What is the slope of a line perpendicular to a line with slope -8 ?

Mathematics

2 answers:

Flauer [41]3 years ago

5 0

It’s going to be (1/8)x or x/8...

Alexandra [31]3 years ago

4 0

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-8\implies \cfrac{-8}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{-8}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{8}}}$

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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

4 years ago

______________ Angles have each of the pairs of opposite angles made by two intersecting lines *

myrzilka [38]

$\huge \bf༆ Answer ༄$