Solve 385.64378/45+100cos20^circ*2=

$$\frac { 385.64378 } { 45 + 100 \cos 20 ^ { \circ } } \times 2 =$$

Evaluate

$$\frac{19282189000000000}{3474231551964771}\approx 5.550058685$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{385.64378}{45 + 100 \cdot 0.9396926207859084} \cdot 2$$

Multiply 100 and 0.9396926207859084 to get 93.96926207859084.

$$\frac{385.64378}{45+93.96926207859084}\times 2$$

Add 45 and 93.96926207859084 to get 138.96926207859084.

$$\frac{385.64378}{138.96926207859084}\times 2$$

Expand \frac{385.64378}{138.96926207859084} by multiplying both numerator and the denominator by 100000000000000.

$$\frac{38564378000000000}{13896926207859084}\times 2$$

Reduce the fraction \frac{38564378000000000}{13896926207859084} to lowest terms by extracting and canceling out 4.

$$\frac{9641094500000000}{3474231551964771}\times 2$$

Express \frac{9641094500000000}{3474231551964771}\times 2 as a single fraction.

$$\frac{9641094500000000\times 2}{3474231551964771}$$

Multiply 9641094500000000 and 2 to get 19282189000000000.

$$\frac{19282189000000000}{3474231551964771}$$

Factor

$$\frac{43 \cdot 269 \cdot 1667 \cdot 2 ^ {9} \cdot 5 ^ {9}}{3 \cdot 13 \cdot 101 \cdot 421 \cdot 16091 \cdot 130199} = 5\frac{1911031240176145}{3474231551964771} = 5.550058685379046$$