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2 years ago

Why is the product of a rational number and an irrational number Irrational?

Mathematics

2 answers:

Llana [10]2 years ago

5 0

Answer:

Because the product is always non-termination,non-repeating decimal.

Step-by-step explanation:

If we have $a$ is irrational; $b$ is rational such that $b \neq 0$ , then $a \cdot b$ is irrational.

A way to represent this is:

$a\in\mathbb{R}\setminus\mathbb{Q}, b\in\mathbb{Q},ab\in\mathbb{Q}\implies a\in\mathbb{Q}\implies\text{Contradiction}\therefore ab\not\in\mathbb{Q}.$

Note that we have a contradiction, because $a$ is not a rational number, as I stated in the beginning. Therefore, ab is irrational.

Marta_Voda [28]2 years ago

5 0

Answer: A

Step-by-step explanation:

Multiplying an irrational number by a rational number will always be an irrational number because irrational numbers do not repeat and terminate.

So for example multiplying pi by a rational like two you will have an irrational number because pi is an irrational number.

$\pi * 2$ = 6.28318530718 as you could see that is an irrational number because there is no repetition or termination.

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What is the maximum number of hot dogs eaten in a hot dog eating contest?

anastassius [24]

According to your graph, it appears that the <span>maximum number of hot dogs eaten in a hot dog eating contest would most likely be C. 66</span>

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3 years ago

There are 4 pints of green paint in a gallon bucket. The paint is made from equal amounts of yellow paint and blue paint. To cre

vovikov84 [41]

Answer:

Brandon is correct.

Step-by-step explanation:

Initially, there id 4 pints of green paint in the bucket.

As the green paint is made from equal amounts of yellow paint and blue paint, so, the initial amount of yellow and blue paint in the bucket is 2 pint each.

Let x pints of yellow paint to be added to the bucket to make the desired shade.

Total amount of the paint in the bucket, after addition of $x$ pints of yellow color become $4 + x$ pint, in which the ampunt of yellow color is $2+x$ pints.

As, the ampunt of yellow color is 80% of the total amount of the mixture, so

$(4+x)\times 80\%=2+x$

$\Rightarrow (4+x)\times \frac{80}{100}=2+x$

$\Rightarrow 4(4+x)=5(2+x)$

$\Rightarrow x=6$

So, 6 pints of yellow paint to be added to the bucket to make the desired shade.

Hence, Brandon is correct.

3 0

2 years ago

16)

elixir [45]

$78

The difference between choice A and B is 5 meals and $80 so 1 meal is $16. So we can subtract $16 from $250 and we get $234 for 3 nights. 1 night is $78

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2 years ago

(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or

olasank [31]

Answer:

(Missing part of the question is attached)

$L(x)=2x+3$

Estimates are too large.

Step-by-step explanation:

Suppose the only information we know about the function is:

$f(1)=5$

where the graph of its derivative is shown in the attachment

If the function $f\\$ is differentiable at point $x=1$ , the tangent line to the graph of $f$ at 1 is given by the equation:

$y=f(1) +f'(1)(x-1)$

So we call the linear function:

$L(x)=f(1) +f'(1)(x-1)$

We know the $f(1)=5$ as it is given in the question, and $f'(1)=2$ from the graph attached. Substitute in the equation of $L(x)$ .

$L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\$

At x=1, $f'(x)$ is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve $f$ . Thus, The estimates are too large.

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2 years ago

Which model represents −8 + 3

pychu [463]

C will be the answer... its ur boi C bandzzzzzzz

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2 years ago