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

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.

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%

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.

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]

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

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

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

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 ▄▀▄▀▄

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

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 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

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.

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 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

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

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!

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,...!

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.

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!

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)

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

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

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.

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..

can someone help me with this please​

Answers

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

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

Help ASAP I'm in school need help​

Answers

Answer:

B

Step-by-step explanation:

this is the answer to this question

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

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

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 :)

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