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1 year ago

15

show that any binary integer is at most four times as long as the corresponding decimal integer. for very large numbers, what is

the ratio of these two lengths, approximately

1 answer:

makkiz [27]1 year ago

4 0

It has been shown that any binary integer is at most four times as long as the corresponding decimal integer.

<h3>What is the binary code?</h3>

The binary code is a method of expressing numbers that makes use of one and zero. It is the method in which the computer encodes data. The data must be transformed into zeros and ones before they can be encoded.

For instance, the number 8 is (1000)2. This shows that any binary integer is at most four times as long as the corresponding decimal integer.

Learn more about binary integer:brainly.com/question/14866711

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Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

2 years ago

Question 3<br> Find the equation of the line joining (-2,4) and (3,7)

otez555 [7]

Answer:

y = (3/5)x+26/5 or 5y = 3x+26

Step-by-step explanation:

Applying,

The equation of a line in two point form

(y₂-y₁)/(x₂-x₁) = (y-y₁)/(x-x₁)............... Equation 1

From the question,

Given: y₂ = 7, y₁ = 4, x₂ = 3, x₁ = -2

Substitute these values into equation 1

(7-4)/[3-(-2)] = (y-4)/(x+2)

3/5 = (y-4)/(x+2)

5(y-4) = 3(x+2)

5y-20 = 3x+6

5y = 3x+6+20

5y = 3x+26

y = (3/5)x+26/5

Hence the equation of the line is y = (3/5)x+26/5 or 5y = 3x+26

7 0

2 years ago

-3(x+0.6)=6(x+2.4)<br> Could you possibly show the work also?

kap26 [50]

Multiple-3(x+0.6) and 6(x+2.4) you will get -3x-1.8=6x+14.4 then you add -3x + 6x you will get -9x=14.4+1.8 you add 14.4+1.8 that will give you 16.2 then divide that by -9

3 0

3 years ago

Which of the following is equivalent to log50^7 rounded to three decimal places

Vitek1552 [10]

Answer:

11.886

Step-by-step explanation:

Given :

$log 50^7$

Applying formula

$log a^m=m log a$

So,

$7 log 50\\=7(1.698)\\=11.886$

Answer will be 11.886

3 0

3 years ago

X + 3 1/2 = 10 What is the value of x?

Evgen [1.6K]

Answer:

X = 6 1/2

Step-by-step explanation:

X is equal to 6 1/2 because, if you subtract 3 1/2 from 10 you will be left with 6 1/2.

3 0

2 years ago