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DaniilM [7]
3 years ago
13

How, Let a = a rational number. Let b = an irrational number. Assume a + b = c and c is rational (attempting to disprove the con

jecture). a + b = c b = c - a Explain how Alfred's argument contradicts his initial assumption proving that the sum cannot be rational?
Mathematics
2 answers:
alisha [4.7K]3 years ago
7 0
If a and c are rational then a can be written as x/y and c  can be w/z  where w,x,y and z are integers

so as alfred said  if  b = c - a = x/y - w/z  =  (zx - wy) / yz  which is  rational.
So b cannot be irrational..
laiz [17]3 years ago
6 0
If 'a' is a rational number and c is rational, then 
a = p/q
c = r/s
where p,q,r,s are integers (q and s can't be zero)

Subtracting c-a gives
b = c-a
b = (p/q) - (r/s)
b = (ps/qs) - (qr/qs)
b = (ps - qr)/(qs)

The quantity pq - qr is an integer. The reason why is because ps and qr are both integers (multiplying any two integers leads to another integer). Subtracting any two integers results in another integer.

So we have (ps - qr)/(qs) in the form (integer)/(integer) = rational number

Therefore, b is a rational number, but this contradicts the given info that b is irrational. If b is irrational, then we CANNOT write it as a ratio of integers.

This contradiction proves the assumption "a+b = c and c is rational" is incorrect
The sum is irrational.

Therefore, if a+b = c, where 'a' is rational and b is irrational, then c is irrational.
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liubo4ka [24]

Answer:

  • distance traveled: 30 m
  • displacement: 21.4 m

Step-by-step explanation:

You want the distance traveled and the displacement after walking 17 m south and 13 m east.

<h3>Distance</h3>

The distance traveled is the sum of the lengths of each leg of the trip:

  17 m + 13 m = 30 m

You have traveled a distance of 30 m.

<h3>Displacement</h3>

The displacement is the distance from your final position to your starting position. If you draw a diagram of the journey, you see the displacement is the hypotenuse of a right triangle with legs 17 m and 13 m. The Pythagorean theorem can help you find this length:

  h = √(a² +b²)

  h = √(17² +13²) = √(289 +169) = √458 ≈ 21.401

At the end of your walking, you are 21.4 m from where you started.

5 0
2 years ago
Find f'(x) and state the domain of f':<br> f(x) = In (2x^2+1)
-Dominant- [34]

Answer:

f'(x) = \frac{4x}{2x^2+1}

Domain: All Real Numbers

General Formulas and Concepts:

<u>Algebra I</u>

  • Domain is the set of x-values that can be inputted into function f(x)

<u>Calculus</u>

The derivative of a constant is equal to 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Chain Rule: \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Derivative: \frac{d}{dx} [ln(u)] = \frac{u'}{u}

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = ln(2x² + 1)

<u>Step 2: Differentiate</u>

  1. Derivative ln(u) [Chain Rule/Basic Power]:                          f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}
  2. Simplify:                                                                                       f'(x) = \frac{1}{2x^2+1} \cdot 4x
  3. Multiply:                                                                                                     f'(x) = \frac{4x}{2x^2+1}

<u>Step 3: Domain</u>

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

5 0
3 years ago
Help me with khan geometry. (Explain or give answer no link to answer thx)
NikAS [45]

Answer:

\boxed{\sf 200\pi}

Step-by-step explanation:

We know that the volume of a cone:-

\boxed{\sf  \pi r^2\cfrac{h}{3}}

(r = 10) (h = 6)

\sf \pi \times 10^2\times\cfrac{6}{3}

<u>Divide numbers:-</u>

\sf \cfrac{6}{3}=\boxed{2}

\sf 10^2\times \:2\pi

\sf 100\times \:2\pi

<u>Multiply numbers:-</u>

\boxed{\sf 200\pi}

Therefore, your answer is 200π³

We could also multiply 200 by 3.14 which will give you 628 units³.

7 0
2 years ago
Solve the system of equations by substitution. Simplify your answer. Write the
pychu [463]

Answer:

x = 5     y = 2

Step-by-step explanation:

3x + 2(3x - 13) = 19

3x + 6x - 26 = 19

9x = 45

x = 5

y = 3(5) - 13

y = 15 - 13

y = 2

4 0
2 years ago
What does the product rule of exponents say? A. When dividing like bases, bring the smaller exponent to the base with the larger
ddd [48]
B is ya answer......................
7 0
3 years ago
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