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Rainbow [258]
3 years ago
5

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0). Find the coordinates of S in terms of a.

Mathematics
2 answers:
FromTheMoon [43]3 years ago
4 0
The x  coordinate of S will be 1/2 * 2a = a.
and since  the half triangle is 30-60-90 the y coordinate will be sqrt3 a

so S  is (a , sqrt3a)
Serhud [2]3 years ago
3 0

Answer:

The S coordinate :

(a,\sqrt{3}a)\text{ and }(a,-\sqrt{3}a)

Step-by-step explanation:

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0)

We need to find the third coordinate of triangle RST.

R(0,0)

T(2a,0)

S(x,y)

RT=RS=ST (because RST is an equilateral triangle)

Using distance formula,

\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}=2a

\sqrt{x^2+y^2}=\sqrt{(x-2a)^2+y^2}

x^2=(x-2a)^2

x^2=x^2+4a^2-4ax

x=a

\sqrt{x^2+y^2}=2a

x^2+y^2=4a^2

y^2=4a^2-a^2=3a^2

y^2=3a^2

y=\pm \sqrt{3}a

Hence, The S coordinate : (a,\pm \sqrt{3}a)

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Step-by-step explanation:

I assume the problem ask to maximize the profit of the company.

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The system of restrictions can be seen in the figure attached. The five points marked are the vertices of the feasible region (the solution is one of these points). Replacing them in the profit function:

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