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Reptile [31]
3 years ago
5

Hey can someone who is good at math tutor me on approximating square roots, you can put your SS or IG and I’ll send the meet cod

e!
Mathematics
2 answers:
Dafna1 [17]3 years ago
8 0

Answer:

  • use linear interpolation for a first approximation
  • use Newton's method iteration to refine the approximation

Step-by-step explanation:

Here's one way.

Multiply your number by an even power of 10 so that it is in the range 1–100. Call this power 2n. Call the scaled number N.

Make use of your knowledge of the squares of small integers to determine if the number you now have is a perfect square. If it is, the integer whose square it is is the square root of your scaled number. Skip to the Last Step.

__

Based on your determination in the previous step, identify the perfect squares on either side of your (scaled) number. If L² is the lower of these squares, and H² is the higher, compute the value ...

  X = (N -L²)/(H² -L²) +L  . . . .  linearly interpolated approximate root

You can use this as an approximation of √N. If it is not close enough for you, you can refine it by computing an iterated value:

  X ← (X² +N)/(2X)    or, equivalently,   X ← (1/2)(N/X +X)

The first of these approximations will get you within 6%; one iteration will get you within 0.2%. (<em>Each additional iteration will approximately double the number of accurate decimal places</em>.)

__

Last step: Using the integer or X (or iterated X) value, multiply by 10^-n to restore the appropriate scale of your root.

_____

<u>Example</u>:

  √199.6 ≈ ?

Multiply your value by 10^-2 to get N = 1.996 (with 2n=-2). The squares on either side are 1² = 1 and 2² = 4. Then the first approximation of the root is ...

  X = (1.996 -1)/(4 -1)+1 = 0.996/3 +1 = 1.332

One iteration of our formula gives ...

  X = (1.332² +1.996)/(2·1.332) = 1.415

Then the last step is to multiply this value by 10^-n = 10^1:

  √199.6 ≈ 14.15 . . . . root of 199.6 within 0.2%

_____

<em>Additional comments</em>

The iteration described above is also called the "Babylonian method".

If you're familiar with squares of integers between 2 and 20, then better linear interpolation accuracy can be had by doing the scaling so that N is between 4 and 400.

A method for developing square roots digit by digit, suitable for hand calculation, is described in some detail on the NIST web site. It can be found by doing a web search on "square root nist algorithm" without the quotes.

Volgvan3 years ago
7 0
It’s not letting me type what i’m trying to say
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Digiron [165]
The answer is g. 47.1

you use the formula
c= π d
then plug is 15 for d and you should get the answer
8 0
3 years ago
An employer with 500 employees gives out gives out 120 surveys but receives only 90 surveys completed by the employees. What are
leva [86]

Answer:

Population 120 given the survey, sample 90 who answered the survey.

Step-by-step explanation:

The entire amount of employees who even received the surveys at all was 120. Because the total number was 120, 120 is the population.

Only 90 out of 120 surveys were received, so 90 is the sample because it is part of 120.

Hope this helps :)

6 0
3 years ago
Find YQ if MQ = 3x-3 and YQ = 2x-6.
Alina [70]

Answer:

• Assume Q is a mid point of line MY

{ \underline{ \sf{ \:  _{l} M \:  \:  \:  \:  \:  \:  \:  \:  _{l} Q \:  \:  \:  \:  \:  \:  \:  \:  _{l}Y}}}

• Then, MQ = YQ

{ \rm{(3x - 3) = (2x - 6)}} \\  \\ { \rm{3x - 2x =  - 6 + 3}} \\  \\ { \boxed{ \rm{ \: x =  - 3 \: }}}

5 0
2 years ago
Identify one characteristic of exponential growth
Sonbull [250]

Answer:

Range is always greater than zero.

Step-by-step explanation:

An exponential growth means that the growth rate of a given quantity increases exponentially.

The graph of an exponential function is shown below.

From the above graph, it's quite clear that the range of the function is never negative.

Hence, one characteristic of exponential growth is that the range(y values on the graph) is always greater than zero.

7 0
3 years ago
A waiter's weekly salary can be modeled by the equation y = 0.2x + 300, where x is the amount spent by the customers in dollars
butalik [34]

Answer:

A. $100

Step-by-step explanation:

y = 0.2x +300

0.2(500) + 300 = 400

0.2(1000) + 300 = 500

3 0
3 years ago
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