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mamaluj [8]
3 years ago
14

Which number produces an irrational number when added to 0.4

Mathematics
2 answers:
erastovalidia [21]3 years ago
6 0

Answer:

0.31311311131111....

Step-by-step explanation:

We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,

<u>Rational</u><u> number</u><u> </u><u>:</u><u>-</u> The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .

<u>Irrational</u><u> number</u><u> </u><u>:</u><u>-</u> Non terminating and non repeating decimals are called irrational number .

Recall the property that :-

<u>Property</u><u> </u><u>:</u><u>-</u><u> </u> Sum of a Rational Number and a Irrational number is Irrational .

So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,

\rm\implies Irrational\ Number = 0.31311311131111...

So when we add this to 0.4 , the result will be Irrational . That is ,

\rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 ..

lesya [120]3 years ago
4 0
The answer is gonna be 0.3
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The perimeter of the quadrilateral ABCD is 105 inches.
Oliga [24]

Answer:

per letter like how much each letter is in incehs is 26.25 thats for each line/letter

Step-by-step explanation:

7 0
2 years ago
Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64
tino4ka555 [31]

a.

x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}

By Fermat's little theorem, we have

x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5

x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7

5 and 7 are both prime, so \varphi(5)=4 and \varphi(7)=6. By Euler's theorem, we get

x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5

x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7

Now we can use the Chinese remainder theorem to solve for x. Start with

x=2\cdot7+5\cdot6

  • Taken mod 5, the second term vanishes and 14\equiv4\pmod5. Multiply by the inverse of 4 mod 5 (4), then by 2.

x=2\cdot7\cdot4\cdot2+5\cdot6

  • Taken mod 7, the first term vanishes and 30\equiv2\pmod7. Multiply by the inverse of 2 mod 7 (4), then by 6.

x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6

\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}

b.

x^5\equiv3\pmod{64}

We have \varphi(64)=32, so by Euler's theorem,

x^{32}\equiv1\pmod{64}

Now, raising both sides of the original congruence to the power of 6 gives

x^{30}\equiv3^6\equiv729\equiv25\pmod{64}

Then multiplying both sides by x^2 gives

x^{32}\equiv25x^2\equiv1\pmod{64}

so that x^2 is the inverse of 25 mod 64. To find this inverse, solve for y in 25y\equiv1\pmod{64}. Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that (-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}.

So we know

25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}

Squaring both sides of this gives

x^4\equiv1681\equiv17\pmod{64}

and multiplying both sides by x tells us

x^5\equiv17x\equiv3\pmod{64}

Use the Euclidean algorithm to solve for x.

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that (-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}, and so x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}

5 0
3 years ago
Mara found the length of time of an investment. The principal of the investment was $4,300, the interest rate was 6.2 percent, a
77julia77 [94]

well, 6.2% of 4,300 can't be over half. she has made a calculation error, and the real answer is (this is where the mistake was made) 4,300 * 0.062 (not 6.2, because percents are always divided by 100 to make them into a usable number), which is equal to $266.60.

3 0
3 years ago
When solving -1/8(x+35)=-7 , what is the correct sequence of operations
TiliK225 [7]

x= -623/18

Hope it helps for you,buddy!


6 0
3 years ago
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Marysya12 [62]
Just look at it this way do 8(1) instead of x and graph that on the x axis
then do 4(1)instead of y and graph on the y axis then figure out which numbers you need to keep inputting until you reach 56 on the graph.
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3 years ago
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