Lahenda 1/2*981t-20cos15^circ/20sin15^circ=tan15^circ

$$\frac { \frac { 1 } { 2 } \times 981 t - 20 \cos 15 ^ { \circ } } { 20 \sin 15 ^ { \circ } } = \tan 15 ^ { \circ }$$

Lahendage ja leidke t

$$t=\frac{517638090205041527491131299117399}{12262500000000000000000000000000000}\approx 0,042213096$$

Juhised lineaarvõrrandi lahendamiseks

Evaluate trigonometric functions in the problem

$$\frac{\frac{1}{2} \cdot 981 t - 20 \cdot 0,9659258262890683}{20 \cdot 0,25881904510252074} = 0,2679491924311227$$

Korrutage \frac{1}{2} ja 981, et leida \frac{981}{2}.

$$\frac{\frac{981}{2}t-20\times 0,9659258262890683}{20\times 0,25881904510252074}=0,2679491924311227$$

Korrutage 20 ja 0,9659258262890683, et leida 19,318516525781366.

$$\frac{\frac{981}{2}t-19,318516525781366}{20\times 0,25881904510252074}=0,2679491924311227$$

Korrutage 20 ja 0,25881904510252074, et leida 5,1763809020504148.

$$\frac{\frac{981}{2}t-19,318516525781366}{5,1763809020504148}=0,2679491924311227$$

Jagage \frac{981}{2}t-19,318516525781366 iga liige 5,1763809020504148-ga, et saada \frac{\frac{981}{2}t}{5,1763809020504148}+\frac{-19,318516525781366}{5,1763809020504148}.

$$\frac{\frac{981}{2}t}{5,1763809020504148}+\frac{-19,318516525781366}{5,1763809020504148}=0,2679491924311227$$

Jagage \frac{981}{2}t väärtusega 5,1763809020504148, et leida \frac{136250000000000000}{1437883583902893}t.

$$\frac{136250000000000000}{1437883583902893}t+\frac{-19,318516525781366}{5,1763809020504148}=0,2679491924311227$$

Saate \frac{-19,318516525781366}{5,1763809020504148} laiendada, korrutades nii lugeja kui ka nimetaja 10000000000000000.

$$\frac{136250000000000000}{1437883583902893}t+\frac{-193185165257813660}{51763809020504148}=0,2679491924311227$$

Taandage murd \frac{-193185165257813660}{51763809020504148} vähimale ühiskordsele, eraldades ja taandades arvu 4.

$$\frac{136250000000000000}{1437883583902893}t-\frac{48296291314453415}{12940952255126037}=0,2679491924311227$$

Liitke \frac{48296291314453415}{12940952255126037} mõlemale poolele.

$$\frac{136250000000000000}{1437883583902893}t=0,2679491924311227+\frac{48296291314453415}{12940952255126037}$$

Teisendage kümnendarv 0,2679491924311227 murdarvuks \frac{2679491924311227}{10000000000}. Taandage murd \frac{2679491924311227}{10000000000} vähimale ühiskordsele, eraldades ja taandades arvu 1.

$$\frac{136250000000000000}{1437883583902893}t=\frac{2679491924311227}{10000000000000000}+\frac{48296291314453415}{12940952255126037}$$

10000000000000000 ja 12940952255126037 vähim ühiskordne on 129409522551260370000000000000000. Teisendage \frac{2679491924311227}{10000000000000000} ja \frac{48296291314453415}{12940952255126037} murdarvudeks, mille nimetaja on 129409522551260370000000000000000.

$$\frac{136250000000000000}{1437883583902893}t=\frac{34675177060507377491131299117399}{129409522551260370000000000000000}+\frac{482962913144534150000000000000000}{129409522551260370000000000000000}$$

Kuna murdudel \frac{34675177060507377491131299117399}{129409522551260370000000000000000} ja \frac{482962913144534150000000000000000}{129409522551260370000000000000000} on sama nimetaja, liitke nende lugejad.

$$\frac{136250000000000000}{1437883583902893}t=\frac{34675177060507377491131299117399+482962913144534150000000000000000}{129409522551260370000000000000000}$$

Liitke 34675177060507377491131299117399 ja 482962913144534150000000000000000, et leida 517638090205041527491131299117399.

$$\frac{136250000000000000}{1437883583902893}t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}$$

Korrutage mõlemad pooled \frac{1437883583902893}{136250000000000000}-ga, mis on \frac{136250000000000000}{1437883583902893} pöördväärtus.

$$t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}\times \frac{1437883583902893}{136250000000000000}$$

Korrutage omavahel \frac{517638090205041527491131299117399}{129409522551260370000000000000000} ja \frac{1437883583902893}{136250000000000000}. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

$$t=\frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 136250000000000000}$$

Tehke korrutustehted murruga \frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 136250000000000000}.

$$t=\frac{744303312308674124392241432979420423814622735307}{17632047447609225412500000000000000000000000000000}$$

Taandage murd \frac{744303312308674124392241432979420423814622735307}{17632047447609225412500000000000000000000000000000} vähimale ühiskordsele, eraldades ja taandades arvu 1437883583902893.

$$t=\frac{517638090205041527491131299117399}{12262500000000000000000000000000000}$$