Zgjidh 1/2*9.81t-20cos15^circ/20sin15^circ=tan15^circ

$$\frac { \frac { 1 } { 2 } \times 9.81 t - 20 \cos 15 ^ { \circ } } { 20 \sin 15 ^ { \circ } } = \tan 15 ^ { \circ }$$

Gjej t

$$t = \frac{517638090205041527491131299117399}{122625000000000000000000000000000} = 4\frac{2.713809020504151 \times 10^{31}}{1.2262499999999998 \times 10^{32}} \approx 4.221309604$$

Hapat për zgjidhjen e ekuacionit linear

Evaluate trigonometric functions in the problem

$$\frac{\frac{1}{2} \cdot 9.81 t - 20 \cdot 0.9659258262890683}{20 \cdot 0.25881904510252074} = 0.2679491924311227$$

Konverto numrin dhjetor 9.81 në thyesën \frac{981}{100}.

$$\frac{\frac{1}{2}\times \frac{981}{100}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Shumëzo \frac{1}{2} herë \frac{981}{100} duke shumëzuar numëruesin me numëruesin dhe emëruesin me emëruesin.

$$\frac{\frac{1\times 981}{2\times 100}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Bëj shumëzimet në thyesën \frac{1\times 981}{2\times 100}.

$$\frac{\frac{981}{200}t-20\times 0.9659258262890683}{20\times 0.25881904510252074}=0.2679491924311227$$

Shumëzo 20 me 0.9659258262890683 për të marrë 19.318516525781366.

$$\frac{\frac{981}{200}t-19.318516525781366}{20\times 0.25881904510252074}=0.2679491924311227$$

Shumëzo 20 me 0.25881904510252074 për të marrë 5.1763809020504148.

$$\frac{\frac{981}{200}t-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Pjesëto çdo kufizë të \frac{981}{200}t-19.318516525781366 me 5.1763809020504148 për të marrë \frac{\frac{981}{200}t}{5.1763809020504148}+\frac{-19.318516525781366}{5.1763809020504148}.

$$\frac{\frac{981}{200}t}{5.1763809020504148}+\frac{-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Pjesëto \frac{981}{200}t me 5.1763809020504148 për të marrë \frac{1362500000000000}{1437883583902893}t.

$$\frac{1362500000000000}{1437883583902893}t+\frac{-19.318516525781366}{5.1763809020504148}=0.2679491924311227$$

Zhvillo \frac{-19.318516525781366}{5.1763809020504148} duke shumëzuar si numëruesin ashtu dhe emëruesin me 10000000000000000.

$$\frac{1362500000000000}{1437883583902893}t+\frac{-193185165257813660}{51763809020504148}=0.2679491924311227$$

Thjeshto thyesën \frac{-193185165257813660}{51763809020504148} në kufizat më të vogla duke zbritur dhe thjeshtuar 4.

$$\frac{1362500000000000}{1437883583902893}t-\frac{48296291314453415}{12940952255126037}=0.2679491924311227$$

Shto \frac{48296291314453415}{12940952255126037} në të dyja anët.

$$\frac{1362500000000000}{1437883583902893}t=0.2679491924311227+\frac{48296291314453415}{12940952255126037}$$

Konverto numrin dhjetor 0.2679491924311227 në thyesën \frac{2679491924311227}{10000000000}. Thjeshto thyesën \frac{2679491924311227}{10000000000} në kufizat më të vogla duke zbritur dhe thjeshtuar 1.

$$\frac{1362500000000000}{1437883583902893}t=\frac{2679491924311227}{10000000000000000}+\frac{48296291314453415}{12940952255126037}$$

Shumëfishi më i vogël i përbashkët i 10000000000000000 dhe 12940952255126037 është 129409522551260370000000000000000. Konverto \frac{2679491924311227}{10000000000000000} dhe \frac{48296291314453415}{12940952255126037} në thyesa me emërues 129409522551260370000000000000000.

$$\frac{1362500000000000}{1437883583902893}t=\frac{34675177060507377491131299117399}{129409522551260370000000000000000}+\frac{482962913144534150000000000000000}{129409522551260370000000000000000}$$

Meqenëse \frac{34675177060507377491131299117399}{129409522551260370000000000000000} dhe \frac{482962913144534150000000000000000}{129409522551260370000000000000000} kanë të njëjtin emërues, mblidhi duke mbledhur numëruesit e tyre.

$$\frac{1362500000000000}{1437883583902893}t=\frac{34675177060507377491131299117399+482962913144534150000000000000000}{129409522551260370000000000000000}$$

Shto 34675177060507377491131299117399 dhe 482962913144534150000000000000000 për të marrë 517638090205041527491131299117399.

$$\frac{1362500000000000}{1437883583902893}t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}$$

Shumëzo të dyja anët me \frac{1437883583902893}{1362500000000000}, të anasjellën e \frac{1362500000000000}{1437883583902893}.

$$t=\frac{517638090205041527491131299117399}{129409522551260370000000000000000}\times \frac{1437883583902893}{1362500000000000}$$

Shumëzo \frac{517638090205041527491131299117399}{129409522551260370000000000000000} herë \frac{1437883583902893}{1362500000000000} duke shumëzuar numëruesin me numëruesin dhe emëruesin me emëruesin.

$$t=\frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 1362500000000000}$$

Bëj shumëzimet në thyesën \frac{517638090205041527491131299117399\times 1437883583902893}{129409522551260370000000000000000\times 1362500000000000}.

$$t=\frac{744303312308674124392241432979420423814622735307}{176320474476092254125000000000000000000000000000}$$

Thjeshto thyesën \frac{744303312308674124392241432979420423814622735307}{176320474476092254125000000000000000000000000000} në kufizat më të vogla duke zbritur dhe thjeshtuar 1437883583902893.

$$t=\frac{517638090205041527491131299117399}{122625000000000000000000000000000}$$