Solve 10^3*0.28*(4*0.28/(0.45)^2*3.14-4*0.28/(0.25)^2*3.14)

$$10 ^ { 3 } \times 0.28 \times ( \frac { 4 \times 0.28 } { ( 0.45 ) ^ { 2 } \times 3.14 } - \frac { 4 \times 0.28 } { ( 0.25 ) ^ { 2 } \times 3.14 } )$$

Evaluate

$$-\frac{14049280}{12717}\approx -1104.763702131$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$1000\times 0.28\left(\frac{4\times 0.28}{0.45^{2}\times 3.14}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Multiply 1000 and 0.28 to get 280.

$$280\left(\frac{4\times 0.28}{0.45^{2}\times 3.14}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Multiply 4 and 0.28 to get 1.12.

$$280\left(\frac{1.12}{0.45^{2}\times 3.14}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Calculate 0.45 to the power of 2 and get 0.2025.

$$280\left(\frac{1.12}{0.2025\times 3.14}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Multiply 0.2025 and 3.14 to get 0.63585.

$$280\left(\frac{1.12}{0.63585}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Expand \frac{1.12}{0.63585} by multiplying both numerator and the denominator by 100000.

$$280\left(\frac{112000}{63585}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Reduce the fraction \frac{112000}{63585} to lowest terms by extracting and canceling out 5.

$$280\left(\frac{22400}{12717}-\frac{4\times 0.28}{0.25^{2}\times 3.14}\right)$$

Multiply 4 and 0.28 to get 1.12.

$$280\left(\frac{22400}{12717}-\frac{1.12}{0.25^{2}\times 3.14}\right)$$

Calculate 0.25 to the power of 2 and get 0.0625.

$$280\left(\frac{22400}{12717}-\frac{1.12}{0.0625\times 3.14}\right)$$

Multiply 0.0625 and 3.14 to get 0.19625.

$$280\left(\frac{22400}{12717}-\frac{1.12}{0.19625}\right)$$

Expand \frac{1.12}{0.19625} by multiplying both numerator and the denominator by 100000.

$$280\left(\frac{22400}{12717}-\frac{112000}{19625}\right)$$

Reduce the fraction \frac{112000}{19625} to lowest terms by extracting and canceling out 125.

$$280\left(\frac{22400}{12717}-\frac{896}{157}\right)$$

Least common multiple of 12717 and 157 is 12717. Convert \frac{22400}{12717} and \frac{896}{157} to fractions with denominator 12717.

$$280\left(\frac{22400}{12717}-\frac{72576}{12717}\right)$$

Since \frac{22400}{12717} and \frac{72576}{12717} have the same denominator, subtract them by subtracting their numerators.

$$280\times \frac{22400-72576}{12717}$$

Subtract 72576 from 22400 to get -50176.

$$280\left(-\frac{50176}{12717}\right)$$

Express 280\left(-\frac{50176}{12717}\right) as a single fraction.

$$\frac{280\left(-50176\right)}{12717}$$

Multiply 280 and -50176 to get -14049280.

$$\frac{-14049280}{12717}$$

Fraction \frac{-14049280}{12717} can be rewritten as -\frac{14049280}{12717} by extracting the negative sign.

$$-\frac{14049280}{12717}$$

Factor

$$-\frac{14049280}{12717} = -1104\frac{9712}{12717} = -1104.7637021310056$$