What is the value of (6(9.81)-6(9.81)sin(30))/(6+6) ?

The value of (6(9.81)-6(9.81)sin(30))/(6+6) is 981/400

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Popular Trigonometry >

(6(9.81)-6(9.81)sin(30))/(6+6)

Solution

\frac{6 ( 9.81 ) - 6 ( 9.81 ) sin ( 3 0 ^{\circ} )}{6 + 6}

Solution

\frac{981}{400}

Decimal

2.4525

Solution steps

\frac{6 ( 9.81 ) - 6 ( 9.81 ) sin ( 3 0 ^{\circ} )}{6 + 6}

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} sin ( 3 0 ^{\circ} )}{6 + 6}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6}

Simplify

\frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6} : \frac{981}{400}

\frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{981}{100} \cdot \frac{1}{2}}{6 + 6}

Add the numbers:

6 + 6 = 12

= \frac{6 \cdot \frac{981}{100} - 6 \cdot \frac{1}{2} \cdot \frac{981}{100}}{12}

6 \cdot \frac{981}{100} = \frac{2943}{50}

6 \cdot \frac{981}{100}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{981 \cdot 6}{100}

Multiply the numbers:

981 \cdot 6 = 5886

= \frac{5886}{100}

Cancel the common factor:

2

= \frac{2943}{50}

6 \cdot \frac{981}{100} \cdot \frac{1}{2} = \frac{2943}{100}

6 \cdot \frac{981}{100} \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{981 \cdot 1 \cdot 6}{100 \cdot 2}

Multiply the numbers:

981 \cdot 1 \cdot 6 = 5886

= \frac{5886}{100 \cdot 2}

Multiply the numbers:

100 \cdot 2 = 200

= \frac{5886}{200}

Cancel the common factor:

2

= \frac{2943}{100}

= \frac{\frac{2943}{50} - \frac{2943}{100}}{12}

Join

\frac{2943}{50} - \frac{2943}{100} : \frac{2943}{100}

\frac{2943}{50} - \frac{2943}{100}

Least Common Multiplier of

50, 100 : 100

50, 100

Least Common Multiplier (LCM)

Prime factorization of

50 : 2 \cdot 5 \cdot 5

50

50

divides by

250 = 25 \cdot 2

= 2 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5 \cdot 5

Prime factorization of

100 : 2 \cdot 2 \cdot 5 \cdot 5

100

100

divides by

2100 = 50 \cdot 2

= 2 \cdot 50

50

divides by

250 = 25 \cdot 2

= 2 \cdot 2 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5 \cdot 5

Multiply each factor the greatest number of times it occurs in either

50

100

= 2 \cdot 2 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 \cdot 5 = 100

= 100

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

100

For

\frac{2943}{50} :

multiply the denominator and numerator by

2

\frac{2943}{50} = \frac{2943 \cdot 2}{50 \cdot 2} = \frac{5886}{100}

= \frac{5886}{100} - \frac{2943}{100}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5886 - 2943}{100}

Subtract the numbers:

5886 - 2943 = 2943

= \frac{2943}{100}

= \frac{\frac{2943}{100}}{12}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2943}{100 \cdot 12}

Multiply the numbers:

100 \cdot 12 = 1200

= \frac{2943}{1200}

Cancel the common factor:

3

= \frac{981}{400}

= \frac{981}{400}

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Frequently Asked Questions (FAQ)

What is the value of (6(9.81)-6(9.81)sin(30))/(6+6) ?
The value of (6(9.81)-6(9.81)sin(30))/(6+6) is 981/400