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3 years ago

Can you ever use a calculator to determine if a number is rational or irrational?

1 answer:

3 0

A rational number is simply a term that can be expressed as a fraction. Otherwise, that is an irrational number. So, you can use a calculator to verify if the number is rational or not.

The key characteristic of an irrational number is when it contains a long line of decimal places. For example, the term π and the Euler's number e are irrational numbers. The exact values of π and e are 3.14159 and 2.71828182846, respectively. In reality, those decimal places go on a long way. Particularly, π has a total of 2.7 trillion digits. Numbers inside radicals or roots can also be irrational numbers. For example √3 is irrational because it is equal to 1.732050808. However, not all radicals are irrational. For example √15.3664 is equal to 98/25 or 3.92. That is a rational number. So, therefore, use the calculator to know the exact value of the term to properly distinguish rational from irrational.

You might be interested in

Simplify the following expression.

Rzqust [24]

Step-by-step explanation:

Step 1: Add the numbers: 9.5 +6.2 = 15.7

$=8.6\left(15.7-3.5^2\right)$

$3.5^2=12.25$

$=8.6\left(15.7-12.25\right)$

Step 2: Subtract the numbers: 15.7 - 12.25 = 3.45

$= 3.45X 8.6$

Step 3: Multiply the numbers: 8.6 × 3.45 = 29.67

$=29.67$

- To solve this equation, the first step is to add the numbers 9.5 + 6.2 into the equation and it will lead to 15.7 as the number for step one.

- To solve this equation, the second step is to subtract the numbers 15.7 - 12.25 into the equation and it will lead to 3.45 as the answer.

- To solve this equation, the third step is to multiply the numbers 8.6 x 3.45 into the equation and it will lead 29.67 as the final answer for the whole equation.

Answer:

$=29.67$

Hope this helps.

3 0

2 years ago

NEED HELP QUICK NO LINKS PLEASE!

Juli2301 [7.4K]

Answer:

3. 4x^2y

Step-by-step explanation:

The GCF of 36 and 14 is 4.

The GCF of x^2y and x^2y^2 is x^2y

Multiply the two GCF and you get 4x^2y

6 0

2 years ago

Read 2 more answers

Please help me please

Lemur [1.5K]

Answer:

The answer would be "j"

Step-by-step explanation:

First, you would want to find the value of the original equation:

5(y + 2) + 4

Use order of operations and distribute the five.

5y + 10 + 4

5y +14

This is the value of the original equation

Now we can work through the other options, but because we already know the answer, lets see about that one.

5 x y + 5 x 2 + 4

Again, use order of operations.

Multiply first

5y + 10 + 4

and complete the equation

5y + 14, which equals our original equation.

4 0

2 years ago

Is 180°, 2` a reflex angle?

Leokris [45]

yes it is .....,...............reflex angle

3 0

3 years ago

Write -3+4i in the form r(cosx+isinx)

Zanzabum

$-3+4i$ is a complex number that satisfies

$\begin{cases}r\cos x=-3\\[1ex]r\sin x=4\\[1ex]r=\sqrt{(-3)^2+4^2}\end{cases}$

The last equation immediately tells you that $r=5$ .

So you have

$\begin{cases}\cos x=-\dfrac35\\[1ex]\sin x=\dfrac45\end{cases}$

Dividing the second equation by the first, you end up with

$\dfrac{\sin x}{\cos x}=\tan x=\dfrac{\dfrac45}{-\dfrac35}=-\dfrac43$

Because the argument's cosine is negative and its sine is positive, you know that $\dfrac\pi2$ . This is important to know because it's only the case that $y=\tan x\implies \arctan y=x$ whenever $-\dfrac\pi2$ . The inverse doesn't exist otherwise.

However, you can restrict the domain of the tangent function so that an inverse can be defined. By shifting the argument of tangent by $\pi$ , we have

$\tan(x-\pi)=y\implies x=\pi+\arctan y$

All this to say

$\tan x=-\dfrac43\implies x=\pi+\arctan\left(-\dfrac43\right)\approx2.2143\text{ rad}\approx126.9^\circ$

So, $-3+4i=5(\cos126.9^\circ+i\sin126.9^\circ)$ .

5 0

3 years ago