All categories

3 years ago

A (nonconstant) harmonic function takes its maximum value and its minimum value

Physics

1 answer:

AURORKA [14]3 years ago

3 0

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

You might be interested in

A boat with a horizontal tow rope pulls a waterskier. She skis off to the side, the rope makes an angle of 15° with the forward

dsp73

Answer:

<h3>13,976.23Joules</h3>

Explanation:

Workdone by the rope is expressed using the formula;

W = Fd sin(theta)

F is the tension in the rope = 180

d is the displacement = 300m

theta is the angle of inclination = 15°

Substitute the given parameters into the formula;

W = 180(300)sin15

W = 54000sin 15

W = 13,976.23

Hence the workdone by the rope is 13,976.23Joules

4 0

3 years ago

What makes science different from other fields of knowledge like art or philosophy?

makkiz [27]

As opposed to art or philosophy, science is an objective phenomenon. It deals with something which is verifiable, meaning that it can be tested, and it is based on facts, which are true and can be proven. On the other hand, art is highly subjective, which means that it can be interpreted in many different ways. Science is more concrete and testable, whereas art and philosophy lie in the domain of the abstract.

5 0

3 years ago

Select the correct answer from each drop-down menu.

sweet-ann [11.9K]

the attraction is maximum between b and c. while the force between a and d is minimum

3 0

3 years ago

Read 2 more answers

The frequency of the lowest standing-wave mode on a 1.0-m-long string is 20 Hz. What is the wave speed on the string?

IRISSAK [1]

Answer:

Wave speed on the spring is 40 m/s

Explanation:

Frequency for standing wave mode of an open- open tube is given by

$f_{} =\frac{v}{2L}$

where v is the velocity, L =1 m is the length

wave speed on the spring is

$v =2fL\\v=2\times 20\times 1\\v=40 m/s$

3 0

3 years ago

Starting from rest a model rocket accelerates upwards at 24 m/s. How long does it take to reach a height of 192 meters

klio [65]

Answer:

$t=4s$

Explanation:

We want to write the equation of displacement (vertical in this case) for accelerated motion, which is $y=y_0+v_yt+\frac{a_yt^2}{2}$ . If we take the upward direction as positive, assume it starts from rest and from the ground, and $a_y=24m/s^2$ (the units are wrong in the text, if accelerates at that magnitude, it's an acceleration, in particular in $m/s^2$ ), then we have $y=(12m/s^2)t^2$ .

We want to know the time when $y=192m$ , so we need to solve $192m=(12m/s^2)t^2$ , for which we have:

$t=\sqrt{\frac{192m}{12m/s^2}}=4s$

This means it takes 4 seconds for a rocket accelerating at $24m/s^2$ to reach a height of 192m.

3 0

3 years ago