What is Range: Definition and 1000 Discussions

The Land Rover Range Rover (generally known simply as the Range Rover) is a 4x4 motor car produced by Land Rover, a marque and sub-brand of Jaguar Land Rover. The Range Rover line was launched in 1970 by British Leyland and is now in its fourth generation.
Additional models have been launched under the Range Rover name, including the Range Rover Sport, Range Rover Evoque, and Range Rover Velar.

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  1. F

    Projectile motion maximum range problem

    Homework Statement A projectile is fired at 30 km/h at the angle θ in x direction of an x-y plane. Ignoring the effects of air resistance, find the maximum range and the value of θ that gives this range Part A: write down the initial horizontal and vertical components of the velocity Part...
  2. P

    Functional Derivative of Long Range Dipole Interaction Energy

    Homework Statement Dear all, Good day. I am currently working on the phase field modeling of ferroelectrics. For this reason, I need to find functional derivative of an expression as presented in attached picture 1. Then in picture 2, it shows the final form of equation that I am...
  3. S

    A Question about the Domain and Range of a Function

    Homework Statement I constructed my own question to try to make sense of the following notation. g(x) = 2√x g : X → Y. What does X and Y equal? Homework Equations For 2√x, x = or > than 0. The Attempt at a Solution g(x) = 2√x g : [0, ∞) → [0, ∞) So X = Y = [0, ∞) The...
  4. A

    Range Equation Limitation question

    Homework Statement First off, this is NOT a homework problem. I do not need an actual "answer", but I do have a conceptual question. Here it is: Consider a projectile motion problem such as a baseball being hit. Assume that it is hit and caught at the same height above the ground. In this...
  5. anemone

    MHB Find the range of values for abc and a + b + c

    Let $a, b, c$ be positive real numbers satisfying \frac{1}{3}\le ab+bc+ca \le 3. Determine the range of values for i) $abc$, ii) $a+b+c$.
  6. S

    Using E-L equations to get through a mountain range

    I'm just trying to get my head around calculus of variations so I gave myself a simple example to work with: Suppose I want to get between two points (a and b) through a mountain range with height described by the scalar field h(x,y) whilst staying as low as possible. I want to know what...
  7. M

    Why is there a peak in the visible range?

    I have always wondered why the intensity of the graph always peaks in the visible portion of spectrum. http://3.bp.blogspot.com/-fOnjOBanbcw/TqG1dI81fnI/AAAAAAAABpM/mRL5kfi-i_Y/s1600/ThermalRadiation.png I understand that the graph represents intensity does not continually increase as...
  8. K

    Calculating the range of an animal based on its movement costs

    Hi all, So I'm looking at how far an animal can move based on its basal metabolic rate and cost of movement. The total cost of these two is 45 Watts. It has 1.5 kg of food reserves with an energy density of 5.2 x 10^6 J per kg = 7800000 J of energetic reserves. All I want to do is see how...
  9. R

    Maximum range of an object projected from a height h

    Homework Statement A particle is projected with an initial speed u from a point at a height h from the horizontal plane. Find the equation for maximum range of the particle. Homework Equations R=u^2sin2θ/g H=(usinθ)^2/2g The...
  10. D

    Finding a basis for the null space and range of a matrix

    Homework Statement ##S## is a linear transformation and ##\{u_{1},u_{2}\}## is a basis for the vector space. $$ S(u_{1})=u_{1}+u_{2}\\ S(u_{2})=-u_{1}-u_{2} $$ I would like to find a basis of the null space and range of ##S##.Homework Equations In my text, it says that the proper matrix...
  11. G

    Calculating Maximum Range of a Catapulted Rock

    Homework Statement Assuming that the rock launched by a catapult is released from ground level, show that the theoretical maximum range is: R=2Mh/m, where M = mass of counterweight m = mass of rock h = height counterweight falls Homework Equations Ep=mgh Ek=(mv^2)/2 The Attempt...
  12. B

    Direct sum of nullspace and range

    Is this true? I am studying direct sums and was wondering if the following statement holds? It seems to be true if one considers the proof of the dimension theorem, but I need to be sure, so I can steer my proof toward a particular direction. ## N(T) \bigoplus R(T) = V ## where ##V## is the...
  13. M

    What Are My Options for Extending Wifi Range Away from Campus?

    I'm 6 blocks away from campus & probably 4 blocks out of range. I'm a student at the university so I do have the security code. I'm only 1st year EE, so I'm looking for advice. I can follow a schematic, but lack theory of operation that many of you have. Options?
  14. Saitama

    Finding the Range of a Trig Function with Cauchy-Schwarz

    Homework Statement ##\forall x \in R##, find the range of function, ##f(x)=\cos x(\sin x+\sqrt{\sin^2x+\sin^2\alpha})##; ##\alpha \in [0,\pi]##. Homework Equations The Attempt at a Solution Honestly, I cannot think of how to approach this problem. I don't see how would I simplify...
  15. T

    Passive long range sensor using radio wave distortions?

    Greetings PFers, I was thinking about how it would be possible to "scan" something without having visual or physical contact (and without have a superconducting magnet, etc...) Lets have this device detect something conductive. If a device were to emit an electric field pulse of very...
  16. marellasunny

    Radar as range detector between cars-static sender vs dynamic sender

    Say I have a radar transmitter on a car,used to detect its distance from a car in front of it by measuring the doppler shift on the reflected wave. i.e Car 1 is the source, its wave gets reflected by Car 2 in front of it. My book splits the problem of calculating the Doppler shift by computing...
  17. Albert1

    MHB Find the Range of y for $a,y \in R$

    $a,y \in R$ $y=\sqrt {a^2+a+1} - \sqrt {a^2-a+1}$ please find the range of y
  18. anemone

    MHB Find the Range of Values for Negative a

    If the inequality $\sin^2 x+a\cos x+a^2 \ge 1+\cos x$ holds for any $x\in R$, determine the range of values for negative $a$.
  19. P

    Projectile Motion: Formula for range for a given angle

    I was watching a YouTube video on projectile motion: It says that the range is given by the formula: d = v*cosθ*t It also says that the time to reach the maximum height is given by the formula: t = \frac{v*sinθ}{a} where v*sinθ is the initial vertical velocity Well, not...
  20. MarkFL

    MHB John's Question: Finding Range of Rational Function

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  21. N

    Solving trigonometric equations with a specific range

    Homework Statement Given that -180 <= x <= 180, solve the following equation in radians cosx = -1/sqrt(2) The Attempt at a Solution I'm not exactly sure how to solve this question with respect to the range -180 <= x <= 180. I know that -1/sqrt(2) means that x is 45 degrees in either...
  22. Saitama

    What is the Range of the Given Expression When ##\sin 2\beta≠0##?

    Homework Statement If ##\beta## is such that ##\sin 2\beta≠0##, then show that the expression ##\displaystyle \frac{x^2+2x\cos\alpha+1}{x^2+2x\cos\beta+1}## (x real) always lies between ##\cos^2\alpha/\cos^2\beta## and ##\sin^2\alpha/\sin^2\beta##. Homework Equations The Attempt at...
  23. J

    Finding range given impact velocity?

    A projectile shot over level ground hits the ground with a velocity of 65m/s at an angle of 25° below the horizontal. What was the horizontal range of the projectile? 170m 330m 780m 360m If something is launched over a horizontal plane, does Vi=Vf? (same magnitude and velocity) (but...
  24. X

    Is a Manometer Designed to Work Below its Natural Frequency?

    Is manometer suppose to work below its natural frequency ? I saw a textbook problem asking to design a manometer with its natural frequency way way below the pressure's fluctuation frequency, so was confused. Thanks
  25. S

    Projectile motion with mass height and range

    Hello all I have a question I was hoping someone could answer for my homework. A 78.0-kg boulder is rolling horizontally at the top of a vertical cliff that is h1 = 16 m above the surface of a lake, as shown in the figure below. The top of the vertical face of a dam is located d = 110 m from...
  26. S

    Gravity at its maximum range question.

    Hey guys. I have an unusual question. Lets say the universe is 100,000,000,000 Light years across. (100 billion I think) Lets say there are only 2 bodies that have mass in said universe. One body is at one end of this universe and the other body is at the opposite end. Do these 2...
  27. N

    Bullet Range Neglecting Air Drag

    Hello All, Homework Statement I was at the firing range the other day when the gun instructor mentioned that the bullet of a AR-15 rifle can travel 5 - 6 miles depending on the angle of the gun when the bullet leaves the muzzle. I wanted to confirm this for myself so, I tried to find the...
  28. R

    Converting data to a specified range

    Hi, I am trying to convert data to a particular range of 0-10. Actual Data may vary from - 50000 - 26214400. I have broken this down into 4 parts as follows - 50000 - 1048576 -----> 0 - 2.5 1048577 - 5242880 -----> 2.6 - 5 5242881 - 15728640 ----->5.1 - 7.5 15728641 - 26214400...
  29. J

    Fourier series coefficient (half range)

    Homework Statement f(x) = 1, 0<x<1 Extend f(x) t generate an even function P(x) and find Fourier coefficients Homework Equations an = 2/T ∫ P(x)cos(2nx/T) dx The Attempt at a Solution P(x) = 1, -1<x<1 0, -2<x<-1 , 1<x<2 even function so b0 = 0 Average of P(x)...
  30. K

    What is the Range of a Twice Differentiable Function?

    A function f :[0,1]→ℝ is twice differentiable with f(0)=f(1)=0 such that f''(x) - 2f'(x) + f(x) ≥ e^x, x ε [0,1]. Then for 0<x<1 which of the following is true 0<f(x)<∞, -1/2<f(x)<1/2, -1/4<f(x)<1, -∞<f(x)<0. I tried to solve it in the following way: I tried to take the e^x to the...
  31. Y

    Determining Range of Values of P for Taut Cables

    Homework Statement Two cables are tied together at C and loaded as shown. Determine the range of values of P for which both cables remain taut. Homework Equations \Sigma F_x=0 \Sigma F_y=0The Attempt at a Solution \Sigma F_x=\frac{ 4 }{ 5 }*P-\frac{ 600 }{ 650 }*T_{AC}=0 \Sigma F_y=\frac{ 250...
  32. N

    Finding the range of values for tan theta > 1

    Homework Statement How to find the values of theta that make tan theta > 1 true? The Attempt at a Solution From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to...
  33. S

    Kernel and Range of a Linear Mapping

    Homework Statement Find the kernel and range of the following linear mapping. b) The mapping T from P^{R} to P^{R}_{2} defined by T(p(x)) = p(2) + p(1)x + p(0)x^{2} The Attempt at a Solution I'm not sure how to go about this one. Normally I would use the formula T(x) = A * v...
  34. D

    Prove that the range of h is the entire R

    Homework Statement The function h: \mathbb{R} \to \mathbb{R} is continuous on \mathbb{R} and let h(\mathbb{R})=\left\{ {h(x):x \in \mathbb{R}} \right\} be the range of h. Prove that if h(\mathbb{R}) is not bounded above and not bounded below, then h(\mathbb{R})=\mathbb{R} Homework Equations...
  35. B

    MHB Find the constants given the domain and range

    Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 6 and the range of f(x) is −3 ≤ y ≤ 5. a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9 B= C= b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1 A= D= I'm working on...
  36. A

    Why is weak force short range action?

    In Deep Down Things, an excellent book of B Schumm, at page 288, he explains that the weak force is short range because the Weak quanta have a large mass. Using de Broglie wavelength relation: Lamda = h / p, he gets a wavelength of 10 ** -18 m, and he concludes that this is the W quanta range...
  37. F

    Virtual photons and long range force carrier

    It is often said that the photon is the long range force carrier like the static force between electrons. Let's say we have two electrons galaxy apart, wouldn't the virtual particles have to travel long distances and "virtually" become real. And isn't the first sentence is wrong anyway since...
  38. B

    Water temperature range in a hot water cylinder

    I am thinking about solar water heating. The way that the system gathers heat is by moving any heated water into into the cylinder where it rises to the top and cold water is taken from the bottom of the cylinder and moved through the heating panel. Because the hot water will always rise...
  39. M

    Range in Linear Transformation

    Homework Statement L: R^3 -> R^2 L(x)=(0,0)^T What is the basis, and dim of the Range? Homework Equations Rank(A)-Nullity(A)=n The Attempt at a Solution So clearly L(x)= (0,0)^T. So the basis must be the empty space and dim is zero, right? Now, going of this same logic, Say...
  40. M

    Why does the range of an inter. vary inv. w/ the mass of its mediator?

    Greetings PF! This is my first post... I keep reading over and over again either "... so and so mediator is massive. Therefore, its interaction is of finite range" or the converse or "... mediator is massless... its interaction is of infinite range..." Makes sense intuitively (inertia?)...
  41. B

    What would happen if pressable ceramic is heated past melting range?

    I'm currently looking into some dental material mechanics. Material: Pressable ceramic powder Melting range: 900-1000°C If I were to heat it up to approx 1200°C, what would happen to it? Would it still be just molten form of the material? Student
  42. K

    Finding saturation range for an opamp?

    Homework Statement This isn't necessarily a direct homework problem that I have, but it is brought up a few times in homework problems for the chapter I'm reading through in my circuits book.. It will ask me if a certain voltage exceeds the saturation (or in other problems, at what value of...
  43. Albert1

    MHB Find Integer $n$ in Range $100$ to $1997$

    $n\in N$ $100\leq n\leq 1997$ $\dfrac{2^n+2}{n} $ also is an integer please find n
  44. totallyclone

    Finding the range of speed on a banked curve without slipping

    Homework Statement A curve of radius 60 m is banked for a design speed of 100km/h. If the coefficient of static friction is 0.30, at what range of speeds can a car safely make the turn. Homework Equations Fun=ma Ff=μsFn Fc=mV2/r The Attempt at a Solution So, when it is...
  45. S

    MHB Image, Range, and Matrix of a Linear Transformation

    Question Consider the linear transformation T(x1,x2,x3)= (2*x1 -2*x2- 4*x3 ,x1+2*x2+x3) (a) Find the image of (3, -2, 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transformation. (d) Is the transformation T onto? Justify your answer (e) Is the...
  46. A

    Domain and Range of this function

    Homework Statement What is the domain and range of the function y = \frac{2}{x^2-4} The Attempt at a Solution I'm lost, and I noticed it seems like a difference of squares so what I did is y = \frac{2}{(x-2)(x+2)}. So the x value of vertex is 0. And i subbed this into the equation...
  47. Fernando Revilla

    MHB Mr.Ask's question at Yahoo Answers (Two variables, domain and range)

    Here is the question: Here is a link to the question: Find the range and domain of function of 2 varibles:? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  48. G

    Dimensions of Matrices Range (equalities).

    Hello everyone, I’d like to find the following range equalities: Considering the following: A=B+C \\ A=B.C^T \\ A=[ B^T C^T ]^T I would like to find the function f for each equality above. .\\ dim( R(A) ) = f( R(B) , R(C) )\\ Considere that all matrices have compatible...
  49. G

    Dichroic mirror spectral range?

    Hi guys, I'm wondering about exactly if there is some sort of range that a dichroic mirror would reflect, like a green mirror would reflect between 532nm - 600nm or something. I'm pretty sure a green dichroic mirror doesn't only reflect only 532.00000 nm and not 533 nm or something. But...
  50. Fernando Revilla

    MHB Myles's question at Yahoo Answers (Domain and range)

    Here is the question: Here is a link to the question: Find the domain and range of f(x)= (e^x)/(1+2e^x)? - Yahoo! AnswersI have posted a link there to this topic so the OP can find my response.
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