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Popular >

sinh(22.69140625-4)-0.72.69140625

Solution

sinh (2 \cdot 2.69140625 - 4) - 0.7 \cdot 2.69140625

\frac{\frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}} - 18.83984 \dots}{10}

Decimal Notation

- 0.01637 \dots

Solution steps

sinh (2 \cdot 2.69140625 - 4) - 0.7 \cdot 2.69140625

= sinh (2 \cdot 2.69140625 - 4) - \frac{7}{10} \cdot 2.69140625

Simplify:

2 \cdot 2.69140625 - 4 = 1.3828125

2 \cdot 2.69140625 - 4

Multiply the numbers:

2 \cdot 2.69140625 = 5.3828125

= 5.3828125 - 4

Subtract the numbers:

5.3828125 - 4 = 1.3828125

= 1.3828125

sinh (1.3828125) - \frac{7}{10} \cdot 2.69140625 = \frac{10 sinh ( 1.3828125 ) - 18.83984 \dots}{10}

sinh (1.3828125) - \frac{7}{10} \cdot 2.69140625

\frac{7}{10} \cdot 2.69140625 = \frac{18.83984 \dots}{10}

\frac{7}{10} \cdot 2.69140625

Multiply fractions:

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

= \frac{7 \cdot 2.69140625}{10}

Multiply the numbers:

7 \cdot 2.69140625 = 18.83984 \dots

= \frac{18.83984 \dots}{10}

= sinh (1.3828125) - \frac{18.83984 \dots}{10}

Convert element to fraction:

sinh (1.3828125) = \frac{sinh ( 1.3828125 ) 10}{10}

= \frac{sinh ( 1.3828125 ) \cdot 10}{10} - \frac{18.83984 \dots}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{sinh ( 1.3828125 ) \cdot 10 - 18.83984 \dots}{10}

= \frac{10 sinh ( 1.3828125 ) - 18.83984 \dots}{10}

Rewrite using trig identities:

sinh (1.3828125) = \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}}

sinh (1.3828125)

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{1.3828125} - e ^{- 1.3828125}}{2}

\frac{e ^{1.3828125} - e ^{- 1.3828125}}{2} = \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}}

\frac{e ^{1.3828125} - e ^{- 1.3828125}}{2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{e ^{1.3828125} - \frac{1}{e ^{1.3828125}}}{2}

Join

e^{1.3828125} - \frac{1}{e ^{1.3828125}} : \frac{e ^{2.765625} - 1}{e ^{1.3828125}}

e^{1.3828125} - \frac{1}{e ^{1.3828125}}

Convert element to fraction:

e^{1.3828125} = \frac{e ^{1.3828125} e ^{1.3828125}}{e ^{1.3828125}}

= \frac{e ^{1.3828125} e ^{1.3828125}}{e ^{1.3828125}} - \frac{1}{e ^{1.3828125}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{1.3828125} e ^{1.3828125} - 1}{e ^{1.3828125}}

e^{1.3828125} e^{1.3828125} - 1 = e^{2.765625} - 1

e^{1.3828125} e^{1.3828125} - 1

e^{1.3828125} e^{1.3828125} = e^{2.765625}

e^{1.3828125} e^{1.3828125}

Apply exponent rule:

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

e^{1.3828125} e^{1.3828125} = e^{1.3828125 + 1.3828125}

= e^{1.3828125 + 1.3828125}

Add the numbers:

1.3828125 + 1.3828125 = 2.765625

= e^{2.765625}

= e^{2.765625} - 1

= \frac{e ^{2.765625} - 1}{e ^{1.3828125}}

= \frac{\frac{e ^{2.765625} - 1}{e ^{1.3828125}}}{2}

Apply the fraction rule:

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

= \frac{e ^{2.765625} - 1}{e ^{1.3828125} \cdot 2}

= \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}}

= \frac{10 \cdot \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}} - 18.83984 \dots}{10}

\frac{10 \cdot \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}} - 18.83984 \dots}{10} = \frac{\frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}} - 18.83984 \dots}{10}

\frac{10 \cdot \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}} - 18.83984 \dots}{10}

10 \cdot \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}} = \frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}}

10 \cdot \frac{e ^{2.765625} - 1}{2 e ^{1.3828125}}

Multiply fractions:

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

= \frac{( e ^{2.765625} - 1 ) \cdot 10}{2 e ^{1.3828125}}

Divide the numbers:

\frac{10}{2} = 5

= \frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}}

= \frac{\frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}} - 18.83984 \dots}{10}

= \frac{\frac{5 ( e ^{2.765625} - 1 )}{e ^{1.3828125}} - 18.83984 \dots}{10}

\frac{10 0 ^{2} sin ( 6 0 ^{\circ} )}{9.8}

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