Solve 12*9.8-0.275*7*9.8*cos(37)-7*9.8*sin(37)/19

$$\frac { 12 \times 9.8 - 0.275 \times 7 \times 9.8 \times \cos ( 37 ) - 7 \times 9.8 \times \sin ( 37 ) } { 19 }$$

Evaluate

$$\frac{15312307628681826987}{4750000000000000000}\approx 3.223643711$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{12 \cdot 9.8 - 0.275 \cdot 7 \cdot 9.8 \cdot 0.7986355100472928 - 7 \cdot 9.8 \cdot 0.6018150231520483}{19}$$

Multiply 12 and 9.8 to get 117.6.

$$\frac{117.6-0.275\times 7\times 9.8\times 0.7986355100472928-7\times 9.8\times 0.6018150231520483}{19}$$

Multiply 0.275 and 7 to get 1.925.

$$\frac{117.6-1.925\times 9.8\times 0.7986355100472928-7\times 9.8\times 0.6018150231520483}{19}$$

Multiply 1.925 and 9.8 to get 18.865.

$$\frac{117.6-18.865\times 0.7986355100472928-7\times 9.8\times 0.6018150231520483}{19}$$

Multiply 18.865 and 0.7986355100472928 to get 15.066258897042178672.

$$\frac{117.6-15.066258897042178672-7\times 9.8\times 0.6018150231520483}{19}$$

Subtract 15.066258897042178672 from 117.6 to get 102.533741102957821328.

$$\frac{102.533741102957821328-7\times 9.8\times 0.6018150231520483}{19}$$

Multiply 7 and 9.8 to get 68.6.

$$\frac{102.533741102957821328-68.6\times 0.6018150231520483}{19}$$

Multiply 68.6 and 0.6018150231520483 to get 41.28451058823051338.

$$\frac{102.533741102957821328-41.28451058823051338}{19}$$

Subtract 41.28451058823051338 from 102.533741102957821328 to get 61.249230514727307948.

$$\frac{61.249230514727307948}{19}$$

Expand \frac{61.249230514727307948}{19} by multiplying both numerator and the denominator by 1000000000000000000.

$$\frac{61249230514727307948}{19000000000000000000}$$

Reduce the fraction \frac{61249230514727307948}{19000000000000000000} to lowest terms by extracting and canceling out 4.

$$\frac{15312307628681826987}{4750000000000000000}$$

Factor

$$\frac{3 \cdot 5827 \cdot 17876327101123 \cdot 7 ^ {2}}{19 \cdot 2 ^ {16} \cdot 5 ^ {18}} = 3\frac{1.0623076286818263 \times 10^{18}}{4.75 \times 10^{18}} = 3.223643711301437$$