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3 years ago

What is the rational number equivalent to __ 3.24?

Mathematics

1 answer:

guajiro [1.7K]3 years ago

5 0

Answer:

$\frac{324}{100}$

Step-by-step explanation:

Think of a rational number as a fraction. The definition of a rational number is that it is the ratio of integers that, when divided, is either an integer, a decimal that terminates, or a decimal that repeats. 6/3 = 2 (6/3 is a rational number that divides to 2); 1/2 = .5 (1/2 is a rational number that divides to .5 which is a terminating decimal, meaning it ends); 1/3 = .33333333 (1/3 is a rational number that divides to .3333333 which is a repeating decimal). If we want to express 3.24 as a rational number, let's first put it into fraction form. The 4 in .24 is in the hundredths place, so as a fraction, .24 is 24/100. Check this on your calculator. Divide 24 by 100 and you get .24. So now what we have is $3\frac{24}{100}$

Now express that mixed fraction as an improper and you're done. 3 times 100 is 300; 300 + 24 = 324. Put that back over 100 and your rational number is 324/100. Check that on your calculator, as well, just to see that it's true.

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General solutions of sin(x-90)+cos(x+270)=-1 {both 90 and 270 are in degrees}

mixer [17]

Answer:

$\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

Step-by-step explanation:

Given:

$\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1$

First, note that

$\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x$

So, the equation is

$-\cos x+\sin x= -1$

Multiply this equation by $\frac{\sqrt{2}}{2}:$

$-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}$

The general solution is

$x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

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3 years ago

Describe a situation where it would be better to use a fraction than a decimal or a percentage

AysviL [449]

I prefer to use fractions for some irrational numbers.

For example, 1/3 is equal to an infinite 0.3333333333333333...

6 0

3 years ago

Read 2 more answers

I need to simplify this complex fraction

vovangra [49]

I see two ways to do it.

First, you have to understand that when you see a 'complex fraction' like this, the top number is a numerator, and the two bottom numbers are both denominators.

Way-1:

Take the top fraction . . . 2/2 . That's equal to 1 . So the whole thing is 1/3.

Way-2:

Multiply the bottom two denominators. Then the whole thing is 2/(2·3) . That's the same thing as 2/6 . Simplify that, and you have 1/3 .

7 0

3 years ago

If i have 2 c's 2 A's 3 b's and 1 d what is my gpa and would i be able to pass 8th grade

IgorC [24]

A= 4 points
B= 3 points
C= 2 points
D= 1 point
F= 0 points

So you add 2+2+4+4+3+3+3+1
Which equals 22
Now divide 22 by 8
You get 2.75
So yes with a 2.75 gpa you should pass 8th grade as most schools require nothing less than a 2.0

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3 years ago

SIZIF [17.4K]

5% of 350,000 is 17,500 so D

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3 years ago