Step-by-step explanation:
f(3)=?
f(x)=2x+5
put x=3,
f(3)=2(3)+5=6+5=11
------------
g(2)=?
g(x)=x^2-3
put x=2,
g(2)=2^2-3=4-3=1
-----------------
g(f(-1))=?
g(x)=x^2-3
and f(-1)=2(-1)+5= -2+5=3
so g(f(-1))=3^2-3=9-3=6
----------------
f(g(-1))=?
f(x)=2x+5
g(x)=g(-1)=(-1)^2-3=1-3= -2
f(g(-1))=2(-2)+5= -4+5=1
----------------
g(f(x))=?
g(x)= x^2-3
put x=f(x),
g(f(x))=f(x)^2-3=(2x+5)^2-3=4x+25+20x-3=24x+25
The Lagrangian,

has critical points where its partial derivatives vanish:





tells us
, so that


Then with
, we get

and
tells us

Then there are two critical points,
. The critical point with the negative
-coordinates gives the maximum value,
.
Answer:
x = 2
Step-by-step explanation:
Answer:
x³/4z²
Step-by-step explanation:
Invert and multiply:
48x^5y²/12z^5 x z³/16x²y²=
(48x^5y²)(z³)/(16x²y²)(12z^5)
the y² cancel out
48÷16=3 (on top)
x^5÷x²=x³
12z^5/z³=z²(on bottom)
This leaves a 3x³ on top and 12z² on the bottom. 3÷12=4 (on bottom):
3x³/12z²
x³/4z²
Answer:
18x/18=36/18
x=2
Step-by-step explanation: