3 years ago

Is 1,250 More than or less than 1.25

Mathematics

2 answers:

garri49 [273]3 years ago

8 0

1,250 is more than 1.25

sweet [91]3 years ago

5 0

1,250 is more then 1.25 because it’s a greater number

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Sophie [7]

The idea is to use the tangent line to $f(x)=\sqrt x$ at $x=25$ in order to approximate $f(25.3)=\sqrt{25.3}$ .

We have

$f(x)=\sqrt x\implies f(25)=\sqrt{25}=5$

$f'(x)=\dfrac1{2\sqrt x}\implies f'(25)=\dfrac1{10}$

so the linear approximation to $f(x)$ is

$L(x)=f(5)+f'(5)(x-5)=5+\dfrac{x-5}{10}=\dfrac x{10}+\dfrac92$

Hence $m=\frac1{10}$ and $b=\frac92$ .

Then

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Is 1,250 More than or less than 1.25​

Is 1,250 More than or less than 1.25