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look at the model

its height is just 2 feet, whereas the actual ramp was 12feet.

so the model is 6 times smaller than the actual ramp

look at the grid now

can you tell me the length of JL ?

yes sorry

np, take ur time :) see if u can find the length of JL

Ok I am looking at the grid nd trying to figure it out.

if you see, both J and L are at same height (60)

J is on left side at 10
L is on right side at 34

yes

so length of JL = distance between JL= 34-10 = 24

ok

so we now knw two lengths of actual ramp.
JK = 12 feet
JL = 24 feet

yes ok

we need to figure out where R goes

ok

look at the ramps, JL of actual ramp is represented by PR in model, right ?

yes it is

so, PR = JL/6 = 24/6 = 4

Yes that makes sense

good :) so what does that mean ?

it means, we need to pick R such that it is 4 feet away from P

look at grid now

P is located at (30, 20)

yes

can we say R can be at (30+4, 20) = (34, 20)

yes

thats it ! point R has to be at (34, 20)

And we explain this usuing reasoning because of all of the above notes?

you can compress it :-

ok

oh ok, thank you so much. :)

np :)

use this :-
sum of first n numbers = (n+2)th numeber - 1

since you want to knw suermnsm of first 12 terms, you need to look for (12+2) = 14th number

ok

google and tell me, whats the 14th number in fibonacci sequence

Ok, I am doing it now.

It is 377

correct! thats the 14th number. subtract 1 to get the sum of first 12 numbers

so 376 is the answer?

sum of first 12 numbers = (12+2)the number - 1
= 14th number - 1
= 377 - 1
= 376

yes thats the answer. you can confirm it by adding manually all 12 numbers !

So is the Fibonacci Sequence always the same?

Yes

Ok so if it asks what the 13th term in the Fibonacci Sequence is then it would be 233?

you're tossing, whether to call 233 ias 13th number or 14th number ?

It asked me : What is the 13th term in the Fibonacci Sequence?

That is a 2nd question, I got and understand the first question.

cuz if u start from 0,1 then 14th number wud be 233
if u start from 1,1 then 13th number wud be 233

Is this what they gave you to use ?

My chart starts with 1 so I was saying the correct answer would be 233, correct?

here it starts from 1,1..

yes, if you start from 1,1, then, 13th number is 233

but actual fibonacci sequence starts from 0,1... but you should use what ur chart shows :)

yea sure

14th number : ?
13th number : ?

377
233

So you just subtract correct

ratio between 14th and 13th terms = \(\large \frac{377}{233}\)

ratio means division !

1.6180258

dont forget to round it to 5 decimal places

Since it says round to 5 decimal places it would be 1.61803 is that correct?

correct

Oh I did it. Thank you so much for explaining that, that actually helped me with 3 problems.