Answer:
Explanation:
Consider that F (any function) <0 .
u(x,y) is a coontinuous function in the closed interval or region R.
Let us consider a point (p,q) that is inside the region and it is a maximum point.
Then it should be must
uxx (p,q) <0 where uxx means double differentiation
and uy(p,q) >0
Since ux(p,q) = 0 = uy(p,q) where ux and uy means single differentiation with respect to x and y respectively.
Say, Maximum limits of the region is T
therefore q<T
then uy (p,q) = 0 if q<T
if q = T then
point (p,q) = (p,T) will be on the boundary of R then we claim that
uy(p,q) >0
Similarly for the minimum also it will work
Answer:
The capacitor having less distance of separation has a stronger electric field.
Explanation:
The capacitors are identical and only difference between them is that one has twice the plate separation of the other. Therefore, capacitance of the given capacitors C1 and C2 is,
C1= Aε/d and C2=Aε/2d
The charges Q1 and Q2 on the capacitors of capacitance C1 and C2 respectively, is then given by the equation,
Q1=VC1
Q1=VAε/d
Q2=VC2
Q2=VAε/2d
Therefore, the surface charge density σ1 and σ2 for the capacitors is,
σ1=Q1/A
σ1=VAε/(d*A)
σ1=Vε/d
Similarly,
σ2=Q2/A
σ2=Vε/2d
The electric field between the plates is directly proportional to the surface charge density. And so electric field is inversely proportional to the distance of separation. Therefore the capacitor whose distance of separation is less has a stronger electric field.
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Answer:
A) vectors: veloicty, force
scalar: speed, work
B) t = 1.75 s, C) v = - 17 2 m / s
Explanation:
We answer each part separately
A) A vector magnitude has magnitude and direction instead a scalar magnitude has only magnitude
vector quantities: the speed of a car number is the magnitude and direction is where it goes
Force, the number is the magnitude and above that applies gives direction
Scalar magnitude: how quickly the number of the speedometer of the car
Temperature, work
B) I = 15 m height to the soil and get to calculate time = 0
y = y₀ + v₀ t - ½ g t²
as the ball is loose its initial velocity is zero
0 = 0 +0 - ½ g t²
t = 
t = 
t = 1.75 s
C) the velocity to the reach the floor
v = vo - g t
v = 0 - g t
v = - 9.8 1.74
v = - 17 2 m / s
The negative signt iindicates that the speed goes down
10 trillion km is the corrct asnwer
Answer:
1.171
Explanation:
if n₁sinΘ₁=n₂sinΘ₂, then n₂=n₁sinΘ₁ / sinΘ₂;
