Find the number of paths from A to B. (Each step can only go up or to the right.)

Mathematics

1 answer:

mash [69]3 years ago

6 0

Answer:

Total ways possible = 104 ways

Step-by-step explanation:

Total ways possible = 104 ways

The figure is attached here for understanding.

In the figure, the blank points are those points where we can not reach.

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Thee vertex of a parabola is (-5,2), and its focus is (-1,2). What is the standard form of the parabola?

Alla [95]

Check the picture below. So the parabola looks more or less like so.

$\bf \textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf \begin{cases} h=-5\\ k=2\\ p=4 \end{cases}\implies 4(4)[x-(-5)]=[y-2]^2\implies 16(x+5)=(y-2)^2 \\\\\\ x+5=\cfrac{1}{16}(y-2)^2\implies x = \cfrac{1}{16}(y-2)^2-5$