The faces of a regular dodecahedron are what type of polygon?

Consider the rational number 3/11 a. What are the value of a and b in a divide by b when you use division to find the decimal fo

PolarNik [594]

Answer:

The decimal form of this rational number is $0.\overline {27}$ .

Step-by-step explanation:

a) Let $\frac{a}{b}$ a rational number. From statement we understand that $a$ represents the numerator, while $b$ corresponds with the denominator of the rational number. Hence, $a$ is 3 and $b$ is 11.

b) The decimal form is obtained by dividing $a$ by $b$ , we presented the step needed to determine the decimal form:

i) Multiply the numerator by 10:

Dividend: 30/Divisor: 11/Known result: 0. /Residue: N/A

ii) Multiply the divisor by 2 and subtract from the dividend:

Known result: 0.2 /Residue: 8

iii) Multiply the residue by 10:

Known result: 0.2 /Residue: 80

iv) Multiply the divisor by 7 and subtract from the residue:

Known result: 0.27 /Residue: 3

v) Multiply the residue by 10:

Known result: 0.27 /Residue: 30

vi) Multiply the divisor by 2 and subtract from the residue:

Known result: 0.272/Residue: 8

vii) Multiply the residue by 10:

Known result: 0.272 /Residue: 80

viii) Multiply the divisor by 7 and subtract from the residue:

Known result: 0.2727/Residue: 3

We have notice that the decimal form of $\frac{3}{11}$ is a periodical decimal number. Hence, we conclude that decimal form of this rational number is $0.\overline {27}$ .

3 0

3 years ago

yesterday a recycling center collected 679 cans.the center collected 225 fewer bottles than cans,and 178 fewer newspaper bundles

ahrayia [7]

276 because 679-225= 154 and 154-178=276

5 0

3 years ago

Evaluate the function at the given numbers( correct to six decimal places). Use the results to guess the value of the limit or e

netineya [11]

Answer:

Value of the limit is 0.5.

Step-by-step explanation:

Given,

$F(x)=\frac{e^x-1-x}{x^2}$

When,

$x=1,F(1)=frac{e^1-1-1}{1}=e-2=0.718281$

$x=0.5, F(0.5)=\frac{e^0.5-1-0.5}{(0.5)^2}=0.594885$

$x=0.1, F(0.1)=\frac{e^0.1-1-0.1}{(0.1)^2}=0.517091$

$x=0.05, F(0.05)=\frac{e^0.05-1-0.05}{(0.05)^2}=0.508438$

$x=0.01, F(0.01)=\frac{e^0.01-1-0.01}{(0.01)^2}=0.501670 \hfill (1)$

Correct upto six decimal places.

Now,

$\lim_{x\to 0}F(x)=\lim_{x\to 0}\frac{e^x-1-x}{x^2}$ $(\frac{0}{0})$ form, applying L-Hospital rule that is differentiating numerator and denominator we get,

$\lim_{x\to 0}F(x)$

$=\lim_{x\to 0}\frac{e^x-1}{2x}$ $(\frac{0}{0})$ form.

$=\lim_{x\to 0}\frac{e^x}{2}=\frac{1}{2}=0.5\hfill (2)$

Limit exist and is 0.5. That is according to (1) we can see as the value of x lesser than 1 and tending to near 0, value of the function decreases respectively. And from (2) it shows ultimately it decreases and reach at 0.5, consider as limit point of F(x).

8 0

3 years ago

19. At a boardroom meeting, the sales manager is happy to announce that sales have risen from $850,000 to $1,750,000 at a

klasskru [66]

The number of years it would take sales to reach $1,750,000 is 14.65 years.

<h3>What is the number of years?</h3>

The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:

Number of years : In (FV / PV) / r

Where:

FV = future level of sales - $1,750,000
PV = present level of sales = 850,000
r = rate of growth - 4.931998%

Number of years : In ($1,750,000 / 850,000) / 0.04931998

Number of years : In (2.06) / 0.04931998

Number of years : 14.65 years

To learn more about how to determine the number of years, please check: brainly.com/question/21841217

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3 0

2 years ago

What is the perimeter of a lawn that is 25 feet long and 20 feet wide?

drek231 [11]

Answer:

a. 90 ft

Step-by-step explanation:

20+20+25+25

4 0

3 years ago

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