Solve =(7*10^-6)(5*10^3)cos(20^circ)+2

$$=(7 \times { 10 }^{ -6 } )(5 \times { 10 }^{ 3 } ) \cos ( 20 ^ { \circ } ) +2$$

Evaluate

$$2.032889241727506794$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(7 \cdot {(10)} ^ {-6})} {(5 \cdot {(10)} ^ {3})} 0.9396926207859084 + 2$$

To multiply powers of the same base, add their exponents. Add -6 and 3 to get -3.

$$7\times 10^{-3}\times 5\times 0.9396926207859084+2$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$7\times \frac{1}{1000}\times 5\times 0.9396926207859084+2$$

Multiply 7 and \frac{1}{1000} to get \frac{7}{1000}.

$$\frac{7}{1000}\times 5\times 0.9396926207859084+2$$

Multiply \frac{7}{1000} and 5 to get \frac{7}{200}.

$$\frac{7}{200}\times 0.9396926207859084+2$$

Multiply \frac{7}{200} and 0.9396926207859084 to get \frac{16444620863753397}{500000000000000000}.

$$\frac{16444620863753397}{500000000000000000}+2$$

Add \frac{16444620863753397}{500000000000000000} and 2 to get \frac{1016444620863753397}{500000000000000000}.

$$\frac{1016444620863753397}{500000000000000000}$$

Factor

$$\frac{1016444620863753397}{2 ^ {17} \cdot 5 ^ {18}} = 2\frac{16444620863753344}{5 \times 10^{17}} = 2.032889241727507$$