All categories

3 years ago

Approximate the value of 44 (Square root) to the nearest hundreth

Mathematics

2 answers:

Svetlanka [38]3 years ago

5 0

I assume that calculators are not allowed, perhaps not even paper and pencil.

With paper and pencil, there is an algorithm to find the square-root of any number accurate to as many digits as we wish. Please post if that is the case.

Without calculator, pen and pencil, we resort to mental arithmetic. Someone with a little practice can memorize or calculate the square of all numbers up to 100, or as many as one can.

Here we can take advantage of exactly the property suggested by Xisca... that is, sqrt(44)=2sqrt(11), which reduces the calculation to more accuracy with a lesser knowledge of the squares of numbers.

As a first approximation, we know that 33*33=1089, or 3.3*3.3=10.89, which is already very close to 11.

Thus a first approximation to sqrt(44)=2sqrt(11)=2*3.3=6.6 (approximately).

To refine the calculation of sqrt(11), we use Newton's approximation, namely

a better approximation is given by 3.3 + (11 - 3.3^2) / (2*3.3) = 3.3+0.11/6.6 = 3.3+1/60

which gives

sqrt(44) = 2(3.3+1/60) = 6.6+1/30 = 6.6333,

actually accurate almost to the nearest 1/10000.

All of the above can be done mentally

For those who need help with rounding to the nearest hundredth (0.01), we drop digits AFTER the 2nd decimal, namely *.**33. If the first digit dropped is 5 or more, add one to the last digit retained, otherwise, retain only the two digits after the decimal. In this case, the first digit dropped is 3, so it will simply be dropped. The final answer is then 6.63, to the nearest hundredth.

Roman55 [17]3 years ago

4 0

Answer:

The answer is 6.63. Good luck learners!

Step-by-step explanation:

You might be interested in

There were 72 runners to start a race. in the first half of the race, 13 of them dropped out. in the second half of the race, 23

Mariana [72]

All you would need to to is do 13+23= 33 to get the total amount of people who dropped out, then do 72 ( the number in the beginning and subtract 33 from it because those are the people who dropped out so 72-33=39. 39 people finished the race.

8 0

3 years ago

Find the equation of the straight line passing through the points (4; 2) and (2; 4).

Alecsey [184]

Use point-slope form.

But first let's find the slope.

(4, 2), (2, 4)

m = y2-y1/x2-x1

m = (4 - 2)/(2 - 4)

m = 2/-2

m = -1

So this is the slope, now we can plug this into the equation along with any point.

y - y1 = m(x - x1)

Where y1 is the y-value of the point, x1 is the x-value, and 'm' is the slope.

Let's plug in point (4, 2):

y - 2 = -1(x - 4)

This can be one of your options.

Distribute -1:

y - 2 = -x + 4

Add 2 to both sides:

y = -x + 6

This can be another of your options.

Add 'x' to both sides:

x + y = 6

This can be another of your options.

8 0

3 years ago

Read 2 more answers

FILL IN THE BLANK

IgorLugansk [536]

Now, we know that he's charging $12 per session to each of his students, and he has 14 students currently, so his revenue is just 14 * 12 or 168 bucks.

now, let's take a peek as the session price goes up in jumps of 2, from 12, to 14, 16, 18 and so on, as each jumps happen, the students drop by 1, from 14, to 13, to 12 and so on.

$\bf \begin{array}{ccccllll}
\stackrel{increase}{x}&\stackrel{new}{price}&students&\stackrel{revenue}{y}\\
------&------&------&------\\
0&12&14&168\\
1&14&13&182\\
2&16&12&192\\
3&18&11&198\\
\boxed{4}&20&10&\boxed{200}\\
5&22&9&198\\
6&24&8&192\\
7&26&7&182\\
8&28&6&168\\
..&..&..&..
\end{array}$

notice, the revenue starts off at 168, goes up up, reaches 200 bucks and then starts to drop back down.

thus, that means the U-turn or vertex of that revenue function is at 4,200, namely h = 4, and k = 200

$\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\
x=a(y-{{ k}})^2+{{ h}}
\end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\
\stackrel{c(x)}{y}=a(x-\stackrel{h}{4})\stackrel{k}{+200}
\\\\\\
\textit{now, we also know that }
\begin{cases}
x=2\\
y=192
\end{cases}\implies 192=a(2-4)^2+200
\\\\\\
-8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a
\\\\\\
$

$\bf therefore\qquad \stackrel{ c(x)}{y}=-2(x-4)^2+200\impliedby \textit{let's expand that}
\\\\\\
y=-2(x^2-8x+16)+200\implies y=-2x^2+16x-32+200
\\\\\\
\stackrel{y}{c(x)}=-2x^2+16x+168$

3 0

3 years ago

Read 2 more answers

Refrigerators-’N-More sells appliances with a 20% markup from their purchase cost. Alice makes a 5% commission rate on her daily

Brut [27]

The price of the washer and the dryer set is $720.

The commission earned by Alice is $36.

<h3>What is the price of the washer and dryer set ? </h3>

Percentage can be described as a fraction an amount expressed as a number out of hundred. Percentage is a measure of frequency.

Price after the mark up = ( + percentage mark up) x cost price

(1 + 0.20) x $600 = $720

Commission earned by Alice = 5% x 720 = $36

To learn more about percentages, please check: brainly.com/question/25764815

#SPJ1

3 0

2 years ago

Determine the value of x in the diagram.<br> 112<br> x<br> <<br> 68<br> 112<br> =

nasty-shy [4]

Answer:

The value of x is 68, all the angles in a parrelelogram equal 360, 68 + 112 + 112 + x = 360, all the angles are 292, and subtracted from 360 you get 68

Step-by-step explanation:

3 0

3 years ago