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8 0

3 years ago

If n lines are drawn in a plane, how many regions do they separate the plane into? induction

grandymaker [24]

Hello,

Let's assume i the number of lines,
u(i) the number of regions:

$u_0=1\\\\
u_1=2=1+1=1+u_0\\\\
u_2=4=2+u_1\\\\
u_3=7=3+u_2\\\\
u_4=11=4+u_3\\\\
u_5=16=5+u_4\\\\
...\\\\
\boxed{u_{n+1}=(n+1)+u_{n}}\\\\

u_{n+1}=(n+1)+n+(n-1)+...+1+u_0\\\\

\boxed{u_{n+1}= \dfrac{(n+1)*(n+2)}{2}+1 }$

6 0

3 years ago

Which best shows the graph of the equation y = x + 10? A. B. C.

Aleksandr [31]

Y=10x is correct but don't want you get me the question again

4 0

3 years ago