Whakaoti i te w=w+5/512(sin14)

$$w = \frac { w + 5 } { 512 } ( \sin 14 )$$

Whakaoti mō w

$$w=\frac{120960947799833865}{51175807810440033227}\approx 0.002363635$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Evaluate trigonometric functions in the problem

$$w = \frac{w + 5}{512} 0.24192189559966773$$

Whakawehea ia wā o w+5 ki te 512, kia riro ko \frac{1}{512}w+\frac{5}{512}.

$$w=\left(\frac{1}{512}w+\frac{5}{512}\right)\times 0.24192189559966773$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{512}w+\frac{5}{512} ki te 0.24192189559966773.

$$w=\frac{1}{512}w\times 0.24192189559966773+\frac{5}{512}\times 0.24192189559966773$$

Me tahuri ki tau ā-ira 0.24192189559966773 ki te hautau \frac{24192189559966773}{10000000000}. Whakahekea te hautanga \frac{24192189559966773}{10000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1.

$$w=\frac{1}{512}w\times \frac{24192189559966773}{100000000000000000}+\frac{5}{512}\times 0.24192189559966773$$

Me whakarea te \frac{1}{512} ki te \frac{24192189559966773}{100000000000000000} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$w=\frac{1\times 24192189559966773}{512\times 100000000000000000}w+\frac{5}{512}\times 0.24192189559966773$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 24192189559966773}{512\times 100000000000000000}.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5}{512}\times 0.24192189559966773$$

Me tahuri ki tau ā-ira 0.24192189559966773 ki te hautau \frac{24192189559966773}{10000000000}. Whakahekea te hautanga \frac{24192189559966773}{10000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5}{512}\times \frac{24192189559966773}{100000000000000000}$$

Me whakarea te \frac{5}{512} ki te \frac{24192189559966773}{100000000000000000} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{5\times 24192189559966773}{512\times 100000000000000000}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 24192189559966773}{512\times 100000000000000000}.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{120960947799833865}{51200000000000000000}$$

Whakahekea te hautanga \frac{120960947799833865}{51200000000000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$w=\frac{24192189559966773}{51200000000000000000}w+\frac{24192189559966773}{10240000000000000000}$$

Tangohia te \frac{24192189559966773}{51200000000000000000}w mai i ngā taha e rua.

$$w-\frac{24192189559966773}{51200000000000000000}w=\frac{24192189559966773}{10240000000000000000}$$

Pahekotia te w me -\frac{24192189559966773}{51200000000000000000}w, ka \frac{51175807810440033227}{51200000000000000000}w.

$$\frac{51175807810440033227}{51200000000000000000}w=\frac{24192189559966773}{10240000000000000000}$$

Me whakarea ngā taha e rua ki te \frac{51200000000000000000}{51175807810440033227}, te tau utu o \frac{51175807810440033227}{51200000000000000000}.

$$w=\frac{24192189559966773}{10240000000000000000}\times \frac{51200000000000000000}{51175807810440033227}$$

Me whakarea te \frac{24192189559966773}{10240000000000000000} ki te \frac{51200000000000000000}{51175807810440033227} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$w=\frac{24192189559966773\times 51200000000000000000}{10240000000000000000\times 51175807810440033227}$$

Mahia ngā whakarea i roto i te hautanga \frac{24192189559966773\times 51200000000000000000}{10240000000000000000\times 51175807810440033227}.

$$w=\frac{1238640105470298777600000000000000000}{524040271978905940244480000000000000000}$$

Whakahekea te hautanga \frac{1238640105470298777600000000000000000}{524040271978905940244480000000000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10240000000000000000.

$$w=\frac{120960947799833865}{51175807810440033227}$$