2 years ago

PLEASE HELP ME WITH NUMBER 11, WORTH 15 POINTS!!! AAAAA

Mathematics

1 answer:

malfutka [58]2 years ago

6 0

Answer: 43.4

Step-by-step explanation: if it was dilated by a bigger number than 1 then it’s goin to have a bigger area and in this case it was dilated by

4 2/3 so you multiply the area by 4 2/3 to round your answer to the nearest tenth and u get 43.4

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2 years ago

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Identify the "inside function" u = f(x) and the "outside function" y = g(u). Then find dy/dx using the Chain Rule.

skad [1K]

DfLet $f(x)=\sec x$ and $g(x)=\sqrt x$ . Then

$y=\sec\sqrt x=\sec(g(x))=f(g(x))=f\circ g(x)$

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

where $u=g(x)=\sqrt x$ , so that $y=f(g(x))=f(u)=\sec u$ . We have

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac1{2\sqrt x}$
$\dfrac{\mathrm d\sec u}{\mathrm du}=\sec u\tan u$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\sec u\tan u\dfrac{\mathrm dy}{\mathrm du}=\dfrac{\sec\sqrt x\,\tan\sqrt x}{2\sqrt x}$