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2 years ago

6

Barun said says, "The number sqrt49 is an irrational number." Do you agree or disagree? Explain using the definition of rational

and irrational numbers.

1 answer:

Brums [2.3K]2 years ago

3 0

<h3>Answer: Disagree. sqrt(49) is rational</h3>

Here's why:

sqrt(49) = sqrt(7^2) = 7

We can write 7 as a ratio or fraction of two integers 7 = 7/1

This shows that 7 is rational, so that makes sqrt(49) rational as well.

An irrational number is one where we cannot write it as a fraction of two integers. An example of an irrational number would be pi. Another irrational number is sqrt(2).

Note: the denominator can never be zero.

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2 years ago

D<br> Evaluate<br> arcsin<br> (6)]<br> at x = 4.<br> dx

sineoko [7]

Answer:

$\frac{1}{2\sqrt{5} }$

Step-by-step explanation:

Let, $\text{sin}^{-1}(\frac{x}{6})$ = y

sin(y) = $\frac{x}{6}$

$\frac{d}{dx}\text{sin(y)}=\frac{d}{dx}(\frac{x}{6})$

$\frac{d}{dx}\text{sin(y)}=\frac{1}{6}$

$\frac{d}{dx}\text{sin(y)}=\text{cos}(y)\frac{dy}{dx}$ ---------(1)

$\frac{1}{6}=\text{cos}(y)\frac{dy}{dx}$

$\frac{dy}{dx}=\frac{1}{6\text{cos(y)}}$

cos(y) = $\sqrt{1-\text{sin}^{2}(y) }$

= $\sqrt{1-(\frac{x}{6})^2}$

= $\sqrt{1-(\frac{x^2}{36})}$

Therefore, from equation (1),

$\frac{dy}{dx}=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}$

Or $\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}$

At x = 4,

$\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}$

$\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}$

$=\frac{1}{6\sqrt{\frac{36-16}{36}}}$

$=\frac{1}{6\sqrt{\frac{20}{36} }}$

$=\frac{1}{\sqrt{20}}$

$=\frac{1}{2\sqrt{5}}$

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2 years ago

A company that manufactures and sells consumer video cameras sells two versions of their popular hard disk camera, a basic came

saul85 [17]

Answer:

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Step-by-step explanation:

In this problem, we have these following percentages.

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This also means that:

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20% of those who select the basic camera also purchase the extended warranty.

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$P = P_{1} + P_{2}$

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$P_{2}$ is the percentage of those who buy the deluxe version with the extended warranty. So it is 40% of 65%. So

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$P = P_{1} + P_{2} = 0.07 + 0.26 = 0.33$

The percentage of customers who buy an extended warranty is 33%.

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3 years ago