Range Definition and 979 Threads

The domain and range of this function will be the same. We can let ##𝑓(𝑥)=\sqrt{x},𝑥≥0## However, ##𝑦=𝑓(𝑥)≥0##, so the domain and range of ##f## are ##[0,+∞)## And since ##f## is a function, ##f^{-1}s## domain is the range of ##f## and ##f^{-1}s## range is ##f’s## domain. In other words...

This is a very confusing situation for me. If the input voltage were constant, then I would be able to understand that by varying load resistance, I can change the current through it, such that the drop across the load = Vz = 6.8V. But the input voltage is also not constant. So what am I to...

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I'm struggling with explanation of part 3. I don't know why they are using adiabatic equation while the gas is constantly heated by condensating vapour. While we are deriving adiabatic equation we use the fact, that there is no additional heat put into the system. Thank you in advance.

I understand how to get the dimensions that equal 8436m^3. What I don't understand is how to find the range of all possible dimensions. I solved the inequality to get ##6w^{3}-13w^{2}-5w-8436## Using systematic guessing I found the root is x=4, so the factor is x-4. Dividing (x-4) into...

I think that the range of a howitzer be increased simply by adding more explosive propellant. Why is this not used? I would think that this would be a straightforward way to increase the gun's effective range. Any ideas?

Why photon interact weakly with their environment over long distances ?

Could I please ask for help with the following question (the second part): A cruiser sailing due north at 24 km/h sights a destroyer 48 km due east sailiing at 56 km/h on a course (360-a) degress where cos(a)=11/14. Show that the destroyer's course realtive to the cruiser is on a bearing of...

Suppose we define our system to contain a few deformable bodies that exert gravitational forces on each other, and are consequently moving towards each other in some vague sense. We might want to express the total energy of the system as the sum of the mechanical energy and internal energy...

##f(x) = 6^x + 3^x + 6^{-x} + 3^{-x} + 2## But, ## AM >= GM## So, ##f(x) >= 5 * 2 ^ {\frac{1}{5}}## But this is not the case. According to the graph, it is ## f(x) >= 6##. If I do the same thing without considering the constant '2' then I am getting the answer. let ##g(x) = 6^x + 3^x +...

Hello guys, i am building a ball launcher to proper a line of baits into the sea, the line has 25 baits, each bait weights 30 grams (about 1oz) ideal shooting degree seems to be 45 to get maximum range, What I would like to figure out is the ideal weight of the ball to achieve the greatest...

Hello! I am reading Introductory Nuclear Physics, Second Edition, by Samuel Wong and in Appendix B-3, he talks about the effective range. In the derivation of the formula, in equation B-34 he writes: $$v_0(k,r)=_{r \to \infty}u_0(k,r)=_{r \to \infty}=A\sin(kr+\delta_0)$$ where ##v_0(k,r)## is...

Hi, it would be really nice if someone could give me a correct answer with a little explanation to this question. Thanks.

Hello everyone, I'm a mechanical engineering student working on a reconnaissance/surveillance UAV system. To summarize it, 1-) It will either have FLIR camera system (If I can afford it) or GoPro with turret system. In either case it will transmit 4K or lower quality video record. It will also...

From integration by parts, and using y(10) = 0, I get the equation ##2e^{3t-30} = \frac{|y-2|}{|y+1|}.## Let ##f(t) = 2e^{3t-30}##. Since it's for t>10, f(10) = 2, and we have ##2=\frac{|y-2|}{|y+1|}##. Depending on the sign I choose to use, I get either that y=-4 or y =0. Since ##t: 10...

I wandering if the size of magnet or if there is vacuum or not change the range of magnet

The strategy here would probably be to find a differential equation that ##f## satisfies, but differentiating with respect to ##x## using Leibniz rule yields ##f'=\int_x^{2x} (-te^{-t^2x}) \ dt + \frac{2e^{-4x^3}-e^{-x^3}}{x}## Continuing to differentiate will yield the integral term again...

I'm contemplating extending the concept of corner reflectors to wavelengths in the audible spectrum, specifically road noise. I read somewhere that road noise is predominantly between 800 Hz and 1300 Hz. The corresponding wavelengths (at 20°C) are 16.9 inches and 10.4 inches. I read elsewhere...

## Let~~f(x)=h(x)+g(x) , where~~h(x)=10^{\sin x}~~and~~g(x)=10^{\csc x}## ##Then,~~D_f = {D_h}\cap {D_g}## ##Clearly,~~D_h=ℝ~~and~~D_g=ℝ-\{nπ|n∈ℤ\}## ##∴~~D_f =ℝ-\{nπ|n∈ℤ\}## After considering the new domain, the range of ##\sin x## in ##10^{\sin x}## is ##[-1,1]-\{0\}## Therefore, the range of...

I have a program where I am supposed to find out the pressure, given the ideal gas equation with Van der Waal's correction, $$\left(p - \frac{a}{v^2}\right)\left(v - b\right) \ = \ Rt$$I have to take a constant value for ##t## (user input), and ##v## will range from 1 to 20 in steps of 0.01. ##a...

I don't know how to show that this limit is zero. It seems that ##\sum_{i=1}^N a_{i,N} /N = 1## and the fact that ## 0 < a_{i,N} < M > 1## implies that some ##a_{i,N}## are less than one. Another conclusion I guess is correct to draw is that ##\lim_{N \to \infty} \sum_{i=1}^N a_{i,N}^2 /N < 1##.

Given that electromagnetic waves transport energy via photons, what is the lowest and highest possible frequency of a photon and what physical phenomena do these relate to? It is clear that the larger the wavelength the lower the energy for a photon. so what are the limits of the wavelength?

Relative DC permeability of copper is 1. Conductors are considered dispersive and therefore the permeability should change with frequency. Where can I find data or how can I calculate permeability of copper in Ghz frequency range?

Okay so I'm not quite sure about the normal reaction forces. The condition is that they are both equal for the sum of frictional forces to be zero but then technically when substituting into the number equations in place of [ n(1) + n(2) ] either 2n(1) or 2n(2) makes me confused as then n(1)...

A theorem from Axler's Linear Algebra Done Right says that if 𝑇 is a linear operator on a complex finite dimensional vector space 𝑉, then there exists a basis 𝐵 for 𝑉 such that the matrix of 𝑇 with respect to the basis 𝐵 is upper triangular. In the proof, he defines U=range(T-𝜆I) (as we have...

About cosmology: https://www.physicsforums.com/threads/what-is-the-probability-that-the-universe-is-absolutely-flat.971984/#post-6180036 Planck paper: https://arxiv.org/pdf/1502.01589.pdf As in PCP13 we adopt a Bayesian framework for testing theoretical models. In the Planck paper, pages 38-40...

So I understand that grounded shielding of audio equipment is necessary to block both EMI and RFI from audio equipment, but what I can't find information about is how, for example, radio frequency interference "RFI" at 150kHz, can interfere with audio equipment in such a way that you will hear...

Hello, The human eye has an average diameter of ##2.5 cm## and an optical power between ##60D## and ##64D##. An object can be brought as close as the near point which is about ##25 cm##. If ##d_{o}=0.25m## (object distance) and ##d_{i}= 0.025m## (distance to the retina), the optical power...

My attempt : Given ##f(x)## and ##g(x)## for ## -1.6 < x < 1.6## we get ##0\leq f(x)<1.6## Thus, for ##f(g(x))## we get ## -3 \leq g(f(x)) < -1.4## Thus the required set should be the interval ##[-3, -1.4)##? My Questions : 1. What have I missed since my answer does not match the given...

To check if it is injective : ##h'(x) = 3(x^2-1)## ##\implies h'(x) \geq 0## for ##x \in (-\infty, -1]## Thus, ##f(x)## is increasing over the given domain and thus is one-one. To check if it is surjective : Range of ##f(x) = (0, e^4]## but co-domain is ##(0, e^5]## thus the function is into...

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Hi all, I recently came across an exercise observing that human cannot hear ultrasounds, but could hear the beat between two different ultrasounds, provided that its frequency falls in the audible range between 20 Hz and 20kHz. The problem gives one frequency and asks for the range of the other...

Homework Statement A particle is projected inside a tunnel which is 2 m high and must not hit the side or ceiling of the tunnel. If the initial speed is U show that the maximum range of the particle inside the tunnel You may assume that the maximum range is attained when the projectile just...

Why do Wi-Fi waves have such short distance and some microwaves are used for sending information through long distances?

Hi everyone! Terahertz time-domain spectroscopy (THz-TDS) is a spectroscopic technique that is using the radiation in the THz range. https://en.wikipedia.org/wiki/Terahertz_time-domain_spectroscopy A THz-TDS setup consists of an emitter and detector. The emitter creates a short broadband...

Homework Statement Allow f:ℤ→ℤ be defined by, for all n∈ℤ f(n) = {n-1 if n is even, n+5 if n is odd Prove that ran(f) = ℤ Homework EquationsThe Attempt at a Solution I am unsure of how exactly to prove this due to the fact now I am working with a piecewise function. Here is what I have so...

See my previous post! https://www.physicsforums.com/threads/do-gravitons-have-frequency-like-photons.957146/ Let's say we had some aliens that had the ability to emit/interact with gravitons with frequency roughly in the range corresponding to human hearing (20Hz-20KHz), and that they had an...

Calculate the range of sizes of the particles. 
 ν= velocity of decent d = diameter ps = density η = viscosity P1 = density v= (d^2 (p_s-p_1 )g)/〖18〗_η Rearrange for the diameter. v= (d^2 (p_s-p_1 )g)/〖18〗_η 〖18〗_η v= d^2 (p_s-p_1 )g (〖18〗_η v)/(p_s-p_1 )g= d^2 √((〖18〗_η...

Homework Statement A has n elements. B={0,1,2,3} {1,2,3}⊆range(f) Homework EquationsThe Attempt at a Solution So in each function we must choose those 3 numbers in the range. So let's first choose all the diffrent possiblites to choose those 3: n*(n-1)*(n-2) now for the remaining elemnts, we...

how do you define x to be from minus pi to plus pi in matlab? i tried: x = -pi : piBut when i said plot (x,y) Matlab says: "Error using plot Data must be numeric, datetime, duration or an array convertible to double" (i already defined y interms of x, that function is ok) so i culd not...

I got something i want to do for fun and help out a...person i know but i never finished high school so that's my degree level. i was wondering if there is a way under $100 to possibly use my internet or posibly 2 peoples internet connections on the other side of the town i live in, split up the...

Find the inverse function $f^{-1}$ of $f$. Find the range of $f$ and the domain and range of $f^{-1}$ $$f(x)=5 \sin x +2; \quad -\frac{\pi}{2}\le x \le \frac{\pi}{2}$$ exchange x for y and solve for y \begin{align*}\displaystyle x&=5\sin y + 2 \\...

Homework Statement Q- a positron emerges normally from a 4-mm thick slab of plastic (density= 1.14g/cm^3) with an energy of 1.62 MeV. What is the energy of the particle when it entered the slab? Homework Equations Range when 0< T <= 2.5 MeV: R= .412+T^[1.27-.0954*ln(T)] where T is kinetic...

Homework Statement A projectile is fired with an initial speed of 46.6 m/s at an angle of 42.2 ∘ above the horizontal on a long flat firing range. 1-Determine the maximum height reached by the projectile. 2-Determine the total time in the air. 3-Determine the total horizontal distance...

It is said (hopefully no need to give references for such a common statement) that the electromagnetic field of a given charged particle is infinite in range (albeit converging to zero as the distance goes to infinity). However, given that charged particles apparently did not exist at the...

Problem: https://drive.google.com/open?id=19PDuyshgP6u4U9mXU3BfrF031J8wL12B Attempt: I tried to solve the range by listing out the Newton's 2nd laws of each drum https://drive.google.com/open?id=1Eslg2Wy3orG41eywwm_O6qN4OQ3QN-bA and from the equations of the drum 2, I get...

Homework Statement 1-A rifle can shoot a projectile with a velocity of 207m/s. At what angle should the rifle be pointed to give the maximum range? 2-Evaluate the maximum range Homework Equations N/A The Attempt at a Solution I considered at first that the problem seemed like it could be...

Homework Statement Why we use range with continuous random and why is time continuous var and why we associate a range with it? Homework Equations Theoreticl topic The Attempt at a Solution Hi, I can't understand about the continuous random var and its range. It says that measurable values are...

How do you find the domain and range of a graph?