Lutasin ang 100/sqrt{2}7*3/sqrt{2}cos(433)

$$\frac{ 100 }{ \sqrt{ 2 } } \frac{ 7 \cdot 3 }{ \sqrt{ 2 } } \cos ( 433 )$$

I-evaluate

$$306.990289958873115$$

Mga Hakbang ng Solution

Evaluate trigonometric functions in the problem

$$\frac{100}{\sqrt{2}} \frac{7 \cdot 3}{\sqrt{2}} 0.2923717047227363$$

I-rationalize ang denominator ng \frac{100}{\sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{2}.

$$0.2923717047227363\times \frac{100\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{7\times 3}{\sqrt{2}}$$

Ang square ng \sqrt{2} ay 2.

$$0.2923717047227363\times \frac{100\sqrt{2}}{2}\times \frac{7\times 3}{\sqrt{2}}$$

I-divide ang 100\sqrt{2} gamit ang 2 para makuha ang 50\sqrt{2}.

$$0.2923717047227363\times 50\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

I-multiply ang 0.2923717047227363 at 50 para makuha ang 14.618585236136815.

$$14.618585236136815\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

I-multiply ang 7 at 3 para makuha ang 21.

$$14.618585236136815\sqrt{2}\times \frac{21}{\sqrt{2}}$$

I-rationalize ang denominator ng \frac{21}{\sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{2}.

$$14.618585236136815\sqrt{2}\times \frac{21\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ang square ng \sqrt{2} ay 2.

$$14.618585236136815\sqrt{2}\times \frac{21\sqrt{2}}{2}$$

Ipakita ang \sqrt{2}\times \frac{21\sqrt{2}}{2} bilang isang single fraction.

$$14.618585236136815\times \frac{\sqrt{2}\times 21\sqrt{2}}{2}$$

I-multiply ang \sqrt{2} at \sqrt{2} para makuha ang 2.

$$14.618585236136815\times \frac{2\times 21}{2}$$

I-cancel out ang 2 at 2.

$$14.618585236136815\times 21$$

I-multiply ang 14.618585236136815 at 21 para makuha ang 306.990289958873115.

$$306.990289958873115$$

I-factor

$$\frac{3 \cdot 7 \cdot 373 \cdot 25679 \cdot 305244889}{2 ^ {15} \cdot 5 ^ {14}} = 306\frac{198057991774624}{200000000000000} = 306.9902899588731$$