Application of Trigonometric Ratios:

Mathematics

1 answer:

Irina-Kira [14]2 years ago

5 0

9514 1404 393

Answer:

15.46 m

Step-by-step explanation:

Side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. That is, the height of the tree above eye-height is √3 times the distance from the trunk. The top of the crown will be at a height of ...

1.6 m + (8 m)√3 ≈ 15.46 m

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If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

3 years ago

Write 368% as a mixed number.

Allushta [10]

Answer:

$3\frac{17}{25}$

Step-by-step explanation:

368%

convert to a fraction

$\frac{368}{100}$

divide top and bottom by 2

$\frac{184}{50}$

divide top and bottom by 2

$\frac{92}{25}$

92/25 = 3 remainder 17

$3\frac{17}{25}$

8 0

3 years ago

At a school assembly four out of the first 10

Ilya [14]

Answer:

125

Step-by-step explanation:

Well if 10 x 50 is 500 (just to show how you get doesn't affect problem) you would simply divide by 4 thus, you get 125 (edit: sorry if this is wrong I'm in my first year of middle lol)

5 0

2 years ago

the function y =³√-x – 3 is graphed only over the domain of {x | –8 < x < 8}. what is the range of the graph? a). {y | –5

Fittoniya [83]

$y=\sqrt[3]{-x}-3\ and\ x\in(-8;\ 8)\\\\subtitute\ x=-8\ and\ x=8\ to\ the\ equation:\\\\y=\sqrt[3]{-(-8)}-3=\sqrt[3]8-3=2-3=-1\\\\y=\sqrt[3]{-8}-3=-2-3=-5\\\\Answer:\boxed{\{y|-5 \ \textless \ y \ \textless \ -1\}}\to\fbox{b.}$