What is the value of 25*sin(60)*1.76-(9.8)/2*(1.76)^2 ?

The value of 25*sin(60)*1.76-(9.8)/2*(1.76)^2 is 22sqrt(3)-47432/3125

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25sin(60)1.76-(9.8)/2*(1.76)^2

Solution

25 \cdot sin (6 0^{\circ}) \cdot 1.76 - \frac{9.8}{2} \cdot (1.76)^{2}

Solution

223 - \frac{47432}{3125}

Decimal Notation

22.92687 \dots

Solution steps

25 sin (6 0^{\circ}) \cdot 1.76 - \frac{9.8}{2} (1.76)^{2}

= 25 sin (6 0^{\circ}) \frac{44}{25} - \frac{\frac{49}{5}}{2} (\frac{44}{25})^{2}

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}

= 25 \cdot \frac{3}{2} \cdot \frac{44}{25} - \frac{\frac{49}{5}}{2} (\frac{44}{25})^{2}

Simplify

25 \cdot \frac{3}{2} \cdot \frac{44}{25} - \frac{\frac{49}{5}}{2} (\frac{44}{25})^{2} : 223 - \frac{47432}{3125}

25 \cdot \frac{3}{2} \cdot \frac{44}{25} - \frac{\frac{49}{5}}{2} (\frac{44}{25})^{2}

25 \cdot \frac{3}{2} \cdot \frac{44}{25} = 223

25 \cdot \frac{3}{2} \cdot \frac{44}{25}

Multiply fractions:

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

= \frac{3 \cdot 44 \cdot 25}{2 \cdot 25}

Cancel the common factor:

25

= \frac{3 \cdot 44}{2}

Divide the numbers:

\frac{44}{2} = 22

= 223

\frac{\frac{49}{5}}{2} (\frac{44}{25})^{2} = \frac{47432}{3125}

\frac{\frac{49}{5}}{2} (\frac{44}{25})^{2}

\frac{\frac{49}{5}}{2} = \frac{49}{10}

\frac{\frac{49}{5}}{2}

Apply the fraction rule:

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

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

Multiply the numbers:

5 \cdot 2 = 10

= \frac{49}{10}

= (\frac{44}{25})^{2} \frac{49}{10}

(\frac{44}{25})^{2} = \frac{4 4 ^{2}}{2 5 ^{2}}

(\frac{44}{25})^{2}

Apply exponent rule:

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

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

= \frac{49}{10} \cdot \frac{4 4 ^{2}}{2 5 ^{2}}

Multiply fractions:

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

= \frac{49 \cdot 4 4 ^{2}}{10 \cdot 2 5 ^{2}}

Factor

4 4^{2} : 2^{4} \cdot 1 1^{2}

Factor

44 = 2^{2} \cdot 11

= (2^{2} \cdot 11)^{2}

Apply exponent rule:

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

= 1 1^{2} (2^{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}

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

Factor

10 : 2 \cdot 5

Factor

10 = 2 \cdot 5

= \frac{2 ^{4} \cdot 1 1 ^{2} \cdot 49}{2 5 ^{2} \cdot 2 \cdot 5}

Cancel the common factor:

2

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

2^{3} \cdot 1 1^{2} \cdot 49 = 47432

2^{3} \cdot 1 1^{2} \cdot 49

2^{3} = 8

= 1 1^{2} \cdot 8 \cdot 49

1 1^{2} = 121

= 8 \cdot 121 \cdot 49

Multiply the numbers:

8 \cdot 121 \cdot 49 = 47432

= 47432

= \frac{47432}{2 5 ^{2} \cdot 5}

2 5^{2} \cdot 5 = 3125

2 5^{2} \cdot 5

2 5^{2} = 625

= 625 \cdot 5

Multiply the numbers:

625 \cdot 5 = 3125

= 3125

= \frac{47432}{3125}

= 223 - \frac{47432}{3125}

= 223 - \frac{47432}{3125}

Popular Examples

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Frequently Asked Questions (FAQ)

What is the value of 25*sin(60)*1.76-(9.8)/2*(1.76)^2 ?
The value of 25*sin(60)*1.76-(9.8)/2*(1.76)^2 is 22sqrt(3)-47432/3125