Submitted by danedison on Sat, 05/02/2020 - 12:05 am.

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## New forum topics

- At 2:00 pm,thermometer reading 80oF.itis taken outside where the air temp is 20oF. At 2:03 pm, the temp reading yielded by the thermometer is 42oF. Later it was brought inside at 80oF. At 2:10 the reading is 71oF. When was the thermometer brought indoors?
- What 'positive' values of x, y, and z that will make x/(y+z) + y/(z+x) + z/(x+y) = 4?
- A man wishes his son to receive P200,000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
- Among 10000 random digits, find the probability that the 3 appears at most 950 times.
- Is this a rule in semi circles?

## Active forum topics

- At 2:00 pm,thermometer reading 80oF.itis taken outside where the air temp is 20oF. At 2:03 pm, the temp reading yielded by the thermometer is 42oF. Later it was brought inside at 80oF. At 2:10 the reading is 71oF. When was the thermometer brought indoors?
- Find the differential equation of family of circles with center on the line y= -x and passing through the origin.
- What 'positive' values of x, y, and z that will make x/(y+z) + y/(z+x) + z/(x+y) = 4?
- A man wishes his son to receive P200,000 ten years from now. What amount should he invest now if it will earn interest of 10% compounded annually during the first 5 years and 12% compounded quarterly during the next 5 years.
- Among 10000 random digits, find the probability that the 3 appears at most 950 times.

## $(x - h)^2 + (y - k)^2 = r^2…

$(x - h)^2 + (y - k)^2 = r^2$

$(x - h)^2 + (y + h)^2 = 2h^2$

$2(x - h) + 2(y + h)y' = 0$

$(x - h) + (y + h)y' = 0$

$-h(1 - y') = -(x + yy')$

$h = \dfrac{x + yy'}{1 - y'}$

$\left( x - \dfrac{x + yy'}{1 - y'} \right)^2 + \left( y + \dfrac{x + yy'}{1 - y'} \right)^2 = 2\left( \dfrac{x + yy'}{1 - y'} \right)^2$

$\left[ \dfrac{(x - xy') - (x + yy')}{1 - y'} \right]^2 + \left[ \dfrac{(y - yy') + (x + yy')}{1 - y'} \right]^2 = 2\left( \dfrac{x + yy'}{1 - y'} \right)^2$

$\left[ (x - xy') - (x + yy') \right]^2 + \left[ (y - yy') + (x + yy') \right]^2 = 2\left( x + yy' \right)^2$

$(x + y)^2 (y')^2 + (x + y)^2 = 2(x + yy')^2$

## $$\begin{eqnarray} (x-h)^2 +…

$$\begin{eqnarray}

(x-h)^2 + (y+h)^2 &=& 2h^2\\

x^2 + y^2 - 2hx - 2hy &=& 0\\

\dfrac{x^2 + y^2}{x+y} &=& 2h\\

\dfrac{(2x + 2yy')(x+y) - (x^2+y^2)(1+y')}{(x+y)^2} &=& 0\\

(2x+2yy')(x+y) - (x^2+y^2)(1+y') &=& 0\\

(2xy+2y^2 -x^2 - y^2)y' + (2x^2 +2xy - x^2 - y^2) &=& 0\\

(-x^2 + 2xy + y^2)y' + (x^2 + 2xy - y^2) &=& 0\\

(x^2 - 2xy - y^2)dy - (x^2 + 2xy - y^2)dx &=& 0 \leftarrow Answer

\end{eqnarray}$$

## This solution is elegant. I…

In reply to $$\begin{eqnarray} (x-h)^2 +… by Infinitesimal

This solution is elegant. I like it.