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:
average speed, accelerated speed
Explanation:
Pace was first moving at 38 km/h which was his average speed but the fastest speed he went was 60 km/h so he accelerated.
Answer:
formula used K=F/∆l
∆l is the elongation of the spring
- F=10N
- ∆l=20mm===> 0.02m
- K=10N divided 0.02m= 500N/m
If he wants to increase power, force must increase and decrease time.
Answer:
a) P = 807.85 N, b) P = 392.15 N, c) P = 444.12 N
Explanation:
For this exercise, let's use Newton's second law, let's set a reference frame with the x-axis parallel to the plane and the direction rising as positive, and the y-axis perpendicular to the plane.
Let's use trigonometry to break down the weight
sin θ = Wₓ / W
cos θ = W_y / W
Wₓ = W sin θ
W_y = W cos θ
Wₓ = 1200 sin 30 = 600 N
W_y = 1200 cos 30 = 1039.23 N
Y axis
N- W_y = 0
N = W_y = 1039.23 N
Remember that the friction force always opposes the movement
a) in this case, the system will begin to move upwards, which is why friction is static
P -Wₓ -fr = 0
P = Wₓ + fr
as the system is moving the friction coefficient is dynamic
fr = μ N
fr = 0.20 1039.23
fr = 207.85 N
we substitute
P = 600+ 207.85
P = 807.85 N
b) to avoid downward movement implies that the system is stopped, therefore the friction coefficient is static
P + fr -Wx = 0
fr = μ N
fr = 0.20 1039.23
fr = 207.85 N
we substitute
P = Wₓ -fr
P = 600 - 207,846
P = 392.15 N
c) as the movement is continuous, the friction coefficient is dynamic
P - Wₓ + fr = 0
P = Wₓ - fr
fr = 0.15 1039.23
fr = 155.88 N
P = 600 - 155.88
P = 444.12 N
