Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
To determine which of the given equations is equivalent to the equation [tex]\( S = \pi \pi^2 n \)[/tex], follow these steps:
1. Analyze the given equation:
The equation given is:
[tex]\[ S = \pi \pi^2 n \][/tex]
2. Evaluate each option one by one:
### Option 1: [tex]\( h = S - \pi \pi^2 \)[/tex]
- This equation does not involve the variable [tex]\( n \)[/tex] at all.
- Attempting to solve for [tex]\( n \)[/tex] from [tex]\( S = \pi \pi^2 n \)[/tex] by manipulating this equation would not yield an expression similar to [tex]\( h = S - \pi \pi^2 \)[/tex].
Hence, this option does not match the form of the given equation.
### Option 2: [tex]\( n = \frac{S}{\pi \pi^2} \)[/tex]
- Rearrange the given equation [tex]\( S = \pi \pi^2 n \)[/tex] to solve for [tex]\( n \)[/tex]:
[tex]\[ S = \pi \pi^2 n \][/tex]
[tex]\[ n = \frac{S}{\pi \pi^2} \][/tex]
This matches the second option exactly. Therefore, this option is equivalent to the given equation.
### Option 3: [tex]\( h = \frac{\pi \pi^2}{S} \)[/tex]
- Again, this equation does not involve [tex]\( n \)[/tex].
- Furthermore, trying to rearrange [tex]\( S = \pi \pi^2 n \)[/tex] into this form does not result in any meaningful similarity.
Thus, this option is not equivalent to the given equation.
### Option 4: [tex]\( h = S + \pi r^2 \)[/tex]
- This equation introduces [tex]\( r \)[/tex], which is not present in the original equation.
- It also does not involve a multiplication or division that would correspond to isolating [tex]\( n \)[/tex] from [tex]\( S = \pi \pi^2 n \)[/tex].
Consequently, this option too does not match the given equation in any form.
3. Conclusion:
After analyzing all the given options, the only equation that is mathematically equivalent to the given equation [tex]\( S = \pi \pi^2 n \)[/tex] is:
[tex]\[ n = \frac{S}{\pi \pi^2} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
1. Analyze the given equation:
The equation given is:
[tex]\[ S = \pi \pi^2 n \][/tex]
2. Evaluate each option one by one:
### Option 1: [tex]\( h = S - \pi \pi^2 \)[/tex]
- This equation does not involve the variable [tex]\( n \)[/tex] at all.
- Attempting to solve for [tex]\( n \)[/tex] from [tex]\( S = \pi \pi^2 n \)[/tex] by manipulating this equation would not yield an expression similar to [tex]\( h = S - \pi \pi^2 \)[/tex].
Hence, this option does not match the form of the given equation.
### Option 2: [tex]\( n = \frac{S}{\pi \pi^2} \)[/tex]
- Rearrange the given equation [tex]\( S = \pi \pi^2 n \)[/tex] to solve for [tex]\( n \)[/tex]:
[tex]\[ S = \pi \pi^2 n \][/tex]
[tex]\[ n = \frac{S}{\pi \pi^2} \][/tex]
This matches the second option exactly. Therefore, this option is equivalent to the given equation.
### Option 3: [tex]\( h = \frac{\pi \pi^2}{S} \)[/tex]
- Again, this equation does not involve [tex]\( n \)[/tex].
- Furthermore, trying to rearrange [tex]\( S = \pi \pi^2 n \)[/tex] into this form does not result in any meaningful similarity.
Thus, this option is not equivalent to the given equation.
### Option 4: [tex]\( h = S + \pi r^2 \)[/tex]
- This equation introduces [tex]\( r \)[/tex], which is not present in the original equation.
- It also does not involve a multiplication or division that would correspond to isolating [tex]\( n \)[/tex] from [tex]\( S = \pi \pi^2 n \)[/tex].
Consequently, this option too does not match the given equation in any form.
3. Conclusion:
After analyzing all the given options, the only equation that is mathematically equivalent to the given equation [tex]\( S = \pi \pi^2 n \)[/tex] is:
[tex]\[ n = \frac{S}{\pi \pi^2} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.