What is the value of ((50sqrt(3))^2sin(60))/(9.8) ?

The value of ((50sqrt(3))^2sin(60))/(9.8) is (18750sqrt(3))/(49)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((50sqrt(3))^2sin(60))/(9.8)

Solution

\frac{( 50 3 ) ^{2} sin ( 6 0 ^{\circ} )}{9.8}

Solution

\frac{18750 3}{49}

Decimal Notation

662.77454 \dots

Solution steps

\frac{( 50 3 ) ^{2} sin ( 6 0 ^{\circ} )}{9.8}

= \frac{( 50 3 ) ^{2} sin ( 6 0 ^{\circ} )}{\frac{49}{5}}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= \frac{( 50 3 ) ^{2} \frac{3}{2}}{\frac{49}{5}}

Simplify

\frac{( 50 3 ) ^{2} \frac{3}{2}}{\frac{49}{5}} : \frac{18750 3}{49}

\frac{( 50 3 ) ^{2} \frac{3}{2}}{\frac{49}{5}}

Apply the fraction rule:

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

= \frac{( 50 3 ) ^{2} \frac{3}{2} \cdot 5}{49}

(503)^{2} = 5 0^{2} \cdot 3

(503)^{2}

Apply exponent rule:

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

= 5 0^{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

= 5 0^{2} \cdot 3

= \frac{5 0 ^{2} \cdot 3 \cdot 5 \cdot \frac{3}{2}}{49}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{5 0 ^{2} \cdot 15 \cdot \frac{3}{2}}{49}

Multiply

15 \cdot 5 0^{2} \cdot \frac{3}{2} : 187503

15 \cdot 5 0^{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 15 \cdot 5 0 ^{2}}{2}

Factor

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

Factor

50 = 5^{2} \cdot 2

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

Apply exponent rule:

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

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

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}

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

= \frac{5 ^{4} \cdot 2 ^{2} \cdot 15 3}{2}

Cancel the common factor:

2

= 5^{4} \cdot 15 \cdot 23

Multiply the numbers:

15 \cdot 2 = 30

= 5^{4} \cdot 303

5^{4} = 625

= 30 \cdot 6253

Multiply the numbers:

30 \cdot 625 = 18750

= 187503

= \frac{18750 3}{49}

= \frac{18750 3}{49}

Popular Examples

2(sin(pi/2)+cos(pi/2))

2 (sin (\frac{π}{2}) + cos (\frac{π}{2}))

6sin(pi/2+0.1)

6 sin (\frac{π}{2} + 0.1)

arctan((2.5)/2)

arctan (\frac{2.5}{2})

tan(-1590)

tan (- 159 0^{\circ})

-picos(-pi)

- π cos (- π)

Frequently Asked Questions (FAQ)

What is the value of ((50sqrt(3))^2sin(60))/(9.8) ?
The value of ((50sqrt(3))^2sin(60))/(9.8) is (18750sqrt(3))/(49)