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stepladder [879]
3 years ago
12

Is 0.12112111211112 a rational number ?

Mathematics
2 answers:
Elden [556K]3 years ago
8 0

Answer:  The given number is NOT rational.

Step-by-step explanation:  We are given to check whether the number 0.12112111211112 . . . a rational number or not.

We know that

if the digits after the decimal in a number are either repeating or terminating, then the number is rational.

The given number is

x=0.12112111211112 . . .

We can see that the digits after the decimal are neither repeating nor terminating.

Therefore, the given number is NOT rational.

tangare [24]3 years ago
5 0
No, it is not rational because it is not repeating and it is never ending...so it cant be made into a fraction
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A retangle has an area of 30 square meters and a perimeter of 34 meters what are the dimensions of the retangle
s344n2d4d5 [400]

Answer: Length = 15 meters

Width = 2 meters

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where l = length

w = width

Therefore,

2l + 2w = 34 ...... i

l × w = 30 ........ ii

From equation i

2l + 2w = 34

Divide through by 2.

l + w = 17 ...... iii

Then, l = 17 - w ........ iv

Put equation iv into ii

l × w = 30

(17 - w) × w = 30

17w - w² = 30

w² - 17w + 30 = 0

w² - 15w - 2w + 30 = 0

w(w - 15) - 2(w - 15) = 0

(w - 2) = 0

w = 0 + 2 = 2

w - 15 = 0

w = 0 + 15 = 15

Length = 15 meters

Width = 2 meters

6 0
3 years ago
What is 286 over 465 in simplest form?
Sholpan [36]
\frac{286}{465
}
7 0
3 years ago
Which graph represents the function?<br><br> f(x)=2x√+1
gogolik [260]

Answer:

the 3rd one

Step-by-step explanation:

I just think

4 0
2 years ago
Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y
DiKsa [7]

The area of the surface is given exactly by the integral,

\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx

We have

y(x)=\dfrac15x^5\implies y'(x)=x^4

so the area is

\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the i-th subinterval are, respectively,

\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2

r_i=\dfrac{5-0}{10}i=\dfrac i2

with midpoint

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4

with 1\le i\le10.

Over each subinterval, we interpolate f(x)=\sqrt{1+x^8} with the quadratic polynomial,

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

Then

\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It turns out that the latter integral reduces significantly to

\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)

which is about 651.918, so that the area is approximately 651.918\pi\approx\boxed{2048}.

Compare this to actual value of the integral, which is closer to 1967.

4 0
3 years ago
Write the fraction decimal and percent for the shaded area below
Nastasia [14]

Answer:

Decimial: 0.47

Percent: 47%

Fraction: 47/100

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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