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Alenkasestr [34]
3 years ago
11

Maria is play a game where you score -5 points each time you guess the correct answer.The goal is to get the lowest score.To win

the game,Maria must have a score less than -80 points.How many correct answers does Maria need to win the game?
Mathematics
1 answer:
oee [108]3 years ago
5 0

Answer:

7

Step-by-step explanation:

Just notice that correct answers are whole numbers.

And, to win the game,Maria must have a score less than -80, it means she needs to score al least -85 ( it can not be -81, -82.. because 1 correct answer score -5, only multiples of -5 are accepted)

So,  we take: \frac{-85}{-5} = 7 correct answers to win the game.

Hope it will find you well.

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Answer:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

Step-by-step explanation:

We want to write the trignometric expression:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)

Take the secant of both sides:

\displaystyle \sec(\theta)=\frac{u}{10}

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}

By substitutition:

\displaystyle= \sin(2\theta)

Using an double-angle identity:

=2\sin(\theta)\cos(\theta)

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)

Simplify. Therefore:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

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