Use the figure below to estimate the indicated derivatives

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Ответ:

tyrique86

30.01.2022

Mathematics

Let the ratio be m:n

(x,y)=(4,5)Points be (x1,y1)=(2,3)(x2,y2)=(7,8)

We know

$\boxed{\sf (x,y)=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}$

$\\ \sf\longmapsto (4,5)=\left(\dfrac{7m+2n}{m+n},\dfrac{8m+3n}{m+n}\right)$

Now

. $\\ \sf\longmapsto \dfrac{7m+2n}{m+n}=4\dots(1)$

$\\ \sf\longmapsto \dfrac{8m+3n}{m+n}=5\dots(2)$

Adding both

$\\ \sf\longmapsto \dfrac{7m+2n+8m+3n}{m+n}=4+5$

$\\ \sf\longmapsto \dfrac{7m+8m+2n+3n}{m+n}=9$

$\\ \sf\longmapsto \dfrac{15m+5n}{m+n}=9$

$\\ \sf\longmapsto 15m+5n=9(m+n)$

$\\ \sf\longmapsto 15m+5n=9m+9n$

$\\ \sf\longmapsto 15m-9m=9n-5n$

$\\ \sf\longmapsto 6m=4n$

$\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{6}{4}$

$\\ \sf\longmapsto \dfrac{m}{n}=\dfrac{3}{2}$

$\\ \sf\longmapsto m:n=3:2$

Option B is correct

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