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Mazyrski [523]
3 years ago
12

Write an algebraic expression for the sum of 3 coins and c coins...

Mathematics
1 answer:
JulijaS [17]3 years ago
4 0
The answer is 3 + c

3 coins are 3
c coins are c

Their sum is 3 + c


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Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
jok3333 [9.3K]

Answer:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

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\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}

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(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6

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\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}

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We can cancel the x² terms and continue squaring:

y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4

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2y+9=3\sqrt{x^2+(y+2)^2}

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4y^2+36y+81=9(x^2+(y^2+4y+4))

Distribute:

4y^2+36y+81=9x^2+9y^2+36y+36

The 36y will cancel. So:

4y^2+81=9x^2+9y^2+36

Subtracting 4y² and 36 from both sides yields:

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