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2 years ago

Which is the least value? 6 2/9, 6 2/7, 6 2/11, 6 2/5, 6 2/3.

Mathematics

2 answers:

erma4kov [3.2K]2 years ago

8 0

Answer:

6 2/11

Step-by-step explanation:

If you convert it into a decimal, its less than all the other values listed.

BlackZzzverrR [31]2 years ago

4 0

Answer:

6 2/11 has the least value

Step-by-step explanation:

To know the one with the least value, it is important to convert this fractions into decimals

6 2/9 = 6.222

6 2/7 = 6.286

6 2/11 = 6.182

6 2/5 = 6.4

6 2/3 = 6.667

Therefore, the fraction with the least value is 6 2/11

and the fraction with the highest value is 6 2/3

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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:

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

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Answer:

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Step-by-step explanation:

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