Solve 1024*9.8*(pi*5^2*x+4/3pi*5^3)=65*10^6

$$1024 \times 9.8 \times ( \pi \times 5 ^ { 2 } \times x + \frac { 4 } { 3 } \pi \times 5 ^ { 3 } ) = 65 \times 10 ^ { 6 }$$

Solve for x

$$x=\frac{203125}{784\pi }-\frac{20}{3}\approx 75.803608373$$

Steps for Solving Linear Equation

Multiply 1024 and 9.8 to get 10035.2.

$$10035.2\left(\pi \times 5^{2}x+\frac{4}{3}\pi \times 5^{3}\right)=65\times 10^{6}$$

Calculate 5 to the power of 2 and get 25.

$$10035.2\left(\pi \times 25x+\frac{4}{3}\pi \times 5^{3}\right)=65\times 10^{6}$$

Calculate 5 to the power of 3 and get 125.

$$10035.2\left(\pi \times 25x+\frac{4}{3}\pi \times 125\right)=65\times 10^{6}$$

Express \frac{4}{3}\times 125 as a single fraction.

$$10035.2\left(\pi \times 25x+\frac{4\times 125}{3}\pi \right)=65\times 10^{6}$$

Multiply 4 and 125 to get 500.

$$10035.2\left(\pi \times 25x+\frac{500}{3}\pi \right)=65\times 10^{6}$$

Use the distributive property to multiply 10035.2 by \pi \times 25x+\frac{500}{3}\pi .

$$10035.2\pi \times 25x+10035.2\times \frac{500}{3}\pi =65\times 10^{6}$$

Multiply 10035.2 and 25 to get 250880.

$$250880\pi x+10035.2\times \frac{500}{3}\pi =65\times 10^{6}$$

Convert decimal number 10035.2 to fraction \frac{100352}{10}. Reduce the fraction \frac{100352}{10} to lowest terms by extracting and canceling out 2.

$$250880\pi x+\frac{50176}{5}\times \frac{500}{3}\pi =65\times 10^{6}$$

Multiply \frac{50176}{5} times \frac{500}{3} by multiplying numerator times numerator and denominator times denominator.

$$250880\pi x+\frac{50176\times 500}{5\times 3}\pi =65\times 10^{6}$$

Do the multiplications in the fraction \frac{50176\times 500}{5\times 3}.

$$250880\pi x+\frac{25088000}{15}\pi =65\times 10^{6}$$

Reduce the fraction \frac{25088000}{15} to lowest terms by extracting and canceling out 5.

$$250880\pi x+\frac{5017600}{3}\pi =65\times 10^{6}$$

Calculate 10 to the power of 6 and get 1000000.

$$250880\pi x+\frac{5017600}{3}\pi =65\times 1000000$$

Multiply 65 and 1000000 to get 65000000.

$$250880\pi x+\frac{5017600}{3}\pi =65000000$$

Subtract \frac{5017600}{3}\pi from both sides.

$$250880\pi x=65000000-\frac{5017600}{3}\pi$$

The equation is in standard form.

$$250880\pi x=-\frac{5017600\pi }{3}[phone]$$

Divide both sides by 250880\pi .

$$\frac{250880\pi x}{250880\pi }=\frac{-\frac{5017600\pi }{3}[phone]}{250880\pi }$$

Dividing by 250880\pi undoes the multiplication by 250880\pi .

$$x=\frac{-\frac{5017600\pi }{3}[phone]}{250880\pi }$$

Divide 65000000-\frac{5017600\pi }{3} by 250880\pi .

$$x=\frac{203125}{784\pi }-\frac{20}{3}$$