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3 years ago

Why is .3 repeating a rational number

Mathematics

2 answers:

s2008m [1.1K]3 years ago

5 0

Answer:

.333333... can be expressed as 1/3.

Step-by-step explanation:

A rational number is defined as:

any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

aka, any number that you can express as a fraction.

Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.

If you didn't know this, don't worry. You'll get it soon enough.

Hope this helped!

Murrr4er [49]3 years ago

4 0

Because it can be written as a fraction 1/3

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Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim

Zigmanuir [339]

Answer:

Time (secs) => distance (ft)

1 => ⅔

15 => 10

24 => 16

45 => 30

Step-by-step explanation:

Equation to represent this proportional relationship is $d = tk$ , where,

t = time

d = distance

k = constant of proportionality

To complete the table, let's find k given that the turtles swarm 16 ft (d) in 24 secs (t).

Substitute d = 16, t = 24 into the equation.

$d = tk$

$16 = 24k$

$\frac{16}{24} = k$ (division property of equality)

$\frac{2}{3} = k$

Let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:

For 1 sec, let's find distance (d):

$d = tk$

$d = 1*\frac{2}{3}$

d = ⅔ ft

For 10 ft, let's find the time (t) taken:

$d = tk$

$10 = t*\frac{2}{3}$

Multiply both sides by 3

$10*3 = t*\frac{2}{3}*3$

$30 = t*2$

Divide both sides by 2

$\frac{30}{2} = \frac{t*2}{2}$

$15 = t$

t = 15 secs

For 45 secs, let's find distance (d):

$d = tk$

$d = 45*\frac{2}{3} = 15*2$

d = 30 ft

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3 years ago

2 sin^2 (x) + 3 sin (x) + 1 = 0 help me find the solution

Fed [463]

Answer:

Step-by-step explanation:

\[2~ sin^2 x+3sin x+1=0\]

\[2sin^2x+2sin x+sin x+1=0\]

2sinx(sin x+1)+1(sin x+1)=0

(sin x+1)(2 sin x+1)=0

either sin x+1=0

sin x=-1=sin 3π/2=sin (2nπ+3π/2)

x=2nπ+3π/2,where n is an integer.

or 2sin x+1=0

sin x=-1/2=-sin π/6=sin (π+π/6),sin (2π-π/6)=sin (2nπ+7π/6),sin (2nπ+11π/6)

x=2nπ+7π/6,2nπ+11π/6,

where n is an integer.

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3 years ago

What is the percent of change from 35 to 62? round to the nearest percent.

Leona [35]

In order to change from 35 to 62, we have to add 27. So, the question becomes: which percentage of 35 is 27?

To answer this question, we set this simple equation

$27 = 35\cdot\dfrac{x}{100}$

And solving for x we have

$x = \dfrac{2700}{35} \approx 77.14$

So, if you change from 35 to 62, you have an increase of about 77%

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3 years ago

The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is four feet high an

Sav [38]

Let x = the width

then

2x = the length

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Given the surface area:

2(2x*x) + 2(2x*4) + 2(x*4) = 220

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A quadratic equation:

4x^2 + 24x - 220 = 0

simplify, divide by 4

x^2 + 6x - 55 = 0

Factor

(x+11)(x-5) = 0

The positive solution is what we want here:

x = 5 ft is the width

then

2(5) = 10 ft is the length

Find the volume

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3 years ago

Which function will produce the same graph as the function shown below?

pav-90 [236]

I think the correct answer from the choices listed above is option D. The function that will produce the same graph as the function y=(x+1)(x-3) would be y=x^2-2x-3. Both equations are the same. You can confirm it by simplifying the equation. Hope this answers the question.

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3 years ago

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