(PLEASE SHOW PICTURES ON HOW TO SOLVE THIS)

Mathematics

1 answer:

son4ous [18]1 year ago

3 0

Answer:

Fred is $\frac{17}{24}$ ft taller than Benny

Step-by-step explanation:

Subtract Benny's height from Fred's height

4 $\frac{1}{12}$ - 3 $\frac{3}{8}$ ( change to improper fractions )

$\frac{49}{12}$ - $\frac{27}{8}$

The LCM of 12 and 8 is 24 , then

= $\frac{49(2)}{12(2)}$ - $\frac{27(3)}{8(3)}$

= $\frac{98}{24}$ - $\frac{81}{24}$

= $\frac{17}{24}$

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Help math question derivative!

atroni [7]

Let $f(x)=\sec^{-1}x$ . Then $\sec f(x)=x$ , and differentiating both sides with respect to $x$ gives

$(\sec f(x))'=\sec f(x)\tan f(x)\,f'(x)=1$
$f'(x)=\dfrac1{\sec f(x)\tan f(x)}$

Now, when $x=\sqrt2$ , you get

$(\sec^{-1})'(\sqrt2)=f'(\sqrt2)=\dfrac1{\sec\left(\sec^{-1}\sqrt2\right)\tan\left(\sec^{-1}\sqrt2\right)}$

You have $\sec^{-1}\sqrt2=\dfrac\pi4$ , so $\sec\left(\sec^{-1}\sqrt2\right)=\sqrt2$ and $\tan\left(\sec^{-1}\sqrt2\right)=1$ . So $(\sec^{-1})'(\sqrt2)=\dfrac1{\sqrt2\times1}=\dfrac1{\sqrt2}$