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tiny-mole [99]
3 years ago
14

How many integers between 100 and 400 contain the digit 2?

Mathematics
1 answer:
Semenov [28]3 years ago
8 0
102, 112, 120-129, 132, 142, 152, 162, 172, 182, 192, 200-299, 302, 312, 320-329, 332, 342, 352, 362, 372, 382, 392
2+10+7+100+2+10+7
138 integers.
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Read 2 more answers
Find d for the arithmetic series with S17=-170 and a1=2
Irina18 [472]
So, we know the sum of the first 17 terms is -170, thus S₁₇ = -170, and we also know the first term is 2, well

\bf \textit{ sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
n=17\\
S_{17}=-170\\
a_1=2
\end{cases}
\\\\\\
-170=\cfrac{17(2+a_{17})}{2}\implies \cfrac{-170}{17}=\cfrac{(2+a_{17})}{2}
\\\\\\
-10=\cfrac{(2+a_{17})}{2}\implies -20=2+a_{17}\implies -22=a_{17}

well, since the 17th term is that much, let's check what "d" is then anyway,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=17\\
a_{17}=-22\\
a_1=2
\end{cases}
\\\\\\
-22=2+(17-1)d\implies -22=2+16d\implies -24=16d
\\\\\\
\cfrac{-24}{16}=d\implies -\cfrac{3}{2}=d
6 0
3 years ago
Im stuck on this question, Please help!
Alexxx [7]
= (x^18y^24)/(x^2y^2)

Simplified = x^16y^22

The last answer is correct (x^16y^22)
3 0
2 years ago
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