how does pih^3/12 simplify to pih^2/4?
If you divide denominator by 3 you get 4 and then I guess the 3 goes away leaving a 2? But if this is correct why does this work?
Did you do the anti-derivative?
INT PI*H^2/4 dh = PI H^3/12
and likewise,
d/dh (PI H^3/12)= PI H^2/4
no i took the derivative. i see now
d/dh (PI*h^3/12) = 3PI*h^2/12 = PI*h^2/4
sorry i guess this was the wrong forum
To understand how the expression "pi * h^3/12" simplifies to "pi * h^2/4," we need to know the rules of simplifying exponents and basic algebraic manipulation.
Let's break down the steps:
Step 1: Start with the original expression: "pi * h^3/12."
Step 2: Simplify the denominator by dividing it by 3. The expression becomes "pi * h^3/4."
Step 3: Now, let's focus on the exponent h^3. To simplify this, we need to apply the rule of exponentiation. When we divide two exponents with the same base, we subtract the exponents. In this case, since we have h^3 divided by h^2, we subtract the exponents: h^3 / h^2 = h^(3-2) = h^1.
Step 4: Simplify further. We simplify "pi * h^3/4" to "pi * h^1/4."
Step 5: Finally, any number or variable raised to the power of 1 is equal to itself, so h^1 is simply h. The expression becomes "pi * h/4."
So, the final simplified expression is "pi * h/4," or "pih/4." The reason this works is due to the rules of exponentiation and the division of exponents of the same base.