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lys-0071 [83]
3 years ago
9

What is the equation of the perpendicular to y=2/3x+1 that passes through the point (12,-6)

Mathematics
1 answer:
postnew [5]3 years ago
7 0
Well, first off let's check what is the slope of y = 2/3x+1.... .hmmmmm, notice    \bf y=\stackrel{slope}{\cfrac{2}{3}}x+1  , since the equation is already in slope-intercept form, we can see it has a slope of 2/3.

well then, a line perpendicular to that one, will have a negative reciprocal to it.

\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
slope=\cfrac{2}{{{ 3}}}\qquad negative\implies  -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}

so, we're really looking for the equation of a line whose slope is -3/2 and goes through 12, -6.

 \bf \begin{array}{lllll}
&x_1&y_1\\
%   (a,b)
&({{ 12}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-6)=-\cfrac{3}{2}(x-12)
\\\\\\
y+6=-\cfrac{3}{2}x+18\implies y=-\cfrac{3}{2}x+12
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Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

v_1 = 60\ mph

Sheyna drives back from the lake with average speed of 36 mph

v_2 = 36\ mph

It took 2 hours less time to get there than it did to get back.

Let t_1 be the time taken to drive to lake.

Let t_2 be the time taken to drive back from lake.

t_2-t_1 = 2 hrs ..... (1)

To find:

Total time taken = ?

t_1+t_2 = ?

Solution:

Let D be the distance to lake.

Formula for time is given as:

Time =\dfrac{Distance}{Speed }

t_1 = \dfrac{D}{60}\ hrs

t_2 = \dfrac{D}{36}\ hrs

Putting in equation (1):

\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles

So,

t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs

t_2 = \dfrac{180}{36}\ hrs = 5\ hrs

So, the answer is:

t_1+t_2 = \bold{8\ hrs}

8 0
3 years ago
A construction worker needs to determine the volume of a sandpille in a construction yard as shown
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Answer:
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Step-by-step explanation:
The answer is 6580cm because....
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Step two Now lets find the Volume of the larger shape. So lets do LxWxH so Lx?x14 it does not give us the length so we need to add up all of the numbers along the line. We got 7cm then 5 from the bottom of the smaller shape and 10cm. all ads up to 22cm so 20x22x14=6160
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3 years ago
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Answer:

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