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MATHirang MATHibay 2025 (Orals, 1.3.2)
BinariouslyRandom 0
Find the third smallest number 
which satisfies all the following properties:
Give your answer in base 10.
which satisfies all the following properties:
Give your answer in base 10.
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Word problem of Absolute-Value Function
Sukardy 1
N
by Mathzeus1024
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 
.
1 reply
Functional Equations
burntpizza001 1
N
by alexheinis
Let 
is a function satisfying 
and 
, 
.
(i) If
then minimum possible number of values of 
satisfying 
, for ![$x\in[0,170]$](//latex.artofproblemsolving.com/3/d/2/3d2c6ead3059f96f853bba6cfc7440e394227ab9.png)
is?
(ii) Graph of
$ is symmetrical about which line?
is a function satisfying 
and 
, 
.(i) If
then minimum possible number of values of 
satisfying 
, for ![$x\in[0,170]$](http://latex.artofproblemsolving.com/3/d/2/3d2c6ead3059f96f853bba6cfc7440e394227ab9.png)
is?(ii) Graph of
$ is symmetrical about which line?
1 reply
then
aand 
Prove that
prove that 
and 
Prove that
Can anyone help me with this inequality problem
a9opsow_ 3
N
by sqing
Let a, b, c be nonnegative real numbers, not all equal. Prove that
\frac{(a - bc)^2 + (b - ca)^2 + (c - ab)^2}{(a - b)^2 + (b - c)^2 + (c - a)^2} \geq \frac{1}{2}.
\frac{(a - bc)^2 + (b - ca)^2 + (c - ab)^2}{(a - b)^2 + (b - c)^2 + (c - a)^2} \geq \frac{1}{2}.
3 replies
Prove that
