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8_murik_8 [283]
4 years ago
13

A cross-country train travels at a steady speed. It covers 15 miles in 20

Mathematics
1 answer:
skelet666 [1.2K]4 years ago
5 0

Answer:

i think its 225 but i can still be wrong

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Suppose triangle ABC will be dilated using the rule . What will be the distance from the center of dilation, Q, to the image of
Blababa [14]

Answer:

4

Step-by-step explanation:

The rule of dilation is D_{Q,\frac{2}{3}}. This means that each distance QX' is equal to \dfrac{2}{3}QX, where X is initial point and X' is its image after dilation.

Since QA=6, then

QA'=\dfrac{2}{3}\cdot 6=4.

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3 years ago
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Find dy/dx in the following<br> 1) y=x^[10] +10^[x] +e^[x]<br> 2) y=㏒ x +e^[x]+√x - 1/x
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1. in picture 1

2. in picture 2

Hope this helps :T

Also I am not so shure about 2, but I am 98% shure 1 is right.

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\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\&#10;slope=\cfrac{a}{{{ b}}}\qquad negative\implies  -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\&#10;-------------------------------\\\\

\bf \boxed{5i+12j}\implies &#10;\begin{array}{rllll}&#10;\ \textless \ 5&,&12\ \textgreater \ \\&#10;x&&y&#10;\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}&#10;\\\\\\&#10;slope=\cfrac{12}{{{ 5}}}\qquad negative\implies  -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}&#10;\\\\\\&#10;\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}&#10;\\\\\\&#10;\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}&#10;\\\\\\&#10;\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}
4 0
3 years ago
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