AfroThundr3007730

When you divide by a fraction, you flip the fraction and multiply it.

So: 60/5/3 = 60 * 3/5 = 180/5 = 36

Hmm don't know what you mean exactly by that, but it reminds me of this:

Basically using an infinite series this pattern will converge to 1/3 as n→∞.

Closest thing I could think of to your question.

I would like to add to the above answer.

Since you can't have 3.3 or 2.6 notebooks, the highest you could go would be 4 spiral and 2 three-ring notebooks for a total of $18. Or you could just buy 6 spiral notebooks for $12 which would be the most efficient use of the money...

First, imagine the following segment:

If you know the endpoint A and the midpoint B, then finding the other endpoint C is easy.

You would first have to find the change in X (ΔX) and change in Y (ΔY)when moving from point A to point B.

Lets give point A the coordinates (2,4) and point B the coordinates (5,8).

To find ΔX we subtract the X coordinate in point B from point A: ΔX=5-2=3 ΔX=3

To find ΔY we subtract the Y coordinate in point B from point A: ΔY=8-4=4 ΔY=4

To verify, simply add the ΔX and ΔY to the point A coordinates and you will get the coordinates of point B. 2+3=5 and 4+4=8

Since B is the midpoint, the distance between A and B is equal to the distance between B and C, which means the ΔX and ΔY are the same.

So take the coordinates of point B and add the ΔX and ΔY: 5+3=8 and 8+4=12

With that we find that the coordinates of point C are (8,12)

Well this one can be solved with the Side-Angle-Side theorem.

Assuming the lamp post is at a 90 degree angle from the ground we have this:

Where B is the height of the lamp post, A is the length of the shadow, and b is the elevation of the sun casting the shadow.

The sum of the angles in a triange always add up to 180 degrees, so since we know two of the angles, the third is easy. 180 - 64 - 90 = 26 (Assuming the lamp post is angled 90 degrees relative to the ground.)

So far we have a=26 b=64 c=90 and A=8 B=? C=?

So the law of sines states that A/sin(a) = B/sin(b) = C/sin(c), therefore:

8/sin(26) = B/sin(64) = C/sin(90) = 18.25. (Fun fact: sin(90) = 1)

So solving for C: C/sin(90) = C/1 = C = 18.25

So now we have a=26 b=64 c=90 and A=8 B=? C=18.25

now to solve for B:  B/sin(64) = 18.25    B=18.25*sin(64) = 16.4

Finally all the cards are on the table: a=26 b=64 c=90 and A=8 B=16.4 C=18.25

So to answer the question, the height of the lamp post is 16.4 feet.