English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(arccosh(10000.69))/(arccosh(2))

Solution

\frac{arccosh ( 10000.69 )}{arccosh ( 2 )}

\frac{ln ( \frac{1000069 + 100006 9 ^{2} - 10000}{100} )}{ln ( 2 + 3 )}

Decimal Notation

7.52002 \dots

Solution steps

\frac{arccosh ( 10000.69 )}{arccosh ( 2 )}

= \frac{arccosh ( \frac{1000069}{100} )}{arccosh ( 2 )}

Rewrite using trig identities:

arccosh (\frac{1000069}{100}) = ln (\frac{1000069 + 100006 9 ^{2} - 10000}{100})

arccosh (\frac{1000069}{100})

Use the Hyperbolic identity:

arccosh (x) = ln (x + x^{2} - 1)

= ln \frac{1000069}{100} + (\frac{1000069}{100})^{2} - 1

ln \frac{1000069}{100} + (\frac{1000069}{100})^{2} - 1 = ln (\frac{1000069 + 100006 9 ^{2} - 10000}{100})

ln \frac{1000069}{100} + (\frac{1000069}{100})^{2} - 1

(\frac{1000069}{100})^{2} - 1 = \frac{100006 9 ^{2} - 10000}{100}

(\frac{1000069}{100})^{2} - 1

(\frac{1000069}{100})^{2} = \frac{100006 9 ^{2}}{10000}

(\frac{1000069}{100})^{2}

Apply exponent rule:

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

= \frac{100006 9 ^{2}}{10 0 ^{2}}

10 0^{2} = 10000

= \frac{100006 9 ^{2}}{10000}

= \frac{100006 9 ^{2}}{10000} - 1

Join

\frac{100006 9 ^{2}}{10000} - 1 : \frac{100006 9 ^{2} - 10000}{10000}

\frac{100006 9 ^{2}}{10000} - 1

Convert element to fraction:

1 = \frac{1 \cdot 10000}{10000}

= \frac{100006 9 ^{2}}{10000} - \frac{1 \cdot 10000}{10000}

Since the denominators are equal, combine the fractions:

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

= \frac{100006 9 ^{2} - 1 \cdot 10000}{10000}

Multiply the numbers:

1 \cdot 10000 = 10000

= \frac{100006 9 ^{2} - 10000}{10000}

= \frac{100006 9 ^{2} - 10000}{10000}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{100006 9 ^{2} - 10000}{10000}

10000 = 100

10000

Factor the number:

10000 = 10 0^{2}

= 10 0^{2}

Apply radical rule:

10 0^{2} = 100

= 100

= \frac{100006 9 ^{2} - 10000}{100}

= ln (\frac{1000069}{100} + \frac{100006 9 ^{2} - 10000}{100})

Join

\frac{1000069}{100} + \frac{100006 9 ^{2} - 10000}{100} : \frac{1000069 + 100006 9 ^{2} - 10000}{100}

\frac{1000069}{100} + \frac{100006 9 ^{2} - 10000}{100}

Since the denominators are equal, combine the fractions:

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

= \frac{1000069 + 100006 9 ^{2} - 10000}{100}

= ln (\frac{1000069 + 100006 9 ^{2} - 10000}{100})

= ln (\frac{1000069 + 100006 9 ^{2} - 10000}{100})

= \frac{ln ( \frac{1000069 + 100006 9 ^{2} - 10000}{100} )}{arccosh ( 2 )}

Rewrite using trig identities:

arccosh (2) = ln (2 + 3)

arccosh (2)

Use the Hyperbolic identity:

arccosh (x) = ln (x + x^{2} - 1)

= ln (2 + 2^{2} - 1)

Simplify

= ln (2 + 3)

= \frac{ln ( \frac{1000069 + 100006 9 ^{2} - 10000}{100} )}{ln ( 2 + 3 )}

sin (4 5^{\circ}) \cdot 50

sin (12. 5^{\circ})

arccos (0.642)

tan (\frac{5}{2})

arccos (- \frac{14}{5 26})