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just olya [345]
3 years ago
9

Two friends, Alejandra and Mia, agreed to split the check at a restaurant. Alejandra ordered $12 worth of food and Mia ordered $

18 worth. At the end of the meal, Alejandra put her $12 contribution on the table, plus a 20% tip and Mia put her $18 contribution on the table, plus a 15% tip. The total tip left by Alejandra and Mia is equal to r\% of the total check for their table, where the "total check" amount does not include the tip. What is r?
Mathematics
1 answer:
dedylja [7]3 years ago
6 0
12+18=30 so together they have $30.00 in all.
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Write each expression as an algebraic​ (nontrigonometric) expression in​ u, u > 0.
max2010maxim [7]

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

4 0
3 years ago
I NEED HELPPP<br><br> Whats the length of LN?
andre [41]

Answer:

LN = 66 cm

Step-by-step explanation:

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3 years ago
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cos 62° = 350 / x
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