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3 years ago

{[3×(4+6)]-8}+[4×(24-17)]=

1 answer:

6 0

So pemdas
parenthasees first
do inner first to outer
(4+6) is innermost
4+6=10
and
(24-17)
24-17=7

we now have
{[3 times 10]-8}+[4 times 7]
we do the multilication
3 itme s10=30
4 tim es7=28
now we have
{[30]-8}+[28]
addition
{22}+[28]
22+28=50

the answer is 50

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$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

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$y(t)=(A+Bt)e^{-5t}.$

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$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

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