What is the value of sinh(((2*2.47832)-4)-0.7*2.47832) ?

The value of sinh(((2*2.47832)-4)-0.7*2.47832) is -(e^{97273/62500}-1)/(2e^{97273/125000)}

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sinh(((22.47832)-4)-0.72.47832)

Solution

sinh (((2 \cdot 2.47832) - 4) - 0.7 \cdot 2.47832)

Solution

- \frac{e ^{\frac{97273}{62500}} - 1}{2 e ^{\frac{97273}{125000}}}

Decimal Notation

- 0.85913 \dots

Solution steps

sinh (((2 \cdot 2.47832) - 4) - 0.7 \cdot 2.47832)

= sinh (2 \cdot \frac{30979}{12500} - 4 - \frac{7}{10} \cdot \frac{30979}{12500})

Simplify:

2 \cdot \frac{30979}{12500} - 4 - \frac{7}{10} \cdot \frac{30979}{12500} = - \frac{97273}{125000}

2 \cdot \frac{30979}{12500} - 4 - \frac{7}{10} \cdot \frac{30979}{12500}

Group like terms

= - \frac{7}{10} \cdot \frac{30979}{12500} + 2 \cdot \frac{30979}{12500} - 4

Add similar elements:

- \frac{7}{10} \cdot \frac{30979}{12500} + 2 \cdot \frac{30979}{12500} = \frac{13}{10} \cdot \frac{30979}{12500}

- \frac{7}{10} \cdot \frac{30979}{12500} + 2 \cdot \frac{30979}{12500}

Factor out common term

\frac{30979}{12500}

= \frac{30979}{12500} (- \frac{7}{10} + 2)

- \frac{7}{10} + 2 = \frac{13}{10}

- \frac{7}{10} + 2

Convert element to fraction:

2 = \frac{2 \cdot 10}{10}

= - \frac{7}{10} + \frac{2 \cdot 10}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{- 7 + 2 \cdot 10}{10}

- 7 + 2 \cdot 10 = 13

- 7 + 2 \cdot 10

Multiply the numbers:

2 \cdot 10 = 20

= - 7 + 20

Add/Subtract the numbers:

- 7 + 20 = 13

= 13

= \frac{13}{10}

= \frac{13}{10} \cdot \frac{30979}{12500}

= \frac{13}{10} \cdot \frac{30979}{12500} - 4

\frac{13}{10} \cdot \frac{30979}{12500} = \frac{402727}{125000}

\frac{13}{10} \cdot \frac{30979}{12500}

Multiply fractions:

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

= \frac{13 \cdot 30979}{10 \cdot 12500}

Multiply the numbers:

13 \cdot 30979 = 402727

= \frac{402727}{10 \cdot 12500}

Multiply the numbers:

10 \cdot 12500 = 125000

= \frac{402727}{125000}

= \frac{402727}{125000} - 4

Convert element to fraction:

4 = \frac{4 \cdot 125000}{125000}

= \frac{402727}{125000} - \frac{4 \cdot 125000}{125000}

Since the denominators are equal, combine the fractions:

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

= \frac{402727 - 4 \cdot 125000}{125000}

402727 - 4 \cdot 125000 = - 97273

402727 - 4 \cdot 125000

Multiply the numbers:

4 \cdot 125000 = 500000

= 402727 - 500000

Subtract the numbers:

402727 - 500000 = - 97273

= - 97273

= \frac{- 97273}{125000}

Apply the fraction rule:

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

= - \frac{97273}{125000}

= sinh (- \frac{97273}{125000})

Use the following property:

sinh (- x) = - sinh (x)

sinh (- \frac{97273}{125000}) = - sinh (\frac{97273}{125000})

= - sinh (\frac{97273}{125000})

Rewrite using trig identities:

sinh (\frac{97273}{125000}) = \frac{e ^{\frac{97273}{62500}} - 1}{2 e ^{\frac{97273}{125000}}}

sinh (\frac{97273}{125000})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{97273}{125000}} - e ^{- \frac{97273}{125000}}}{2}

\frac{e ^{\frac{97273}{125000}} - e ^{- \frac{97273}{125000}}}{2} = \frac{e ^{\frac{97273}{62500}} - 1}{2 e ^{\frac{97273}{125000}}}

\frac{e ^{\frac{97273}{125000}} - e ^{- \frac{97273}{125000}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{97273}{125000}} - \frac{1}{e ^{\frac{97273}{125000}}}}{2}

Join

e^{\frac{97273}{125000}} - \frac{1}{e ^{\frac{97273}{125000}}} : \frac{e ^{\frac{97273}{62500}} - 1}{e ^{\frac{97273}{125000}}}

e^{\frac{97273}{125000}} - \frac{1}{e ^{\frac{97273}{125000}}}

Convert element to fraction:

e^{\frac{97273}{125000}} = \frac{e ^{\frac{97273}{125000}} e ^{\frac{97273}{125000}}}{e ^{\frac{97273}{125000}}}

= \frac{e ^{\frac{97273}{125000}} e ^{\frac{97273}{125000}}}{e ^{\frac{97273}{125000}}} - \frac{1}{e ^{\frac{97273}{125000}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{97273}{125000}} e ^{\frac{97273}{125000}} - 1}{e ^{\frac{97273}{125000}}}

e^{\frac{97273}{125000}} e^{\frac{97273}{125000}} - 1 = e^{2 \cdot \frac{97273}{125000}} - 1

e^{\frac{97273}{125000}} e^{\frac{97273}{125000}} - 1

e^{\frac{97273}{125000}} e^{\frac{97273}{125000}} = e^{2 \cdot \frac{97273}{125000}}

e^{\frac{97273}{125000}} e^{\frac{97273}{125000}}

Apply exponent rule:

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

e^{\frac{97273}{125000}} e^{\frac{97273}{125000}} = e^{\frac{97273}{125000} + \frac{97273}{125000}}

= e^{\frac{97273}{125000} + \frac{97273}{125000}}

Add similar elements:

\frac{97273}{125000} + \frac{97273}{125000} = 2 \cdot \frac{97273}{125000}

= e^{2 \cdot \frac{97273}{125000}}

= e^{2 \cdot \frac{97273}{125000}} - 1

= \frac{e ^{2 \cdot \frac{97273}{125000}} - 1}{e ^{\frac{97273}{125000}}}

Multiply

2 \cdot \frac{97273}{125000} : \frac{97273}{62500}

2 \cdot \frac{97273}{125000}

Multiply fractions:

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

= \frac{97273 \cdot 2}{125000}

Multiply the numbers:

97273 \cdot 2 = 194546

= \frac{194546}{125000}

Cancel the common factor:

2

= \frac{97273}{62500}

= \frac{e ^{\frac{97273}{62500}} - 1}{e ^{\frac{97273}{125000}}}

= \frac{\frac{e ^{\frac{97273}{62500}} - 1}{e ^{\frac{97273}{125000}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{\frac{97273}{62500}} - 1}{e ^{\frac{97273}{125000}} \cdot 2}

= \frac{e ^{\frac{97273}{62500}} - 1}{2 e ^{\frac{97273}{125000}}}

= - \frac{e ^{\frac{97273}{62500}} - 1}{2 e ^{\frac{97273}{125000}}}

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Frequently Asked Questions (FAQ)

What is the value of sinh(((2*2.47832)-4)-0.7*2.47832) ?
The value of sinh(((2*2.47832)-4)-0.7*2.47832) is -(e^{97273/62500}-1)/(2e^{97273/125000)}