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3 years ago

Estimate the square root of 24 to the nearest hundredth

Mathematics

1 answer:

fenix001 [56]3 years ago

3 0

9514 1404 393

Answer:

√24 ≈ 4.90

Step-by-step explanation:

The square root can be estimated using a linear interpolation between the perfect squares on either side of the number of interest.

4² = 16

5² = 25

So, √24 can be estimated to be ...

(24 -16)/(25 -16) +4 = 8/9 +4 = 44/9 ≈ 4.8888...

This estimate can be refined by doing one iteration of the Babylonian method. That averages the current guess with the value obtained by dividing 24 by that guess.

√24 ≈ (44/9 +24(9/44))/2 = 4 89/99 ≈ 4.898989...

√24 ≈ 4.90

_____

A calculator gives the root as approximately 4.89897948557. Rounded to hundredths, that is 4.90.

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A wire 31ft long is stretched from the top of a flagpole to the ground at a point of a flagpole to the ground at a point 15ft fr

Nat2105 [25]

Answer:the height of the flagpole is 27.12 ft

Step-by-step explanation:

The wire makes an angle with the ground and forms a right angle triangle with the flag pole. The length of the wire represents the hypotenuse of the right angle triangle. The height of the flag pole and the ground distance from the wire represents the adjacent and opposite sides respectively.

To determine the height of the flagpole, x we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

31² = x² + 15²

x² = 961 - 225 = 736

x = √736. = 27.12 ft

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3 years ago

Suppose that the functions r and a are defined for all real numbers x as follows. r(x)=2x-1 S(x)=5x write the expressions for (r

NeTakaya

$\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}$

<h2>Explanation:</h2>

In this exercise, we have the following functions:

$r(x)=2x-1 \\ \\ s(x)=5x$

And they are defined for all real numbers x. So we have to write the following expressions:

First expression:

$(r-s)(x)$

That is, we subtract s(x) from r(x):

$(r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}$

Second expression:

$(r\cdot s)(x)$

That is, we get the product of s(x) and r(x):

$(r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}$

Third expression:

Here we need to evaluate:

$(r+s)(-2)$

First of all, we find the sum of functions r(x) and s(x):

$(r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1$

Finally, substituting x = -2:

$(r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}$

<h2>Learn more: </h2>

Parabola: brainly.com/question/12178203

#LearnWithBrainly

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3 years ago

The diameter of cold virus cell is about 3x10-9 meter,and the diameter of a streptoccus bacterium cell is about 9x10-7 meter. Wh

Archy [21]

Here we need to compare the orders of magnitude of two measures.

We will see that the bacteria is<em> 300 times larger than the virus.</em>

We know that:

The diameter of the virus-cell is:

$D_v = 3 \cdot 10^{-9} m$

The diameter of the bacteria cell is:

$D_b = 9 \cdot 10^{-7} m$

So, to compare them, first notice that both are in the same units, meters, so we only need to <u>compare the numbers</u>.

Is common sense to identify the one with the largest exponent as the largest number, and the largest exponent is -7, thus <u>the bacteria should be the larger one.</u>

But let's prove this with math, remember the property:

$\frac{a^n}{a^m} = a^{n - m}$

Let's take the quotient between the diameters and see what we get, I will use the <u>diameter of the bacteria in the numerator</u>, thus <u>if the quotient is larger than 1, it would mean that the bacteria is greater and by how much.</u>

$quotient = \frac{ 9 \cdot 10^{-7} m}{ 3 \cdot 10^{-9} m} = \frac{9}{3} \cdot 10^{-7 + 9}\\\\= 3*10^2$

So we can say that the bacteria is 3*10^2 = 3*100 = 300 times larger than the virus.

If you want to learn more, you can read:

brainly.com/question/4953281

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Dima020 [189]

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