To find the lower bound of the value of [tex]\( M \)[/tex] given the measurements for [tex]\( h \)[/tex], [tex]\( p \)[/tex], and [tex]\( y \)[/tex]:
1. Determine the lower and upper bounds of given values:
- [tex]\( h = 23 \)[/tex] correct to the nearest whole number:
[tex]\[
\text{Lower bound of } h = 23 - 0.5 = 22.5
\][/tex]
- [tex]\( p = 2.2 \)[/tex] correct to one decimal place:
[tex]\[
\text{Lower bound of } p = 2.2 - 0.05 = 2.15
\][/tex]
- [tex]\( y = 2 \)[/tex] correct to 1 significant figure:
[tex]\[
\text{Upper bound of } y = 2 + 0.5 = 2.5
\][/tex]
2. Substitute the bounds into the expression for [tex]\( M \)[/tex]:
We need to find the lower bound of
[tex]\[
M = \frac{h}{p - y}
\][/tex]
To determine the lower bound for [tex]\( M \)[/tex], we should use the lower bound of [tex]\( h \)[/tex], lower bound of [tex]\( p \)[/tex], and the upper bound of [tex]\( y \)[/tex]:
[tex]\[
M_{\text{lower}} = \frac{\text{Lower bound of } h}{\text{Lower bound of } p - \text{Upper bound of } y}
\][/tex]
3. Calculate the values for the bounds:
[tex]\[
h_{\text{lower}} = 22.5
\][/tex]
[tex]\[
p_{\text{lower}} = 2.15
\][/tex]
[tex]\[
y_{\text{upper}} = 2.5
\][/tex]
4. Substitute these values into the formula:
[tex]\[
M_{\text{lower}} = \frac{22.5}{2.15 - 2.5}
\][/tex]
[tex]\[
M_{\text{lower}} = \frac{22.5}{2.15 - 2.5}
\][/tex]
[tex]\[
M_{\text{lower}} = \frac{22.5}{-0.35}
\][/tex]
[tex]\[
M_{\text{lower}} = -64.28571428571426
\][/tex]
Therefore, the lower bound of the value of [tex]\( M \)[/tex] is approximately [tex]\(-64.29\)[/tex].
