diff --git a/academic/misc/2024-math-calendar.html b/academic/misc/2024-math-calendar.html index e7d069c..977e659 100644 --- a/academic/misc/2024-math-calendar.html +++ b/academic/misc/2024-math-calendar.html @@ -347,7 +347,7 @@

Math Calendar 2024

04 05 06 - 07 + 07 08 09 @@ -5070,6 +5070,19 @@

Jun 06

\[\log_{10}15625+\log_{10}64=\log_{10}5^6+\log_{10}2^6=\log_{10}(5^6\cdot2^6) =\log_{10}10^6=6\] +

Jun 07

+ +\[\begin{align}&f(u)=u^2-2\ \text{and}\\&g(u)=(u-5)^2+3\\ +&\text{intersect at}\ (y,x)\end{align}\] + +

+It should be more clearly stated, but it asks us to find the \(x\). To find the +intersection point, we first find \(u\) such that \(f(u)=g(u)\). +\[u^2-2=(u-5)^2+3\Rightarrow u^2-2=u^2-10u+25+3\Rightarrow10u=30\Rightarrow +u=3\] Then we can evaluate \(f(3)=g(3)=7\) so the intersection point is +\((3,7)\) so the answer would be 7. +

+