What is the value of 0-6tan(30)+1/2*9.8*(6/(7.5*cos(30)))^2 ?

The value of 0-6tan(30)+1/2*9.8*(6/(7.5*cos(30)))^2 is 1568/375-2sqrt(3)

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Popular >

0-6tan(30)+1/29.8(6/(7.5*cos(30)))^2

Solution

0 - 6 tan (3 0^{\circ}) + \frac{1}{2} \cdot 9.8 \cdot (\frac{6}{7.5 \cdot cos ( 3 0 ^{\circ} )})^{2}

Solution

\frac{1568}{375} - 23

Decimal Notation

0.71723 \dots

Solution steps

0 - 6 tan (3 0^{\circ}) + \frac{1}{2} \cdot 9.8 (\frac{6}{7.5 cos ( 3 0 ^{\circ} )})^{2}

= 0 - 6 tan (3 0^{\circ}) + \frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} cos ( 3 0 ^{\circ} )})^{2}

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 0 - 6 \cdot \frac{3}{3} + \frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2}

Simplify

0 - 6 \cdot \frac{3}{3} + \frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2} : \frac{1568}{375} - 23

0 - 6 \cdot \frac{3}{3} + \frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2}

6 \cdot \frac{3}{3} = 23

6 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 23

\frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2} = \frac{1568}{375}

\frac{1}{2} \cdot \frac{49}{5} (\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2}

(\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2} = \frac{8 ^{2}}{5 ^{2} \cdot 3}

(\frac{6}{\frac{15}{2} \cdot \frac{3}{2}})^{2}

\frac{6}{\frac{15}{2} \cdot \frac{3}{2}} = \frac{8}{5 3}

\frac{6}{\frac{15}{2} \cdot \frac{3}{2}}

Multiply

\frac{15}{2} \cdot \frac{3}{2} : \frac{15 3}{4}

\frac{15}{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{15 3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{15 3}{4}

= \frac{6}{\frac{15 3}{4}}

Apply the fraction rule:

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

= \frac{6 \cdot 4}{15 3}

Multiply the numbers:

6 \cdot 4 = 24

= \frac{24}{15 3}

Cancel the common factor:

3

= \frac{8}{5 3}

= (\frac{8}{5 3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{8 ^{2}}{( 5 3 ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(53)^{2} = 5^{2} (3)^{2}

= \frac{8 ^{2}}{5 ^{2} ( 3 ) ^{2}}

(3)^{2} : 3

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= \frac{8 ^{2}}{5 ^{2} \cdot 3}

= \frac{1}{2} \cdot \frac{49}{5} \cdot \frac{8 ^{2}}{5 ^{2} \cdot 3}

Multiply fractions:

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

= \frac{1 \cdot 49 \cdot 8 ^{2}}{2 \cdot 5 \cdot 5 ^{2} \cdot 3}

Multiply the numbers:

1 \cdot 49 = 49

= \frac{8 ^{2} \cdot 49}{5 ^{2} \cdot 2 \cdot 5 \cdot 3}

Multiply the numbers:

2 \cdot 5 \cdot 3 = 30

= \frac{8 ^{2} \cdot 49}{5 ^{2} \cdot 30}

Factor

8^{2} : 2^{6}

Factor

8 = 2^{3}

= (2^{3})^{2}

Simplify

(2^{3})^{2} : 2^{6}

(2^{3})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 2^{6}

= 2^{6}

Factor

30 : 2 \cdot 3 \cdot 5

Factor

30 = 2 \cdot 3 \cdot 5

= \frac{2 ^{6} \cdot 49}{5 ^{2} \cdot 2 \cdot 3 \cdot 5}

2 \cdot 3 \cdot 5 \cdot 5^{2} = 2 \cdot 3 \cdot 5^{3}

2 \cdot 3 \cdot 5 \cdot 5^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

5 \cdot 5^{2} = 5^{1 + 2}

= 2 \cdot 3 \cdot 5^{1 + 2}

Add the numbers:

1 + 2 = 3

= 2 \cdot 3 \cdot 5^{3}

= \frac{2 ^{6} \cdot 49}{5 ^{3} \cdot 2 \cdot 3}

Cancel the common factor:

2

= \frac{2 ^{5} \cdot 49}{5 ^{3} \cdot 3}

2^{5} \cdot 49 = 1568

2^{5} \cdot 49

2^{5} = 32

= 32 \cdot 49

Multiply the numbers:

32 \cdot 49 = 1568

= 1568

= \frac{1568}{5 ^{3} \cdot 3}

5^{3} \cdot 3 = 375

5^{3} \cdot 3

5^{3} = 125

= 125 \cdot 3

Multiply the numbers:

125 \cdot 3 = 375

= 375

= \frac{1568}{375}

= 0 - 23 + \frac{1568}{375}

0 - 23 + \frac{1568}{375} = - 23 + \frac{1568}{375}

= \frac{1568}{375} - 23

= \frac{1568}{375} - 23

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Frequently Asked Questions (FAQ)

What is the value of 0-6tan(30)+1/2*9.8*(6/(7.5*cos(30)))^2 ?
The value of 0-6tan(30)+1/2*9.8*(6/(7.5*cos(30)))^2 is 1568/375-2sqrt(3)