be a positive odd integer. Find the smallest positive
such that 
| 
− 
be the function defined by 
and 
whenever 
is a prime number and 
that satisfy 
and 
and 
are chosen uniformly and at random from the disk 
.
and 
,
are all real numbers. The probability that
can be written as 
, where 
are positive integers, gcd 
,
is not divisible by the square of any prime. Compute 
.
groups, such that
,
. . . , 
in the interval ![$[-1,1]$](http://latex.artofproblemsolving.com/3/9/f/39f506ebeeeb72f62147990614a67f4e30b7c751.png)
where the
be the product of all
to the other 
ad 
be two circles intersecting at 
and 
The tangent like closer to 
touches 
and 
respectively. If 
and 
find 
Prove that
Prove that
Let 
Prove that
Let 
Prove that
Y by Adventure10
Please help me solve the following word problems. It is about absolute-value function. Any sketch of function's graph will be greatly appreciated.
Problem:
A combat plane is flying
m above the sea. The plane will aim an enemy submarine in the distance of 
m. To be aimed on the target, a missile shot by the plane plunges into the sea with a depth of 
m. Suppose the surface of the sea to be 
-axis and the plane's motion is represented by a function 
for 
. Find the value of 
.
Problem:
A combat plane is flying
m above the sea. The plane will aim an enemy submarine in the distance of 
m. To be aimed on the target, a missile shot by the plane plunges into the sea with a depth of 
m. Suppose the surface of the sea to be 
-axis and the plane's motion is represented by a function 
for 
. Find the value of 
.This post has been edited 2 times. Last edited by Sukardy, Nov 6, 2019, 7:42 AM
and the sub at 
in the 
p
.
