Answer:
Hence, the relation R is a reflexive, symmetric and transitive relation.
Given :
A be the set of all lines in the plane and R is a relation on set A.
To find :
Which type of relation R on set A.
Explanation :
A relation R on a set A is called reflexive relation if every 
then 
.
So, the relation R is a reflexive relation because a line always parallels to itself.
A relation R on a set A is called Symmetric relation if 
then 
for all 
.
So, the relation R is a symmetric relation because if a line 
is parallel to the line 
the always the line is parallel to the line .
A relation R on a set A is called transitive relation if and 
then 
for all 
.
So, the relation R is a transitive relation because if a line s parallel to the line and the line is parallel to the line 
then the always line is parallel to the line .
Therefore the relation R is a reflexive, symmetric and transitive relation.
Answer:
for which problems if it is all the ones you haven't done yet then say that.
Step-by-step explanation:
i dont know how to gragh pionts on this thing plz tell me how
I'm reading this as
with
.
The value of the integral will be independent of the path if we can find a function
that satisfies the gradient equation above.
You have
Integrate
with respect to
. You get
Differentiate with respect to
. You get
![\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3D%5Cdfrac%7B%5Cpartial%7D%7B%5Cpartial%20y%7D%5Bx%5E2e%5E%7B-y%7D%2Bg%28y%29%5D)
Integrate both sides with respect to
to arrive at
So you have
The gradient is continuous for all
, so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is
Answer:
a) x₁ = 14
x₂ = - 6
b) x = 4
c) P(max ) = 4000000 $
Step-by-step explanation:
To find the axis of symmetry we solve the equation
a) -4x² + 32x + 336 = 0
4x² - 32x - 336 = 0 or x² - 8x - 84 = 0
x₁,₂ = [ -b ± √b² -4ac ]/2a
x₁,₂ = [ 8 ±√(64) + 336 ]/2
x₁,₂ = [ 8 ± √400 ]/2
x₁,₂ =( 8 ± 20 )/2
x₁ = 14
x₂ = -6
a) Axis of symmetry must go through the middle point between the roots
x = 4 is the axis of symmetry
c) P = -4x² + 32x + 336
Taking derivatives on both sides of the equation we get
P´(x) = - 8x + 32 ⇒ P´(x) = 0 - 8x + 32
x = 32/8
x = 4 Company has to sell 4 ( 4000 snowboard)
to get a profit :
P = - 4*(4)² + 32*(4) + 336
P(max) = -64 + 128 + 336
P(max) = 400 or 400* 10000 = 4000000
Answer and Step-by-step explanation:
< 
