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3 years ago

How do you simplify 2/3 divided by 1/3

Mathematics

1 answer:

suter [353]3 years ago

8 0

Answer:

Step-by-step explanation:

Solve. To do so, change the division sign into a multiplication sign, and flip the second fraction:

(2/3)/(1/3) = (2/3) x (3/1)

Multiply across:

(2 * 3)/(3 * 1) = (6)/(3)

Simplify:

6/3 = 2

2 is your answer.

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Part A: Using complete sentences, explain how to convert zero point 22 repeating to a fraction. (2 points)

Helen [10]

Answer:

a) $\frac{2}{9}$

b) Irrational

Step-by-step explanation:

a) Let $y=0.\bar2.....(a)$

Then $100y=22.\bar2.....(b)$

Subtract (a) from (b)

$100y-y=22.\bar2-0.\bar2$

$\implies 99y=22$

$y=\frac{22}{99}=\frac{2}{9}$

b) From part a) $0.\bar2$ is a rational number but $\sqrt{112}=4\sqrt{7}$ is an irrational number.

But $0.\bar2\times \sqrt{112}$ is not a rational number because the product of a rational number and an irrational number is an irrational number.

3 0

4 years ago

I need help with finding the answer to a) and b). Thank you!

shtirl [24]

Answer:

$\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }$

$\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}$

$\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}$

Step-by-step explanation:

We are given that:

$\displaystyle \sin(x)=-\frac{21}{29}$

Where x is in QIII.

First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:

$a=\sqrt{29^2-21^2}=20$

So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.

Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.

And if x is in QIII, this means that:

$180$

So:

$\displaystyle 90 < \frac{x}{2} < 135$

Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.

Recall that:

$\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}$

Since x/2 is in QII, this will be positive.

Using the above information, cos(x) is -20/29. Therefore:

$\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 + 20/29}{2}$

Simplify:

$\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}$

Likewise:

$\displaystyle \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }$

Since x/2 is in QII, this will be negative.

Using the above information, cos(x) is -20/29. Therefore:

$\displaystyle \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }$

Simplify:

$\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}$

Finally:

$\displaystyle \tan\Big(\frac{x}{2}\Big) = \frac{\sin(x/2)}{\cos(x/2)}$

Therefore:

$\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}$

5 0

3 years ago

Joanna needs a book to prop up a table leg. She randomly selects a book , and selects another book . What is probability that sh

Stolb23 [73]

Id say 40%
because 8 are math so 9 of them are other

3 0

3 years ago

Help? SOH, CAH, or TOA

tatyana61 [14]

First you'd find angle C as it is opposite the side AB that you want to find
But to find angle c you first have to find angle A using the soh
Then you'd do 180 - (90 + angle A) =angle C as angles in a triangle add up to 180
Then you'd use the soh using angle A and 12 to find side AB

Working out
Sin(x)=12/7
Sin-1(7/12)
=35.685

180- (90+35.685)
=54.315

Sin(54.315)=o/12
Sin(54.315)*12
=9.746794345

7 0

3 years ago

Find the limit for this function

Wewaii [24]

Let pi/2 - x = y , cosx = siny , when x approaches pi/2 , y approaches 0

lim ((e^siny - 1)/siny) (siny / y)

y-->0

= lne * 1 = 1

5 0

3 years ago