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i love your post

Here's a third explanation lol 

How many pairs of apples are there in a batch of 10 apples? 10 ÷ 2 = 5 pairs of apples

How many \(\frac12\times\frac12=\frac14\) square feet tiles are there in \( 11\frac12\times9\frac12 = \frac{437}{4} \) square feet?

\(\frac{437}{4} \div \frac14 =\frac{437}{4}\times\frac41=437\) one-fourth square feet, or tiles

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The area of the floor is  11.5 x 9.5  =  109.25 square feet.

The area of each tile is:  0.5 x 0.5  =  0.25 square feet.

Dividing  109.25  by  0.25  gives an answer of  437  tiles.

First, let's find where the line y = (x - 2)/2 intersects the circle x² + y²  =  8 by substituting the first value for y into the second equation:

--->     x² + [ (x-2)/2 ]²  =  8

Expand the second term:

--->     x² + ( x² - 4x + 4 ) / 4  =  8

Multiply all term by 4:

--->     4x² + x² - 4x + 4  =  32

Simplify the left side and subtract 32 from both sides:

--->     5x² - 4x - 28  =  0

Factor (or use the quadratic formula):

--->     (5x - 14)(x + 2)  =  0

Solve for x and put this value into the linear equation to find the corresponding y-value:

--->     5x - 14  =  0     --->     x = 14/5  =  2.8   and   y  =  0.4

    or   x + 2  =  0         --->     x  =  -2   and  y  =  -2

The points of intersection are:  (2.8, 0.4)  and  (-2, -2)

Use the midpoint formula to find the midpoint of these two points of intersection:

Their midpoint is:     (0.2, -0.8)

Triangle ABC is a 45º 45º 90º triangle where the side across from the 90º angle is \(6\sqrt2\)

So the sides across from the 45º angles are \( \frac{6\sqrt2}{\sqrt2}=6\)

BC = 6

Triangle BCD is a 30º 60º 90º triangle where the side across from the 90º angle is 6

So the side across from the 30º angle is 6/2 = 3

Type it in like this: " log(x,b) ",

where b is the base and x is the thing you want the log_b of.

So, If you wanted to do

log₅ 2   type: " log(2,5) "

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volume of cone = (1/3) * (π * radius²) * (height)

radius = 8/2 = 4  cm

height = 7  cm

Plug in:

volume of cone = (1/3) * (π * 4²) * 7 = (1/3)(16π)(7) = 112π / 3 ≈ 117.286 cm³