C.mr Lee spent 7 hours giving drums lessons yesterday. iF each lesson lasted 1/4 hour, how many lessons did he give
Let

be the amount of pennies received for lawn

. Then,

and

.
We claim by induction that

. The base case is trivial (

is given). Then, we complete the inductive step. If

, we have:

This completes the proof.
Thus,

.
24 times
-
Because a dime is worth 10 , I divide 240 into 10 & got 24.
( 2 sin x cos x )` = ( 2 sin x )` cos x + 2 sin x ( cos x )` =
= 2 cos x cos x + 2 sin x *( - sin x ) =
= 2 cos² x - 2 sin² x = 2 ( cos² x - sin² x ) = 2 cos ( 2 x )
Another way ( using trigonometric identities first ):
2 sin x cos x = sin ( 2 x )
( sin ( 2 x ) )` = 2 cos ( 2 x )