Solve =18*250/33(2*9.8*0.98/(9.50)^2-(10.5*10^-3)^2)

$$= \frac { 18 \times 250 } { 33 } ( \frac { 2 \times 9.8 \times 0.98 } { ( 9.50 ) ^ { 2 } } - ( 10.5 \times 10 ^ { - 3 } ) ^ { 2 } )$$

Evaluate

$$\frac{921506397}{31768000}\approx 29.0073784$$

Solution Steps

Multiply 18 and 250 to get 4500.

$$\frac{4500}{33}\left(\frac{2\times 9.8\times 0.98}{9.5^{2}}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Reduce the fraction \frac{4500}{33} to lowest terms by extracting and canceling out 3.

$$\frac{1500}{11}\left(\frac{2\times 9.8\times 0.98}{9.5^{2}}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Multiply 2 and 9.8 to get 19.6.

$$\frac{1500}{11}\left(\frac{19.6\times 0.98}{9.5^{2}}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Multiply 19.6 and 0.98 to get 19.208.

$$\frac{1500}{11}\left(\frac{19.208}{9.5^{2}}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Calculate 9.5 to the power of 2 and get 90.25.

$$\frac{1500}{11}\left(\frac{19.208}{90.25}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Expand \frac{19.208}{90.25} by multiplying both numerator and the denominator by 1000.

$$\frac{1500}{11}\left(\frac{19208}{90250}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

Reduce the fraction \frac{19208}{90250} to lowest terms by extracting and canceling out 2.

$$\frac{1500}{11}\left(\frac{9604}{45125}-\left(10.5\times 10^{-3}\right)^{2}\right)$$

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

$$\frac{1500}{11}\left(\frac{9604}{45125}-\left(10.5\times \frac{1}{1000}\right)^{2}\right)$$

Multiply 10.5 and \frac{1}{1000} to get \frac{21}{2000}.

$$\frac{1500}{11}\left(\frac{9604}{45125}-\left(\frac{21}{2000}\right)^{2}\right)$$

Calculate \frac{21}{2000} to the power of 2 and get \frac{441}{4000000}.

$$\frac{1500}{11}\left(\frac{9604}{45125}-\frac{441}{4000000}\right)$$

Subtract \frac{441}{4000000} from \frac{9604}{45125} to get \frac{307168799}{1444000000}.

$$\frac{1500}{11}\times \frac{307168799}{1444000000}$$

Multiply \frac{1500}{11} and \frac{307168799}{1444000000} to get \frac{921506397}{31768000}.

$$\frac{921506397}{31768000}$$

Factor

$$\frac{3 \cdot 6268751 \cdot 7 ^ {2}}{11 \cdot 2 ^ {6} \cdot 5 ^ {3} \cdot 19 ^ {2}} = 29\frac{234397}{31768000} = 29.007378399647443$$