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شائع علم المثلثات >

100=211.49-20.96cosh(0.03291765x)

الحلّ

100 = 211.49 - 20.96 cosh (0.03291765 x)

الحلّ

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096}), x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

درجات

x = - 4099.95343 \dots^{\circ}, x = 4099.95343 \dots^{\circ}

خطوات الحلّ

100 = 211.49 - 20.96 cosh (0.03291765 x)

بدّل الأطراف

211.49 - 20.96 cosh (0.03291765 x) = 100

Rewrite using trig identities

211.49 - 20.96 cosh (0.03291765 x) = 100

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

:Use the Hyperbolic identity

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 100

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 100

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 100 : x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096}), x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 100

فعّل قانون القوى

211.49 - 20.96 \cdot \frac{e ^{0.03291765 x} + e ^{- 0.03291765 x}}{2} = 100

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

:فعّل قانون القوى

e^{0.03291765 x} = (e^{x})^{0.03291765}, e^{- 0.03291765 x} = (e^{x})^{- 0.03291765}

211.49 - 20.96 \cdot \frac{( e ^{x} ) ^{0.03291765} + ( e ^{x} ) ^{- 0.03291765}}{2} = 100

211.49 - 20.96 \cdot \frac{( e ^{x} ) ^{0.03291765} + ( e ^{x} ) ^{- 0.03291765}}{2} = 100

e^{x} = u

أعد كتابة المعادلة، بحيث أنّ

211.49 - 20.96 \cdot \frac{( u ) ^{0.03291765} + ( u ) ^{- 0.03291765}}{2} = 100

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 100

حلّ:

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}, u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 100

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2}

وسّع:

211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}}

211.49 - 20.96 \cdot \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2}

\frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = \frac{u ^{0.0658353} + 1}{2 u ^{0.03291765}}

\frac{u ^{0.03291765} + u ^{- 0.03291765}}{2}

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

:فعّل قانون القوى

= \frac{u ^{0.03291765} + \frac{1}{u ^{0.03291765}}}{2}

u^{0.03291765} + \frac{1}{u ^{0.03291765}}

وحّد:

\frac{u ^{0.0658353} + 1}{u ^{0.03291765}}

u^{0.03291765} + \frac{1}{u ^{0.03291765}}

u^{0.03291765} = \frac{u ^{0.03291765} u ^{0.03291765}}{u ^{0.03291765}}

:حوّل الأعداد لكسور

= \frac{u ^{0.03291765} u ^{0.03291765}}{u ^{0.03291765}} + \frac{1}{u ^{0.03291765}}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{u ^{0.03291765} u ^{0.03291765} + 1}{u ^{0.03291765}}

u^{0.03291765} u^{0.03291765} + 1 = u^{0.0658353} + 1

u^{0.03291765} u^{0.03291765} + 1

u^{0.03291765} u^{0.03291765} = u^{0.0658353}

u^{0.03291765} u^{0.03291765}

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

:فعّل قانون القوى

u^{0.03291765} u^{0.03291765} = u^{0.03291765 + 0.03291765}

= u^{0.03291765 + 0.03291765}

0.03291765 + 0.03291765 = 0.0658353 :

اجمع الأعداد

= u^{0.0658353}

= u^{0.0658353} + 1

= \frac{u ^{0.0658353} + 1}{u ^{0.03291765}}

= \frac{\frac{u ^{0.0658353} + 1}{u ^{0.03291765}}}{2}

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

: استخدم ميزات الكسور التالية

= \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2}

= 211.49 - 20.96 \cdot \frac{u ^{0.0658353} + 1}{2 u ^{0.03291765}}

20.96 \cdot \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2} = \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

20.96 \cdot \frac{u ^{0.0658353} + 1}{u ^{0.03291765} \cdot 2}

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

:اضرب كسور

= \frac{( u ^{0.0658353} + 1 ) \cdot 20.96}{u ^{0.03291765} \cdot 2}

(u^{0.0658353} + 1) \cdot 20.96

وسٌع:

20.96 u^{0.0658353} + 20.96

(u^{0.0658353} + 1) \cdot 20.96

= 20.96 (u^{0.0658353} + 1)

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = 20.96, b = u^{0.0658353}, c = 1

= 20.96 u^{0.0658353} + 20.96 \cdot 1

= 20.96 u^{0.0658353} + 1 \cdot 20.96

1 \cdot 20.96 = 20.96 :

اضرب الأعداد

= 20.96 u^{0.0658353} + 20.96

= \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

= 211.49 - \frac{20.96 u ^{0.0658353} + 20.96}{2 u ^{0.03291765}}

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

: استخدم ميزات الكسور التالية

\frac{20.96 u ^{0.0658353} + 20.96}{u ^{0.03291765} \cdot 2} = - (\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}) - (\frac{20.96}{u ^{0.03291765} \cdot 2})

= 211.49 - (\frac{20.96 u ^{0.0658353}}{2 u ^{0.03291765}}) - (\frac{20.96}{2 u ^{0.03291765}})

(a) = a

:احذف الأقواس

= 211.49 - \frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2} - \frac{20.96}{u ^{0.03291765} \cdot 2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

اختزل:

\frac{20.96 u ^{0.03291765}}{2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

اختزل:

\frac{20.96 u ^{0.03291765}}{2}

\frac{20.96 u ^{0.0658353}}{u ^{0.03291765} \cdot 2}

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

:فعّل قانون القوى

\frac{u ^{0.0658353}}{u ^{0.03291765}} = u^{0.0658353 - 0.03291765}

= \frac{20.96 u ^{0.0658353 - 0.03291765}}{2}

0.0658353 - 0.03291765 = 0.03291765 :

اطرح الأعداد

= \frac{20.96 u ^{0.03291765}}{2}

= \frac{20.96 u ^{0.03291765}}{2}

= 211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}}

211.49 - \frac{20.96 u ^{0.03291765}}{2} - \frac{20.96}{2 u ^{0.03291765}} = 100

a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)} :

استخدم الميزة الأسيّة التالية

u^{0.03291765} = (u^{\frac{1}{8901}})^{(0.03291765 \cdot 8901)}

211.49 - \frac{20.96 ( u ^{\frac{1}{8901}} ) ^{293}}{2} - \frac{20.96}{2 ( u ^{\frac{1}{8901}} ) ^{293}} = 100

u^{\frac{1}{8901}} = v

أعد كتابة المعادلة، بحيث أنّ

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 100

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 100

حلّ:

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 100

انقل

211.49

إلى الجانب الأيمن

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = 100

من الطرفين

211.49

اطرح

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} - 211.49 = 100 - 211.49

بسّط

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 111.49

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 111.49

v^{293}

اضرب الطرفين بـ

- \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}} = - 111.49

v^{293}

اضرب الطرفين بـ

- \frac{20.96 v ^{293}}{2} v^{293} - \frac{20.96}{2 v ^{293}} v^{293} = - 111.49 v^{293}

بسّط

- \frac{20.96 v ^{293}}{2} v^{293} - \frac{20.96}{2 v ^{293}} v^{293} = - 111.49 v^{293}

- \frac{20.96 v ^{293}}{2} v^{293}

بسّط:

- \frac{20.96 v ^{586}}{2}

- \frac{20.96 v ^{293}}{2} v^{293}

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

:اضرب كسور

= - \frac{20.96 v ^{293} v ^{293}}{2}

20.96 v^{293} v^{293} = 20.96 v^{586}

20.96 v^{293} v^{293}

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

:فعّل قانون القوى

v^{293} v^{293} = v^{293 + 293}

= 20.96 v^{293 + 293}

293 + 293 = 586 :

اجمع الأعداد

= 20.96 v^{586}

= - \frac{20.96 v ^{586}}{2}

- \frac{20.96}{2 v ^{293}} v^{293}

بسّط:

- \frac{20.96}{2}

- \frac{20.96}{2 v ^{293}} v^{293}

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

:اضرب كسور

= - \frac{20.96 v ^{293}}{2 v ^{293}}

v^{293} :

إلغ العوامل المشتركة

= - \frac{20.96}{2}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

حلّ:

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

100

اضرب الطرفين بـ

- \frac{20.96 v ^{586}}{2} - \frac{20.96}{2} = - 111.49 v^{293}

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- \frac{20.96 v ^{586}}{2} \cdot 100 - \frac{20.96}{2} \cdot 100 = - 111.49 v^{293} \cdot 100

بسّط

- 1048 v^{586} - 1048 = - 11149 v^{293}

- 1048 v^{586} - 1048 = - 11149 v^{293}

انقل

11149 v^{293}

إلى الجانب الأيسر

- 1048 v^{586} - 1048 = - 11149 v^{293}

للطرفين

11149 v^{293}

أضف

- 1048 v^{586} - 1048 + 11149 v^{293} = - 11149 v^{293} + 11149 v^{293}

بسّط

- 1048 v^{586} - 1048 + 11149 v^{293} = 0

- 1048 v^{586} - 1048 + 11149 v^{293} = 0

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

اكتب بالصورة الاعتياديّة

- 1048 v^{586} + 11149 v^{293} - 1048 = 0

u^{2} = v^{586}

وكذلك

u = v^{293}

اكتب المعادلة مجددًا، بحيث أنّ

- 1048 u^{2} + 11149 u - 1048 = 0

- 1048 u^{2} + 11149 u - 1048 = 0

حلّ:

u = \frac{11149 - 119906985}{2096}, u = \frac{11149 + 119906985}{2096}

- 1048 u^{2} + 11149 u - 1048 = 0

حلّ بالاستعانة بالصيغة التربيعيّة

- 1048 u^{2} + 11149 u - 1048 = 0

الصيغة لحلّ المعادلة التربيعيّة

a = - 1048, b = 11149, c = - 1048

لـ

u_{1, 2} = \frac{- 11149 \pm 1114 9 ^{2} - 4 ( - 1048 ) ( - 1048 )}{2 ( - 1048 )}

u_{1, 2} = \frac{- 11149 \pm 1114 9 ^{2} - 4 ( - 1048 ) ( - 1048 )}{2 ( - 1048 )}

1114 9^{2} - 4 (- 1048) (- 1048) = 119906985

1114 9^{2} - 4 (- 1048) (- 1048)

- (- a) = a

فعّل القانون

= 1114 9^{2} - 4 \cdot 1048 \cdot 1048

4 \cdot 1048 \cdot 1048 = 4393216 :

اضرب الأعداد

= 1114 9^{2} - 4393216

1114 9^{2} = 124300201

= 124300201 - 4393216

124300201 - 4393216 = 119906985 :

اطرح الأعداد

= 119906985

u_{1, 2} = \frac{- 11149 \pm 119906985}{2 ( - 1048 )}

Separate the solutions

u_{1} = \frac{- 11149 + 119906985}{2 ( - 1048 )}, u_{2} = \frac{- 11149 - 119906985}{2 ( - 1048 )}

u = \frac{- 11149 + 119906985}{2 ( - 1048 )} : \frac{11149 - 119906985}{2096}

\frac{- 11149 + 119906985}{2 ( - 1048 )}

(- a) = - a

:احذف الأقواس

= \frac{- 11149 + 119906985}{- 2 \cdot 1048}

2 \cdot 1048 = 2096 :

اضرب الأعداد

= \frac{- 11149 + 119906985}{- 2096}

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

: استخدم ميزات الكسور التالية

- 11149 + 119906985 = - (11149 - 119906985)

= \frac{11149 - 119906985}{2096}

u = \frac{- 11149 - 119906985}{2 ( - 1048 )} : \frac{11149 + 119906985}{2096}

\frac{- 11149 - 119906985}{2 ( - 1048 )}

(- a) = - a

:احذف الأقواس

= \frac{- 11149 - 119906985}{- 2 \cdot 1048}

2 \cdot 1048 = 2096 :

اضرب الأعداد

= \frac{- 11149 - 119906985}{- 2096}

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

: استخدم ميزات الكسور التالية

- 11149 - 119906985 = - (11149 + 119906985)

= \frac{11149 + 119906985}{2096}

حلول المعادلة التربيعيّة هي

u = \frac{11149 - 119906985}{2096}, u = \frac{11149 + 119906985}{2096}

u = \frac{11149 - 119906985}{2096}, u = \frac{11149 + 119906985}{2096}

Substitute back

u = v^{293},

solve for

v

v^{293} = \frac{11149 - 119906985}{2096}

حلّ:

v = 293 \frac{11149 - 119906985}{2096}

v^{293} = \frac{11149 - 119906985}{2096}

x = n f (a)

فرديّ، الحلّ هو

n, x^{n} = f (a)

لـ

v = 293 \frac{11149 - 119906985}{2096}

v^{293} = \frac{11149 + 119906985}{2096}

حلّ:

v = 293 \frac{11149 + 119906985}{2096}

v^{293} = \frac{11149 + 119906985}{2096}

x = n f (a)

فرديّ، الحلّ هو

n, x^{n} = f (a)

لـ

v = 293 \frac{11149 + 119906985}{2096}

The solutions are

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

افحص الإجبات

جد نقاط غير معرّفة:

v = 0

وقم بمساواتها لصفر

211.49 - \frac{20.96 v ^{293}}{2} - \frac{20.96}{2 v ^{293}}

خذ المقامات في

2 v^{293} = 0

حلّ:

v = 0

2 v^{293} = 0

2

اقسم الطرفين على

2 v^{293} = 0

2

اقسم الطرفين على

2 v^{293} = 0

2

اقسم الطرفين على

\frac{2 v ^{293}}{2} = \frac{0}{2}

بسّط

v^{293} = 0

v^{293} = 0

x^{n} = 0 \Rightarrow x = 0

فعّل القانون

v = 0

النقاط التالية غير معرّفة

v = 0

ضمّ النقاط غير المعرّفة مع الحلول

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

v = 293 \frac{11149 - 119906985}{2096}, v = 293 \frac{11149 + 119906985}{2096}

Substitute back

v = u^{\frac{1}{8901}},

solve for

u

u^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

حلّ:

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

8901

ارفع طرفيّ المعادلة للقوّة:

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

(u^{\frac{1}{8901}})^{8901} = 293 \frac{11149 - 119906985}{2096}^{8901}

(u^{\frac{1}{8901}})^{8901}

وسّع:

u

(u^{\frac{1}{8901}})^{8901}

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

:فعّل قانون القوى

= u^{\frac{1}{8901} \cdot 8901}

\frac{1}{8901} \cdot 8901 = 1

\frac{1}{8901} \cdot 8901

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

:اضرب كسور

= \frac{1 \cdot 8901}{8901}

8901 :

إلغ العوامل المشتركة

= 1

= u

293 \frac{11149 - 119906985}{2096}^{8901}

وسّع:

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

293 \frac{11149 - 119906985}{2096}^{8901}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

= (\frac{11149 - 119906985}{2096})^{\frac{1}{293}}^{8901}

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

:فعّل قانون القوى

= (\frac{11149 - 119906985}{2096})^{\frac{1}{293} \cdot 8901}

\frac{1}{293} \cdot 8901 = \frac{8901}{293}

\frac{1}{293} \cdot 8901

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

:اضرب كسور

= \frac{1 \cdot 8901}{293}

1 \cdot 8901 = 8901 :

اضرب الأعداد

= \frac{8901}{293}

= (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

افحص الإجبات:

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

صحيح

للتحقّق من دقّة الحلول

u^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

عوّض الحلول في

إلغي الحلول التي تعطي قضيّة كذب

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

استبدل:

صحيح

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{11149 - 119906985}{2096}

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}}

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

:فعّل قانون القوى

= (\frac{11149 - 119906985}{2096})^{\frac{8901}{293} \cdot \frac{1}{8901}}

بسّط

= (\frac{11149 - 119906985}{2096})^{\frac{1}{293}}

a^{\frac{1}{n}} = n a

= 293 \frac{11149 - 119906985}{2096}

293 \frac{11149 - 119906985}{2096} = 293 \frac{11149 - 119906985}{2096}

صحيح

الحل للمعادلة هو

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

حلّ:

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

8901

ارفع طرفيّ المعادلة للقوّة:

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

(u^{\frac{1}{8901}})^{8901} = 293 \frac{11149 + 119906985}{2096}^{8901}

(u^{\frac{1}{8901}})^{8901}

وسّع:

u

(u^{\frac{1}{8901}})^{8901}

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

:فعّل قانون القوى

= u^{\frac{1}{8901} \cdot 8901}

\frac{1}{8901} \cdot 8901 = 1

\frac{1}{8901} \cdot 8901

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

:اضرب كسور

= \frac{1 \cdot 8901}{8901}

8901 :

إلغ العوامل المشتركة

= 1

= u

293 \frac{11149 + 119906985}{2096}^{8901}

وسّع:

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

293 \frac{11149 + 119906985}{2096}^{8901}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

= (\frac{11149 + 119906985}{2096})^{\frac{1}{293}}^{8901}

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

:فعّل قانون القوى

= (\frac{11149 + 119906985}{2096})^{\frac{1}{293} \cdot 8901}

\frac{1}{293} \cdot 8901 = \frac{8901}{293}

\frac{1}{293} \cdot 8901

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

:اضرب كسور

= \frac{1 \cdot 8901}{293}

1 \cdot 8901 = 8901 :

اضرب الأعداد

= \frac{8901}{293}

= (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

افحص الإجبات:

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

صحيح

للتحقّق من دقّة الحلول

u^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

عوّض الحلول في

إلغي الحلول التي تعطي قضيّة كذب

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

استبدل:

صحيح

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}} = 293 \frac{11149 + 119906985}{2096}

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{\frac{1}{8901}}

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

:فعّل قانون القوى

= (\frac{11149 + 119906985}{2096})^{\frac{8901}{293} \cdot \frac{1}{8901}}

بسّط

= (\frac{11149 + 119906985}{2096})^{\frac{1}{293}}

a^{\frac{1}{n}} = n a

= 293 \frac{11149 + 119906985}{2096}

293 \frac{11149 + 119906985}{2096} = 293 \frac{11149 + 119906985}{2096}

صحيح

الحل للمعادلة هو

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}, u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

افحص الإجبات:

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

صحيح

, u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

صحيح

للتحقّق من دقّة الحلول

211.49 - 20.96 \frac{u ^{0.03291765} + u ^{- 0.03291765}}{2} = 100

عوّض الحلول في

إلغي الحلول التي تعطي قضيّة كذب

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

استبدل:

صحيح

211.49 - 20.96 \cdot \frac{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 100

211.49 - 20.96 \cdot \frac{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 99.99999 \dots

211.49 - 20.96 \cdot \frac{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

\frac{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = \frac{10.63835 \dots}{2}

\frac{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{0.03291765} = 0.09484 \dots

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{0.03291765}

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

:فعّل قانون القوى

= (\frac{11149 - 119906985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

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

:اضرب كسور

= \frac{8901 \cdot 0.03291765}{293}

8901 \cdot 0.03291765 = 293.00000 \dots :

اضرب الأعداد

= \frac{293.00000 \dots}{293}

\frac{293.00000 \dots}{293} = 1.00000 \dots :

اقسم الأعداد

= 1.00000 \dots

= (\frac{11149 - 119906985}{2096})^{1.00000 \dots}

\frac{11149 - 119906985}{2096} = \frac{198.79520 \dots}{2096}

\frac{11149 - 119906985}{2096}

حوّل لتمثيل عشريّ

119906985 = 10950.20479 \dots

= \frac{11149 - 10950.20479 \dots}{2096}

11149 - 10950.20479 \dots = 198.79520 \dots :

اطرح الأعداد

= \frac{198.79520 \dots}{2096}

= (\frac{198.79520 \dots}{2096})^{1.00000 \dots}

\frac{198.79520 \dots}{2096} = 0.09484 \dots :

اقسم الأعداد

= 0.09484 \dots^{1.00000 \dots}

0.09484 \dots^{1.00000 \dots} = 0.09484 \dots

= 0.09484 \dots

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{- 0.03291765} = 10.54351 \dots

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{- 0.03291765}

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

:فعّل قانون القوى

= \frac{1}{( ( \frac{11149 - 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765}}

(\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}^{0.03291765} : (\frac{11149 - 119906985}{2096})^{1.00000 \dots}

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

:فعّل قانون القوى

= (\frac{11149 - 119906985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

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

:اضرب كسور

= \frac{8901 \cdot 0.03291765}{293}

8901 \cdot 0.03291765 = 293.00000 \dots :

اضرب الأعداد

= \frac{293.00000 \dots}{293}

\frac{293.00000 \dots}{293} = 1.00000 \dots :

اقسم الأعداد

= 1.00000 \dots

= (\frac{11149 - 119906985}{2096})^{1.00000 \dots}

= \frac{1}{( \frac{11149 - 119906985}{2096} ) ^{1.00000 \dots}}

\frac{11149 - 119906985}{2096} = \frac{198.79520 \dots}{2096}

\frac{11149 - 119906985}{2096}

حوّل لتمثيل عشريّ

119906985 = 10950.20479 \dots

= \frac{11149 - 10950.20479 \dots}{2096}

11149 - 10950.20479 \dots = 198.79520 \dots :

اطرح الأعداد

= \frac{198.79520 \dots}{2096}

= \frac{1}{( \frac{198.79520 \dots}{2096} ) ^{1.00000 \dots}}

(\frac{198.79520 \dots}{2096})^{1.00000 \dots} = 0.09484 \dots

= \frac{1}{0.09484 \dots}

\frac{1}{0.09484 \dots} = 10.54351 \dots :

اقسم الأعداد

= 10.54351 \dots

= \frac{0.09484 \dots + 10.54351 \dots}{2}

0.09484 \dots + 10.54351 \dots = 10.63835 \dots :

اجمع الأعداد

= \frac{10.63835 \dots}{2}

= 211.49 - 20.96 \cdot \frac{10.63835 \dots}{2}

20.96 \cdot \frac{10.63835 \dots}{2} = 111.49000 \dots

20.96 \cdot \frac{10.63835 \dots}{2}

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

:اضرب كسور

= \frac{10.63835 \dots \cdot 20.96}{2}

10.63835 \dots \cdot 20.96 = 222.98000 \dots :

اضرب الأعداد

= \frac{222.98000 \dots}{2}

\frac{222.98000 \dots}{2} = 111.49000 \dots :

اقسم الأعداد

= 111.49000 \dots

= 211.49 - 111.49000 \dots

211.49 - 111.49000 \dots = 99.99999 \dots :

اطرح الأعداد

= 99.99999 \dots

99.99999 \dots = 100

صحيح

u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

استبدل:

صحيح

211.49 - 20.96 \cdot \frac{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 100

211.49 - 20.96 \cdot \frac{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = 99.99999 \dots

211.49 - 20.96 \cdot \frac{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

\frac{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2} = \frac{10.63835 \dots}{2}

\frac{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765} + ( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{- 0.03291765}}{2}

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{0.03291765} = 10.54351 \dots

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{0.03291765}

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

:فعّل قانون القوى

= (\frac{11149 + 119906985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

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

:اضرب كسور

= \frac{8901 \cdot 0.03291765}{293}

8901 \cdot 0.03291765 = 293.00000 \dots :

اضرب الأعداد

= \frac{293.00000 \dots}{293}

\frac{293.00000 \dots}{293} = 1.00000 \dots :

اقسم الأعداد

= 1.00000 \dots

= (\frac{11149 + 119906985}{2096})^{1.00000 \dots}

\frac{11149 + 119906985}{2096} = \frac{22099.20479 \dots}{2096}

\frac{11149 + 119906985}{2096}

حوّل لتمثيل عشريّ

119906985 = 10950.20479 \dots

= \frac{11149 + 10950.20479 \dots}{2096}

11149 + 10950.20479 \dots = 22099.20479 \dots :

اجمع الأعداد

= \frac{22099.20479 \dots}{2096}

= (\frac{22099.20479 \dots}{2096})^{1.00000 \dots}

\frac{22099.20479 \dots}{2096} = 10.54351 \dots :

اقسم الأعداد

= 10.54351 \dots^{1.00000 \dots}

10.54351 \dots^{1.00000 \dots} = 10.54351 \dots

= 10.54351 \dots

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{- 0.03291765} = 0.09484 \dots

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{- 0.03291765}

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

:فعّل قانون القوى

= \frac{1}{( ( \frac{11149 + 119906985}{2096} ) ^{\frac{8901}{293}} ) ^{0.03291765}}

(\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}^{0.03291765} : (\frac{11149 + 119906985}{2096})^{1.00000 \dots}

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

:فعّل قانون القوى

= (\frac{11149 + 119906985}{2096})^{\frac{8901}{293} \cdot 0.03291765}

\frac{8901}{293} \cdot 0.03291765 = 1.00000 \dots

\frac{8901}{293} \cdot 0.03291765

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

:اضرب كسور

= \frac{8901 \cdot 0.03291765}{293}

8901 \cdot 0.03291765 = 293.00000 \dots :

اضرب الأعداد

= \frac{293.00000 \dots}{293}

\frac{293.00000 \dots}{293} = 1.00000 \dots :

اقسم الأعداد

= 1.00000 \dots

= (\frac{11149 + 119906985}{2096})^{1.00000 \dots}

= \frac{1}{( \frac{11149 + 119906985}{2096} ) ^{1.00000 \dots}}

\frac{11149 + 119906985}{2096} = \frac{22099.20479 \dots}{2096}

\frac{11149 + 119906985}{2096}

حوّل لتمثيل عشريّ

119906985 = 10950.20479 \dots

= \frac{11149 + 10950.20479 \dots}{2096}

11149 + 10950.20479 \dots = 22099.20479 \dots :

اجمع الأعداد

= \frac{22099.20479 \dots}{2096}

= \frac{1}{( \frac{22099.20479 \dots}{2096} ) ^{1.00000 \dots}}

(\frac{22099.20479 \dots}{2096})^{1.00000 \dots} = 10.54351 \dots

= \frac{1}{10.54351 \dots}

\frac{1}{10.54351 \dots} = 0.09484 \dots :

اقسم الأعداد

= 0.09484 \dots

= \frac{10.54351 \dots + 0.09484 \dots}{2}

10.54351 \dots + 0.09484 \dots = 10.63835 \dots :

اجمع الأعداد

= \frac{10.63835 \dots}{2}

= 211.49 - 20.96 \cdot \frac{10.63835 \dots}{2}

20.96 \cdot \frac{10.63835 \dots}{2} = 111.49000 \dots

20.96 \cdot \frac{10.63835 \dots}{2}

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

:اضرب كسور

= \frac{10.63835 \dots \cdot 20.96}{2}

10.63835 \dots \cdot 20.96 = 222.98000 \dots :

اضرب الأعداد

= \frac{222.98000 \dots}{2}

\frac{222.98000 \dots}{2} = 111.49000 \dots :

اقسم الأعداد

= 111.49000 \dots

= 211.49 - 111.49000 \dots

211.49 - 111.49000 \dots = 99.99999 \dots :

اطرح الأعداد

= 99.99999 \dots

99.99999 \dots = 100

صحيح

The solutions are

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}, u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

u = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}, u = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

Substitute back

u = e^{x},

solve for

x

e^{x} = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

حلّ:

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096})

e^{x} = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

فعّل قانون القوى

e^{x} = (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

ln (f (x)) = ln (g (x))

إذا

, f (x) = g (x)

إذا تحقّق أنّ

ln (e^{x}) = ln (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

ln (e^{a}) = a

:فعّل قانون اللوغارتمات

ln (e^{x}) = x

x = ln (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}}

ln (x^{a}) = a \cdot ln (x)

:فعّل قانون اللوغارتمات

ln (\frac{11149 - 119906985}{2096})^{\frac{8901}{293}} = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096})

e^{x} = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

حلّ:

x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

e^{x} = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

فعّل قانون القوى

e^{x} = (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

ln (f (x)) = ln (g (x))

إذا

, f (x) = g (x)

إذا تحقّق أنّ

ln (e^{x}) = ln (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

ln (e^{a}) = a

:فعّل قانون اللوغارتمات

ln (e^{x}) = x

x = ln (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}}

ln (x^{a}) = a \cdot ln (x)

:فعّل قانون اللوغارتمات

ln (\frac{11149 + 119906985}{2096})^{\frac{8901}{293}} = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096}), x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

x = \frac{8901}{293} ln (\frac{11149 - 119906985}{2096}), x = \frac{8901}{293} ln (\frac{11149 + 119906985}{2096})

رسم

أمثلة شائعة

3sec^2(x)+4cos^2(x)=7

3 sec^{2} (x) + 4 cos^{2} (x) = 7

cos(θ)= 43/90

cos (θ) = \frac{43}{90}

8cos(2x-5)=3

8 cos (2 x - 5) = 3

(sqrt(116))/(sin(90))= 4/(sin(x))

\frac{116}{sin ( 9 0 ^{\circ} )} = \frac{4}{sin ( x )}

3/(cos^2(x))=(7+4)/(cot(x))

\frac{3}{cos ^{2} ( x )} = \frac{7 + 4}{cot ( x )}