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
sineoko [7]
3 years ago
15

Estimate square root of 90 to the nearest hundredths place

Mathematics
2 answers:
Vladimir [108]3 years ago
5 0
The method for doing this will depend on the required accuracy of your estimate.

Using linear approximation between 9^2 = 81 and 10^2 = 100, the estimate is
.. 9 +(90-81)/(100-81) = 9 +9/19 ≈ 9.47

Using one round of "Babylonian Method" on the above estimate,
.. (9.47 +90/9.47)/2 ≈ 9.486 ≈ 9.49 . . . . . . actually accurate to the hundredths place

Using derivatives and linear approximation,
.. √90 ≈ √81 +1/(2√81)*(90-81) = 9.50
or
.. √90 ≈ √100 +1/(2√100)*(90 -100) = 9.50

netineya [11]3 years ago
3 0
Assume no calculators, no paper, no pen, all in the head.

90=9*10, so 9.5 is a good approximation.
in fact, 9.5=9*10+0.562=90.25
We will use this initial estimate x0=9.5 to improve to accurate to the hundredth (and more).

Newton's method gives a better estimate by the following formula (all done in the head)
x1=x0-(x0^2-90)/(2*x0)
=9.5-(90.25-90)/(2*9.5)
=9.5-0.25/19
=9.5-0.013125   [in the head, 0.25/19=0.25/20+5%=0.125+0.0625=0.013125]
=9.486875
=9.49  (to the hundredth)

Exact value = 9.48683298... 
You might be interested in
At the party, 6/16 of the guest were playing games and 3/8 of the guest were singing.Pat said that the number of guest were play
ziro4ka [17]
Yes.  6/16 simplifies to 3/8, which is the same amount of people singing.
8 0
3 years ago
Read 2 more answers
Jonah's house and his grandparents house or 8046.7 I 2 m apart what is this distance in miles
Free_Kalibri [48]

Answer:

1.523

Step-by-step explanation:

1 mile equals 5280 feet

7 0
3 years ago
Given the following data set: 111, 122, 133, 149, 126, 117, 101, 121
Ivanshal [37]

Im pretty sure your answer is gonna be A) 15.5 .

5 0
3 years ago
In planning her​ retirement, Liza deposits some money at 3.5​% ​interest, with twice as much deposited at 4.5​%. Find the amount
KATRIN_1 [288]

a = amount deposited at 3.5%

b = amount deposited at 4.5%

we know that "b" is twice as much as "a", thus b = 2a.

\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.5\% of a}}{\left( \cfrac{3.5}{100} \right)a}\implies 0.035a \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.5\% of 2a}}{\left( \cfrac{4.5}{100} \right)2a}\implies 0.045(2a)

we also know that whatever "a" amount is, their sum is 2250, thus

0.035a+0.045(2a) = 2250\implies 0.035a+0.09a=2250\implies 0.125a=2250 \\\\\\ a=\cfrac{2250}{0.125}\implies \boxed{a=18000}~\hspace{10em}\boxed{\stackrel{2a}{b=36000}}

5 0
2 years ago
Marilyn and Vanessa earn service points for every hour they volunteer at the local library. Marilyn
Tanzania [10]

<em>Answer:</em>

<em>200 points Vanessa</em>

<em>Step-by-step explanation:</em>

<em>M = 165%V</em>

<em>330 = 165V/100</em>

<em>33000 = 165V</em>

<em>V = 33000 : 165</em>

<em>V = 200 points Vanessa</em>

7 0
3 years ago
Read 2 more answers
Other questions:
  • Combine like terms and write an equivalent expression with fewer terms for 4x+3x.
    15·1 answer
  • Name a pair of fractions that use the least common denominator and are equivalent to 9/10 and 5/6
    9·2 answers
  • A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps
    5·1 answer
  • the number of students attending college in 2015 was 20.2million. this number expected to increase to 23.1 million by the year 2
    11·1 answer
  • Person A can paint the neighbors house 2 times as fast as Person B. The year A and B worked together, it took them 2 days. How l
    15·1 answer
  • What is conversion Factor that you can use to convert gallons to pins how did you find it?
    12·1 answer
  • Write a function to represent the set of ordered pairs.<br><br> {(2, -2), (3, 8), (4, 22), (5, 40)}
    11·1 answer
  • Which is the graph of f(x) = 2(3)^x​
    9·1 answer
  • Need Help On This Question !!! (Select All That Apply)
    9·1 answer
  • HURRY
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!