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2 years ago

What is the longest stick that can be placed within a box whose inside dimension are 24 inches, 30 inches, and 18 inches?

Mathematics

1 answer:

Montano1993 [528]2 years ago

3 0

Answer:

42.42 inches

Step-by-step explanation:

Given the dimension of the box are 24 inches, 30 inches, and 18 inches.

Considering the box is in rectangular in shape.

We also know that longest part of the box is the diagonal.

∴ lets calculate the diagonal to find longest stick that can be placed within a box.

Diagonal= $\sqrt{a^{2}+b^{2}+c^{2} }$

Where a,b,c are the dimensions of the box.

Diagonal= $\sqrt{24^{2} +30^{2}+18^{2} }$

⇒ Diagonal= $\sqrt{576+900+324}$

⇒ Diagonal= $\sqrt{1800}$

⇒ Diagonal= 42.42 inches

Hence, 42.42 inches longest stick that can be placed within a box.

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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:

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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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2 years ago

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2 years ago

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Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

because the length (long) of J and K are totally different whereas the breadth(width) of J and K is also different which does make similar in sense

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