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dezoksy [38]
2 years ago
14

Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number

. What value for the rational number disproves Daniel's claim?
Mathematics
1 answer:
jeka942 years ago
7 0

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any <u>nonzero</u> rational number", then his statement would be correct that the result is irrational.

----------------------------------------------

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.

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Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).
shusha [124]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

y = - \frac{1}{5} x +2 ← in slope- intercept form

with slope m = - \frac{1}{5}

• Parallel lines have equal slopes, hence

y = - \frac{1}{5} x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = - \frac{1}{5} + c ⇒ c = \frac{16}{5}

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2 years ago
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wolverine [178]

Answer:

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Step-by-step explanation:

4 0
2 years ago
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17 feet 5 inches - 8 feet 3 inches feet inches equals​
ella [17]

Answer:

9ft. 2in.

Step-by-step explanation:

17ft. 5in. = 209in.

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6 0
2 years ago
Make r the subject of the formula <br><img src="https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20%5C%3A%20h%20%7B%7D%5E%7B2%7D%28r%20-%
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Answer:

\boxed{r =  \frac{h}{3}  +  \frac{v}{\pi {h}^{2} } }

Step-by-step explanation:

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