Which of the following quantities is a velocity?

Mathematics

1 answer:

Elanso [62]3 years ago

3 0

Answer:

Step-by-step explanation:

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Determine the value of r such that the line through (5, r) and (2, 3) is perpendicular to the line y = 2x - 4

d1i1m1o1n [39]

So, what's the slope of y = 2x - 4? well, is in slope-intercept form, thus

$\bf y=\stackrel{slope}{2}x\stackrel{y-intercept}{-4}$ , so is 2.

now, a perpendicular line to that, will have a negative reciprocal slope to it, thus

$\bf \textit{perpendicular, negative-reciprocal slope for}\quad 2\implies \cfrac{2}{1}\\\\
negative\implies -\cfrac{2}{ 1}\qquad reciprocal\implies - \cfrac{ 1}{2}$

so, that's its slope of that perpendicular line.

but we also know that it runs through (5,r) and (2,3), so that slope is equal to -1/2

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 5 &,& r~) 
% (c,d)
&&(~ 2 &,& 3~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-r}{2-5}\implies \qquad \qquad \cfrac{3-r}{-3}~~=~~-\cfrac{1}{2}
\\\\\\
3-r=\cfrac{3}{2}\implies 3-\cfrac{3}{2}=r\implies \cfrac{6-3}{2}=r\implies \cfrac{3}{2}=r\implies 1.5=r$

4 0

4 years ago

What is the product (3a2b4)(-8ab3)

Serggg [28]

<u>Answer:</u>

$-24a^3b^7$