mechanics favorite of many

i have a sheet inclined at angle x

move a block y along the sheet UP THE PLANE

i turn the sheet parallel to the surface

move the same block y again along the sheet

where will i burn my energy more?

Time for vehicle dynamics

What is the relation between the toe angle of rear wheel and understeer and oversteer?

give me an approppriate reason for that

find out the 9 gm coin?

there are 10 rooms

each room is filled with 10 gm coins of gold

except 1 room filled with 9 gm coins of gold

we have a weighing machine which operates on one rupee coin

Now you have only one rupee in your pocket and you need to find out which room contains the 9 gm coin

In short,
you are allowed to use the weighing machine only once
and yes the weghing machine can measure gms i.e. it is accurate to measure gm

Graph for the simple calculus question

these red points is the graph for rhs
and hence it is not differentiable

Where has the one rupee gone?

Three friends went for a dinner and the bill amount was 75rs
all the 3 gave 25 rs each
manager gave 5rs concession
waiter kept 2rs with himself and gave one rupee each
so the bill amount for each person was 24rs
now 24+24+24 = 72 and 2rs of waiter
total 74rs
where the one rupee is?

Lets solve the series

find the nth term of the following series

1,3,4,9,10,12,13......................

The above series is actually the increasing sequence of sum of numbers that are generated by sum of unique powers of 3

for example

4 = 1+3

10 = 1+9

12 = 3+9

13 = 1+3+9

find the nth term of the series

me and patro are not allowed to answer first

i want the explanation for this as this can be or may be done by more than one method

Time For Simple Calculus

we know that

d(x^2)/dx = 2x;

now we also know that

x^2 = x*x = (x+x+x+x+x+x+x+-----------)x times;

thus y differentiating both the side

d(x^2)/dx = (1+1+1+1+1+1+1+----------)x times;

2x = x;

2 = 1

:(

what the hell is this
think about it

I will be happy if you prove it wrong because i dont want my studied mathematics to be a waste