Answer :
To determine the lower bound for the value of [tex]\( p \)[/tex], we first need to find the lower bounds for both [tex]\( q \)[/tex] and [tex]\( r \)[/tex].
1. Determine the lower bound for [tex]\( q \)[/tex]:
- [tex]\( q = 3.37 \)[/tex] is correct to 2 decimal places.
- The smallest possible value for [tex]\( q \)[/tex] when rounded to two decimal places can be calculated as [tex]\( q = 3.37 - 0.005 = 3.365 \)[/tex].
2. Determine the lower bound for [tex]\( r \)[/tex]:
- [tex]\( r = 51.7 \)[/tex] is correct to 1 decimal place.
- The smallest possible value for [tex]\( r \)[/tex] when rounded to one decimal place can be calculated as [tex]\( r = 51.7 - 0.05 = 51.65 \)[/tex].
3. Calculate the lower bound for [tex]\( p \)[/tex]:
- The formula for [tex]\( p \)[/tex] is given by [tex]\( p = 2 \times q \times r \)[/tex].
- Substitute the lower bounds of [tex]\( q \)[/tex] and [tex]\( r \)[/tex] into the equation:
[tex]\[
p_{\text{lower bound}} = 2 \times 3.365 \times 51.65
\][/tex]
4. The lower bound for [tex]\( p \)[/tex]:
- After computing the expression, we find that the lower bound for [tex]\( p \)[/tex] is approximately 347.605.
Thus, the lower bound for [tex]\( p \)[/tex] is [tex]\( 347.605 \)[/tex] when rounded to 3 decimal places.
1. Determine the lower bound for [tex]\( q \)[/tex]:
- [tex]\( q = 3.37 \)[/tex] is correct to 2 decimal places.
- The smallest possible value for [tex]\( q \)[/tex] when rounded to two decimal places can be calculated as [tex]\( q = 3.37 - 0.005 = 3.365 \)[/tex].
2. Determine the lower bound for [tex]\( r \)[/tex]:
- [tex]\( r = 51.7 \)[/tex] is correct to 1 decimal place.
- The smallest possible value for [tex]\( r \)[/tex] when rounded to one decimal place can be calculated as [tex]\( r = 51.7 - 0.05 = 51.65 \)[/tex].
3. Calculate the lower bound for [tex]\( p \)[/tex]:
- The formula for [tex]\( p \)[/tex] is given by [tex]\( p = 2 \times q \times r \)[/tex].
- Substitute the lower bounds of [tex]\( q \)[/tex] and [tex]\( r \)[/tex] into the equation:
[tex]\[
p_{\text{lower bound}} = 2 \times 3.365 \times 51.65
\][/tex]
4. The lower bound for [tex]\( p \)[/tex]:
- After computing the expression, we find that the lower bound for [tex]\( p \)[/tex] is approximately 347.605.
Thus, the lower bound for [tex]\( p \)[/tex] is [tex]\( 347.605 \)[/tex] when rounded to 3 decimal places.
