v = h(6 - (1/3)(2 - (2 h/5))^3 )
i try to solve this equation and i got
(350+4h^2)/75
im not sure if this is correct
please check it for me!
To verify if your solution is correct, we can substitute your answer back into the original equation and check if it holds true.
The equation you provided is:
v = h(6 - (1/3)(2 - (2h/5))^3)
To check if your solution, (350 + 4h^2)/75, is correct, we substitute it into the equation:
(350 + 4h^2)/75 = h(6 - (1/3)(2 - (2h/5))^3)
Let's simplify the equation step by step:
1. Distribute the h on the right side:
(350 + 4h^2)/75 = 6h - (2h/15)^3
2. Cube the term (2h/15):
(350 + 4h^2)/75 = 6h - (8h^3/3375)
3. Multiply both sides by 75 to eliminate the denominator:
350 + 4h^2 = 450h - (8h^3/45)
4. Multiply both sides by 45 to eliminate the denominator:
15,750 + 180h^2 = 20,250h - 8h^3
5. Rearrange the equation to form a polynomial:
8h^3 - 180h^2 + 20,250h - 15,750 = 0
Now, we have a cubic equation. To check if your solution is correct, we can factor or use another method to solve the equation for h.
If your solution indeed satisfies this equation, then it is correct. If not, you might want to double-check your calculations and re-evaluate your steps.