesn't mean make the number negative, but make it the opposite if that makes sense

e.g. F(2,-4) -> F(-2,4)

Choose each correct statement.

1. Sin A = b/c
2. Cos A = b/c
3. Tan A = b/8
4. M 5. m 6. Sin B= 8/c
7. Cos B = b/c
8. Tan B = b/8
9. Sin A = 8/c
10. Tan A =8/b
11. Sin B = b/c
12. Sin A = Cos A
13. Sin A = Cos B

Answers

Answer:

Step-by-step explanation:

Sin(A) = 8/c    Not correct.Cos(A) = b / c CorrectTan(A) = b / 8 Correct and Makes no sense to meSin(B)= b/c     CorrectCos(B) = 8/c   Not correctTan(B) = b/8   CorrectSee (A)           Not CorrectTan(A)  See 3 Not CorrectSee 6Sin(A)=Cos(A) Not correctSin(A) =Cos(B) Correct

2,3,5,6, 8,11,13          Are correct.

What is the GCF of 55,40,80?

Answers

5 because 5x11 = 55, 5x8 = 40, and 5x16 = 60

Answer:

Take help of GCF of two or more numbers Calculator to calculate Greatest Common Factor of 55, 80, 40 i.e. 5 largest number that divides all numbers equally.

How can I work this problem in adding integers with counters 5 + (-7)

Answers

[tex]\\ \rm\longmapsto 5+(-7)[/tex]

[tex]\\ \rm\longmapsto 5-7[/tex]

[tex]\\ \rm\longmapsto -2[/tex]

Note:-

(-)(-)=(+)(+)(-)=(-)(-)(+)=(-)(+)(+)=(-)

Answer:

is -2

Step-by-step explanation:

because we have (-)+(+) is - so our answer is in minus

X= (2a+5)² Y= (a-3)²
X+Y??

Answers

Answer:

X = (2a + 5)^2 = 4a^2 + 20a + 25

Y = (a-3)^2 = a^2 - 6a + 9

4a^2 + 20a + 25 + a^2 - 6a + 9

X + Y = 5a^2 + 14a + 34

Question 4 of 30
Find the probability of rolling two dice and getting 2's on both.
.
A. 1/60
B. 1/30
C. 1/2
D.1/36
HELP ASAP

Answers

Answer:

1/36

Step-by-step explanation:

prob of each dice is 1/6

=1/6 * 1/6

10-7+12 dived (2^3-6) May you answer hope this will help

Answers

Answer:

7.5

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

4. Your first six-month auto insurance premium was $729.00. Based on your good
driving record, your renewal premium is $648.81. What percent decrease did you see
in your premium? (2 points)
I

Answers

Answer: 11%

Step-by-step explanation:

729-648.81=80.10

What percent is 80.10 of 729

%/100 = is/of (this may help you)

X/100 = 80.10/729 (cross multiplication)

(80.19*100)/729 =

11%

6.
Evaluate the function rule for the given value.

f(x)= 3× for x= -4
A. –12
B. 1/81
C. –64
D. 1/243

Answers

Answer:

B. 1/81

Step-by-step explanation:

f(-4) = 3(-4)

f(-4) = -12

Hope that helps.

-12,1/243,-64 or 1/81

1/81 would be the correct answer to the equation hope this helps

evaluate the function rule for the given value.

f(x)=3^x for x=-4

-----

f(-4) = 3^(-4)

---

 

f(-4) = (1/3)^4

---

f(-4) = 1/81

Which of the following graphs represents the equation y-2 = 3(x - 1)?

A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

Answer:

y+2= 3(x-1)

y=3x-3-2

y=3x-5

The y - intercept is at (0,-5)

The only graph that has the y-intercept at -5 is C

Answer is =C

Hope it is helpfully.Thankyou.Have a nice day.

Answer:

GRAPH B!!!

Step-by-step explanation:

hope this helps :)

Find the midpoint between 3pi and pi

Answers

Answer:  2pi

Explanation:

We apply the midpoint formula like so

C = (A+B)/2

C = (3pi+pi)/2

C = (4pi)/2

C = 2pi

This means 2pi is exactly halfway between pi and 3pi

This is similar to saying that 2 is halfway between 1 and 3. Think of the "pi" as "1pi", and we're effectively just looking at the coefficients.

the ground line is 12 cm and width is 10 cm find out the area of the ground and parameter of the ground​

Answers

Answer:

2(x+6) + 2(x) =40

2x +12+2x=40

4x+12=40

4x=28

x=7

Now to find area it is LxW

7x13=91

So the area of the rectangle is 91 meters squared

Step-by-step explanation:

Answer:

Area=120[tex]cm^{2}[/tex]

Perimeter =44[tex]cm^{2}[/tex]

Step-by-step explanation:

area=length(l)*width(w)    

      =12*10                        

     =120[tex]cm^{2}[/tex]

perimeter=2(length+width)

                =2(12+10)

                =2*22

               =44[tex]cm^{2}[/tex]

The population of the city is 5040000 and the rate of growth is 2.5℅ per annum. Find the population After one year.​

Answers

Answer:

5,166,000

Step-by-step explanation:

grown population after 1 year=2.5/100×5040000

which is 126,000

total population after 1year=5040000+126000

which is 5166000

Complete the table for the given rule. Rule: y x/4 (fraction)

x y
fill in | 4
fill in | 2
fill in | 9​

Answers

Answer:

16, 8, 36

Step-by-step explanation:

x = 4y

y = 4, x = 16

y = 2, x = 8

y = 9, x = 36

5) What is the result of subtracting (x2 + 3x)from the polynomial (-2x2 + 4x + 5)?​

Answers

Answer:

- 3x² + x + 5

Step-by-step explanation:

- 2x² + 4x + 5 - (x² + 3x) ← distribute by - 1

= - 2x² + 4x + 5 - x² - 3x ← collect like terms

= - 3x² + x + 5

Hi

Golden rule to know by heart : you can only add or substract element of the same kind.

so X^2 with X^2 , X with X , numbers with numbers...

exemple : 2X^2 +3X^2 = 5X^2

but 5X^2 -3X remains that way as 5X^2 is a " X^2" and " 3X" is a " X" so I can't substract two elements of different kind.

Now you have to translate what is ask of you into a calculus.

so : you have

A ) ( 2x^2+4x +5) - ( x^2+3x)

Math is a sport of the mind. You will only progress and become stronger if you train.

So I let you have a shot. beware of signs rules. If you still have trouble, ask in comment section..

please help me!!!!!!!!

Answers

Answer:

$84,320

Step-by-step explanation:

Simple any income above $9001 is taxed at 5.4%

So take 5.4% of $80,000 ($4,320) and add it back in

SO... $84,320

Given that measure angle AEB equals 4x+1 and measure angle CED equals 3x, determine the missing measures.

Answers

<AEB=<CED

[tex]\\ \rm{:}\dashrightarrow 4x+1=3x[/tex]

[tex]\\ \rm{:}\dashrightarrow 4x-3x=1[/tex]

[tex]\\ \rm{:}\dashrightarrow x=1[/tex]

Now

[tex]\\ \rm{:}\dashrightarrow 3x=3(1)=3[/tex]

[tex]\\ \rm{:}\dashrightarrow 4x+1=4(1)+1=5[/tex]

Answer:

AEB = -3

CED = -3

Step-by-step explanation:

We can make an equation and solve for x.

4x + 1 = 3x

~Subtract 1 to both sides

4x = 3x - 1

~Subtract 3x to both sides

x = -1

Now we can substitute that value of x into both angles.

4(-1) + 1 = -4 + 1 = -3

3(-1) = -3

Best of Luck!

can someone help me with this please​

Answers

NOW FROM THE TOP MAKE IT DROP, THATSA N WAP WAP WAP.

A rectangle has an area of 21 square centimeters. Which of the following could be the rectangle's length and width? Area = length x width Choose all answers that apply

Answers

Width=1cm and length=21cm or width=3cm and length=7cm.
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