Post your math problems here

This is a question I made using shadows.

There is this person who owns a hotel. 20 years ago she planted a tree outside the hotel which is now VERY tall. She is 2m tall and has a long metal pole. A guest complains about the tree blocking the view so she wants to move it somewhere else but she needs to know how tall it is to put it in an appropriate sized cart. She makes meter marks down the pole and then tries to measure the tree but it isn't long enough. She measures her own shadow which goes cleanly on the floor which is 3m long and then she measures the tree's shadow which goes 5m along the floor and 4m up the wall.

How tall is the tree?

I forgot a . in the first sentence after hotel sorry

nvm i can edit

@ForumMathSolver said in #7:

1 + 2 + 3 + ... + x
= (x + 1) + {(x - 1) + 2} + ((x - 2) + 3) + ... + {(x - x/2) + (x/2 + 1)}
= (x + 1)(x + 1)(x + 1)... x/2 times
= x(x + 1)/2 ... (i)

What does x/2 times mean if x is odd?

@kajalmaya said in #43:

What does x/2 times mean if x is odd?
If x is odd, then what I mean by x/2 times is that in the end, there's a term (x + 1)/2, you feel me?
Let's take a random odd number, 11, as x. So the sum becomes 1 + 2 + 3 + ... + 11
= (1 + 11) + (2 + 10) + (3 + 9) + (4 + 8) + (5 + 7) + 6
= 12 x 5 + 6
= 12 x 5 + 12/2
= (11 + 1) x 5 + (11 + 1)/2
= 11(11 + 1)/2
This holds even if x is odd, because once x is odd, (x + 1) becomes even, which is divisible by 2, so x(x + 1)/2 is a natural number.

@Aster_blossom said in #40:

can i hire you to do my maths exam and homework?????
All payments should be made using PayPal lol

@ForumMathSolver said in #44:

If x is odd, then what I mean by x/2 times is that in the end, there's a term (x + 1)/2, you feel me?

You should not have to explain a proof. It should be airtight and stand on its own. Whatever you want to say about x being odd or even should go into the proof. Or write a proof that is general enough so that you do not need special consideration for x even or odd.

what are you, some type of math wizard?

@CrazySnorlax said in #41:

There is this person who owns a hotel. 20 years ago she planted a tree outside the hotel which is now VERY tall. She is 2m tall and has a long metal pole. A guest complains about the tree blocking the view so she wants to move it somewhere else but she needs to know how tall it is to put it in an appropriate sized cart. She makes meter marks down the pole and then tries to measure the tree but it isn't long enough. She measures her own shadow which goes cleanly on the floor which is 3m long and then she measures the tree's shadow which goes 5m along the floor and 4m up the wall.
How tall is the tree?

Let the constant angle of elevation of the sun be theta.
Refer to this diagram: https://imgur.com/a/2UPwCAM
tan theta = DB/BF = EG/GC = AB/BC
Thus, tan theta = 2/3 = 4/GC = AB/(BG + GC)
2/3 = 4/GC
Thus, GC = 4 x 3/2
Thus, GC = 6 m
Thus,2/3 = AB/(BG + GC)
Thus, 2/3 = AB/(5 + 6)
Thus, 2/3 = AB/11
Therefore, AB = 22/3 m
Thus, the height of the tree is 7 (1/3) m.

@FinishMySentence said in #47:

what are you, some type of math wizard?
Nah, I'm just unemployed

@ForumMathSolver said in #45:

All payments should be made using PayPal lol

oh........too bad its not there in my nation XD