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3 years ago

What is 6.892 as a fraction

Mathematics

2 answers:

Doss [256]3 years ago

6 0

6.892

.892 = 892/1000

Answer: 6_892/1000

You can reduce 892/1000 if needed. I'll let you do that.

sweet-ann [11.9K]3 years ago

3 0

Answer:

6 223/250

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

6.892=6.8921

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000

6.8921×10001000=6892/1000

Find the Greatest Common Factor (GCF) of 6892 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 4,

6892÷41000÷4=1723/250

Simplify the improper fraction,

=6 223/250

In conclusion,

6.892=6 223/250

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The set up will give a right angled triangle.

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Using the SOH trig identity to get the distance

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Simplify: cos2x-cos4 all over sin2x + sin 4x

GrogVix [38]

Answer:

$\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)$

Step-by-step explanation:

$\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}$

Apply formula:

$\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)$ and

$\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)$

We get:

$=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}$

$=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}$

$=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}$

$=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}$

$=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}$

$=\frac{\sin\left(x\right)}{\cos\left(x\right)}$

$=\tan\left(x\right)$

Hence final answer is

$\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)$

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