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3 years ago

Try It for Example 3: Is 3.14144144414444... a rational number? Explain your reasoning. *

Mathematics

2 answers:

chubhunter [2.5K]3 years ago

5 0

it's irrational

A rational number can be put over a fraction, while this number continues forever

attashe74 [19]3 years ago

4 0

I will try to make this as simple as possible.

First off, we need to know what a rational number is: A rational number is any number that can be made by dividing 2 integers. For example:

1.5 would be a rational number because 1.5 = 3/2 (3 and 2 are both integers)

With that being said, let's begin.

First off, let's start with -0.3, let's ask ourselves, can we make this number by dividing 2 integers, the answer is yes, we can, by doing we have the equivalent of -0.3, so now we know it's a rational number.

As for the second one, it can't be a rational number because it can't be made by dividing to integers, so the answer is:

-0.3 is a rational number, but 3.14144144414444 is not.

Hope this helped! c:

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The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.

blagie [28]

Answer:

$N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}$

Where $t_{1/2}= 3.3 hr$ represent the half life and the intial amount would be $N_o = 1$

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

$0.05 = 1 (0.5)^{t/3.3}$

If we apply natural log on both sides we got:

$ln(0.05) = \frac{t}{3.3} ln (0.5)$

And solving for t we got:

$t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26$

So then would takes about 14.26 hours in order to have 95% of the lead to decay

Step-by-step explanation:

For this case we can define the variable of interest amount of Pb209 and for the half life would be given:

$N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}$

Where $t_{1/2}= 3.3 hr$ represent the half life and the intial amount would be $N_o = 1$

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

$0.05 = 1 (0.5)^{t/3.3}$

If we apply natural log on both sides we got:

$ln(0.05) = \frac{t}{3.3} ln (0.5)$

And solving for t we got:

$t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26$

So then would takes about 14.26 hours in order to have 95% of the lead to decay

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3 years ago

What is the surface area?<br> 5 m<br> 4 m<br> 1 m<br> square meters

Monica [59]

It’s 4 m, I took the test and got it right

8 0

3 years ago

Read 2 more answers

Me. Ellis is a teacher who tutors after school. Of the students he tutors, 30% need help in computer science and 70% need assist

Anna11 [10]

Answer: There are 82.5% after school students who are enrolled in his classes.

Step-by-step explanation:

Let the total number of students be 100

Percentage of students who need help in computer science = 30%

So, number of students who need help in computer science = 30

Percentage of students who need help in maths = 70%

So, number of students who need assistance in maths = 70

Of the students who need help,

40% are enrolled in Mr. Ellis's class during the school day,

So, it means 60% are enrolled in his class after the school day.

Number of students who are enrolled in his class after the school day = 60

Number of students who need help in Maths is given by

$\frac{70}{100}\times 60=42$

Of the students that need help in maths, percent of students are enrolled in his class during the day = 25%

So, number of students who need help in maths and enrolled in his class after school hours

$\frac{75}{100}\times 42=31.5$

Number of students who need help in computer science and enrolled in his class after school hours

$\frac{30}{100}\times 60=18$

Therefore, there are $31.5+18=49.5$ students who joined his class after school hours,

Percentage of the after students who are enrolled in Mr. Ellis's classes is given by

$\frac{49.5}{60}\times 100=82.5\%$

Hence, there are 82.5% after school students who are enrolled in his classes.

6 0

4 years ago

What is the volume of an equilateral triangular prism?

Nata [24]

Actually, the "slant height" is 4, but the vertical height or "altitude" of the equilateral triangle is not 4

but anyway..... $\bf \begin{array}{cllll}
\textit{height of an equilateral triangle}\\\\
h=\cfrac{s\sqrt{3}}{2}\\
----------\\
\textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}
\end{array}\qquad s=\textit{length of one side}$

and the volume, is the area of the triangle, times the length, so, whatever you get for the area of the triangle * 10

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3 years ago

The perimeter of a triangle is 38cm. The first side is 10cm longer than the second side, the third side is twice as long as the

Natalija [7]

Side 1: 17 Cm.
Side 2: 7 Cm.
Side 3: 14 Cm.

Hope This Helped.

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3 years ago