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evablogger [386]
3 years ago
14

Help math question derivative!

Mathematics
1 answer:
atroni [7]3 years ago
5 0
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}
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In the game of Keno, a player starts by selecting 20 numbers from the numbers 1 to 80. After the player makes his selections, 20
DiKsa [7]

The percentage of winning if 20 winning numbers are randomly selected from numbers 1 to 80 is 12.48%.

Given There are 80 numbers from which 20 numbers are selected randomly in a game of Keno by player and after selection of 20 winning numbers again 20 numbers are selected and player wins if the player has correctly selected 3,4,or 5 of the 20 winning numbers.

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Probability of winning is calculated as under:

Probability=C(20,3)C(60,17)/C(80,20)

We have taken C(20,3) because player will win if 5 numbers are selected from 20 winning numbers.

We have taken C(60,17) because after selection of 20 numbers 60 numbers will left from 80 and after winning from 3 numbers 17  numbers left and from total 80, 20 numbers are taken.

=C(20,3)C(60,17)/C(80,20)

=(20!/3!17!  * 60!/17!43!)/80!/20!60!

=1140*387221678682300/35353161422121743200

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Learn more about probability at brainly.com/question/24756209

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