excans:61ffade529: Difference between revisions

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(Created page with "'''Answer: A''' <math>{ }_{10} p_{x}=\frac{l_{x+10}}{l_{x}}=e^{-\int_{0}^{10} \mu_{x+1} \cdot d t}=>\frac{400}{1000}=e^{-\int_{0}^{10} \beta t^{2} \cdot d t}=>0.4=e^{-\beta t^{3} / 3 b^{10}}</math> <math>==>0.4=e^{-\beta \cdot 100^{3} / 3}==>\ln (0.4)=-\beta\left(\frac{1000}{3}\right)==>\beta=-\ln (0.4)(.003)=0.0027489</math>")
 
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'''Answer: A'''
'''Answer: C'''


<math>{ }_{10} p_{x}=\frac{l_{x+10}}{l_{x}}=e^{-\int_{0}^{10} \mu_{x+1} \cdot d t}=>\frac{400}{1000}=e^{-\int_{0}^{10} \beta t^{2} \cdot d t}=>0.4=e^{-\beta t^{3} / 3 b^{10}}</math>
Let <math>l_{80}=1000 \Rightarrow l_{81}=960 \Rightarrow l_{82}=902.4</math>


<math>==>0.4=e^{-\beta \cdot 100^{3} / 3}==>\ln (0.4)=-\beta\left(\frac{1000}{3}\right)==>\beta=-\ln (0.4)(.003)=0.0027489</math>
<math display = "block">\textrm{Answer} \, =\frac{l_{81.1}-l_{81.6}}{l_{80.6}}=\frac{(960)^{0.9}(902.4)^{0.1}-(960)^{0.4}(902.4)^{0.6}}{(0.4)(1000)+(0.6)(960)}=0.02978</math>

Revision as of 22:04, 15 January 2024

Answer: C

Let [math]l_{80}=1000 \Rightarrow l_{81}=960 \Rightarrow l_{82}=902.4[/math]

[[math]]\textrm{Answer} \, =\frac{l_{81.1}-l_{81.6}}{l_{80.6}}=\frac{(960)^{0.9}(902.4)^{0.1}-(960)^{0.4}(902.4)^{0.6}}{(0.4)(1000)+(0.6)(960)}=0.02978[[/math]]