1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ss7ja [257]
3 years ago
5

Find the rational approximation of √15.

Mathematics
1 answer:
ICE Princess25 [194]3 years ago
7 0

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.

_____

<em>Additional comment</em>

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.

You might be interested in
A pair of dice was rolled many times
Anvisha [2.4K]

Answer:

  6%

Step-by-step explanation:

Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...

  6/100 = 6%

3 0
3 years ago
#15: Which point in the number line below represents the number opposite the number -5 1/2?
densk [106]

Answer: D

Step-by-step explanation:

You have -5 1/2 to find the complete opposite all you have to do is take away the negative sign and find the number on the number line.

Good luck !

3 0
3 years ago
A car is driving northwest at vv mph across a sloping plain whose height, in feet above sea level, at a point nn miles north and
solong [7]
 <span>Northwest is 45 degrees north of west. If a car travels a distance x miles northwest, its northerly component gains x/sqrt(2) miles and its easterly component LOSES xsqrt(2)/ miles. 

Resultant height is h = 4500 + 100x/sqrt(2) - 75x/sqrt(2) = [25/sqrt(2)]x + 4500 
dh/dt = [25/sqrt(2)]dx/dt = [25/sqrt(2)]v </span>
7 0
3 years ago
Which statement describes the translation from the graph y=|x| to the graph y=|x+3|-4?
Pavel [41]

Answer:

B) shift 3 units left and 4 units down

8 0
3 years ago
Graph the following inequality and then select the correct graph below. x + y &lt; 1
saul85 [17]
First one!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11111111111111111111111111111111111111
7 0
3 years ago
Read 2 more answers
Other questions:
  • 35 a lesson(plus a 42 nonrefundable insurance fee per person)
    9·1 answer
  • Does anyone understand how to do this? Solve r4&lt;−5 or −2r−7 ≤ 3 . The solution is _or_
    6·1 answer
  • What is an equation of the line in slope-intercept form?
    9·1 answer
  • Does anyone know the answer to this? Needed asap
    6·1 answer
  • Please help I'm giving 24 points. What is 9% of 16?
    14·2 answers
  • During a math game, a team kept track of their answers. The following diagram describes the number of answers they got right to
    7·2 answers
  • If two-thirds of Sam's weekly income is $480, what is one-fourth of his weekly income?
    12·2 answers
  • NOT RIGHT, PLEASE TRY AGAIN
    11·1 answer
  • (Another one! just for fun!) if you answer all of them and if the answers are correct I will mark you as brainliest! good luck!
    5·2 answers
  • Please help me draw this and send it to me please I really need help
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!