What is the value of ((7.51)^2*sin(30))/(9.4) ?

The value of ((7.51)^2*sin(30))/(9.4) is 564001/188000

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((7.51)^2*sin(30))/(9.4)

Solution

\frac{( 7.51 ) ^{2} \cdot sin ( 3 0 ^{\circ} )}{9.4}

Solution

\frac{564001}{188000}

Decimal Notation

3.00000 \dots

Solution steps

\frac{( 7.51 ) ^{2} sin ( 3 0 ^{\circ} )}{9.4}

= \frac{( \frac{751}{100} ) ^{2} sin ( 3 0 ^{\circ} )}{\frac{47}{5}}

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{( \frac{751}{100} ) ^{2} \frac{1}{2}}{\frac{47}{5}}

Simplify

\frac{( \frac{751}{100} ) ^{2} \frac{1}{2}}{\frac{47}{5}} : \frac{564001}{188000}

\frac{( \frac{751}{100} ) ^{2} \frac{1}{2}}{\frac{47}{5}}

Apply the fraction rule:

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

= \frac{( \frac{751}{100} ) ^{2} \frac{1}{2} \cdot 5}{47}

(\frac{751}{100})^{2} = \frac{75 1 ^{2}}{10 0 ^{2}}

(\frac{751}{100})^{2}

Apply exponent rule:

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

= \frac{75 1 ^{2}}{10 0 ^{2}}

= \frac{5 \cdot \frac{1}{2} \cdot \frac{75 1 ^{2}}{10 0 ^{2}}}{47}

Multiply

\frac{75 1 ^{2}}{10 0 ^{2}} \cdot \frac{1}{2} \cdot 5 : \frac{564001}{4000}

\frac{75 1 ^{2}}{10 0 ^{2}} \cdot \frac{1}{2} \cdot 5

Multiply fractions:

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

= \frac{75 1 ^{2} \cdot 1 \cdot 5}{10 0 ^{2} \cdot 2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{75 1 ^{2} \cdot 5}{10 0 ^{2} \cdot 2}

Factor

10 0^{2} : 2^{4} \cdot 5^{4}

Factor

100 = 2^{2} \cdot 5^{2}

= (2^{2} \cdot 5^{2})^{2}

Apply exponent rule:

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

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

Simplify

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

Apply exponent rule:

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

= 2^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 2^{4}

Simplify

(5^{2})^{2} : 5^{4}

(5^{2})^{2}

Apply exponent rule:

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

= 5^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 5^{4}

= 2^{4} \cdot 5^{4}

= \frac{75 1 ^{2} \cdot 5}{2 ^{4} \cdot 5 ^{4} \cdot 2}

2^{4} \cdot 5^{4} \cdot 2 = 5^{4} \cdot 2^{5}

2^{4} \cdot 5^{4} \cdot 2

Apply exponent rule:

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

2^{4} \cdot 2 = 2^{4 + 1}

= 5^{4} \cdot 2^{4 + 1}

Add the numbers:

4 + 1 = 5

= 5^{4} \cdot 2^{5}

= \frac{75 1 ^{2} \cdot 5}{2 ^{5} \cdot 5 ^{4}}

Cancel the common factor:

5

= \frac{75 1 ^{2}}{2 ^{5} \cdot 5 ^{3}}

75 1^{2} = 564001

= \frac{564001}{2 ^{5} \cdot 5 ^{3}}

2^{5} \cdot 5^{3} = 4000

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

2^{5} = 32

= 5^{3} \cdot 32

5^{3} = 125

= 32 \cdot 125

Multiply the numbers:

32 \cdot 125 = 4000

= 4000

= \frac{564001}{4000}

= \frac{\frac{564001}{4000}}{47}

Apply the fraction rule:

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

= \frac{564001}{4000 \cdot 47}

Multiply the numbers:

4000 \cdot 47 = 188000

= \frac{564001}{188000}

= \frac{564001}{188000}

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Frequently Asked Questions (FAQ)

What is the value of ((7.51)^2*sin(30))/(9.4) ?
The value of ((7.51)^2*sin(30))/(9.4) is 564001/188000