# 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. ### State the domain and range for a given function

Attempt : Let me copy and paste the problem as it appeared in the text. Please note that the given problem appears in part (b), which I have underlined in red ink in this way ##\color{red}{\rule{50pt}{1pt}}## Clearly the domain is ##\boxed{\mathscr{D}\{f(x)\}...
2. ### Find the domain and the range of ##f-3g##

Am refreshing on this, For the domain my approach is as follows, ##(f-3g)x = f(x)-3g(x)## ##=x-3-3\sqrt{x}##. The domain of ##f-3g## is given by ##f∩g = [{x: x ≥0}]## We have ##y= x-3-3\sqrt{x}=(\sqrt x-\frac{3}{2})^2-\dfrac{21}{4}##. The least value is given by...

4. ### To find the range of a given ##\sin## function

Attempt : The domain of the function ##\sin(3x^2+1)## is clearly ##x\in (-\infty, +\infty)##. The values of ##x## go into all quadrants where the ##\sin## curve is positive and negative. Hence the range of the function ...
5. ### How to find range inside square root

Hi, so I know how to find domain but how about range in this problem? I don't understand the way he did it? I always get answers wrong when it comes to range.
6. ### Is it possible to find a number x such that 5 < x < 1?

I don't think it is possible, but can someone please explain why? Many thanks!
7. ### Find the range of values of a + b

The answer is ##a+b \leq \frac{1}{8}## but I don't know how to get it. Tangent to the x-axis means the vertex is at the x-axis so the y coordinate of the vertex = 0 $$y=-\frac{1}{8}x^2+ax+b$$ $$y'=0$$ $$-\frac{1}{4}x+a=0$$ $$x=4a \rightarrow y=2a^2+b$$ So $$2a^2+b=0$$ $$b=-2a^2$$ ##y## will...
8. ### Finding the launch angle for a projectile if the range is 3x the max height of the trajectory

For this problem, The solution is, I don't understand how they got from ##\frac {sin^2\theta_i}{sin2\theta} ## to ##\frac{tan\theta_i}{2}##. Would somebody please show me the immediate steps? I also don't understand is why they say the ignore the trivial case where ##\theta_i = 0~rad##...
9. ### Stopping power and projected range for FLUKA code

How do I calculate the stopping power or projected range for aluminum in Fulka. And in which output file is this data located?How can I edit a change in the input file?
10. ### A Do moon phases affect weighing precision on the microgram range?

Hi, I'm looking to improve the precision of a system over a several hour cycle of operation of +50°C operation. The mass is ~11g and is suspended below the balance via a factory provided point. The "sample" is enclosed within a large borosilicate flask 150mm dia x 450 mm height that is trace...
11. ### What are the implied domain and range of cos(arctan(x))?

Hi everyone I have the solution to this question, but I'm not sure I understand it. Why is the domain of the composite function and not [0, pi]? Is it because tan^-1 (0 and R+) will always give a value between (-pi/2, pi/2)? I.e. the domain of the composite function refers to x. Is 0...
12. ### Is it possible to find the range of this function?

I can get the domain, but getting the range seems impossible. Domain $$x-5=0$$ $$x =5$$ $$\therefore x \in (- \infty ,5) \cup (5, + \infty)$$ Range  I can simplify the function to the form below, but I don't know how to go from there. $$f(x)= x + 5 + \frac {1}{x-5}$$
13. ### Sound Varieties: Rules for Varying Ranges

It seems that a sound (eg aa, ah, ih...) has a variable range of sound.I know that the before is affected by the follow, eg ''d" in do and did are different. Are there any other rules for the variation range?
14. ### I How azimutal quantum number got its range value

it is known that azimutal quantum number takes the values from 0 to n-1. how did they find it ?
15. ### Solving Quadratics to Find the Interquartile Range

I do not have solution for this; looking forward to your insight. $$F_{X}=\int_0^m \dfrac{2}{25} (5-x)dx$$ ... ending up with $$\dfrac{2}{25} (5m-\dfrac{m^2}{2})=\dfrac{1}{4}$$ and $$\dfrac{2}{25} (5m-\dfrac{m^2}{2})=\dfrac{3}{4}$$ we shall end up with two quadratic equations. Solving them...
16. ### F(x)=(x+1)^0.5, h(x)=x^2+3, what is the range of f(h(x))?

Hi everyone I have solutions to this problem, but still don't understand them. I thought the range of h(x) was [3, \infty). Wouldn't this make the domain of f(h(x)) also [3, infinity)? If this is correct, shouldn't the range of f(h(x)) be [13^0.5, infinity)? Below is a graph of f(h(x))...
17. ### For what range of x is (e^x-1)/2x=0.5 correct to 15 decimal digits?

We have ex=1 + x + x2/2 + x3/3! + ... ex - 1 = x + x2/2 + x3/3! + ... (ex - 1)/(2x) = 0.5 + x/4 + x2/(2⋅3!) + ... ((ex - 1)/(2x)) - 0.5 = + x/4 + x2/(2⋅3!) + ... After this, I am unsure of how to proceed to find my error any help would be appreciated thank you. Would we just be trying to...
18. ### Needing some help about time of flight of a launched ball/horiz range

The parts in bold are the questions and also highlights of my attempts at the solutions for each number and letter portion of the question. I attached a word doc to show the diagram and it also has the same questions ;) 4) A launcher is setup at the edge of a table as shown below: (I attached...
19. ### A Range of Difference: Bounds for Length of Stay

Ok, so I'm given hotel data :{Arrival Date, Departure Date}, each in terms of nth day of the year , and I want to estimate whether the range/difference, aka, the length of stay is below a bound. Say a week ( 7 days) for definiteness. I'm thinking of using either the distribution of the range...
20. ### Possible values an expression can take : ##\dfrac{x^2-x-6}{x-3}##

Problem statement : Let me copy and paste the problem as it appears in the text : Attempt 1 (from text) : The book and me independently could solve this problem. I copy and paste the solution from the book below. Attempt 2 (my own) : The problem should afford a solution using the second idea...
21. ### A rocket's maximum range

the first question was At what launch angle will the rocket achieve its maximum range? and i found the right answer it was 42.186deg. but now i don't understand what I am doing wrong i put v0,a,g in the equation of range and its wrong and i don't undertand why here is what i try...
22. ### B Gravity and projectile range

Calculated maximum range of arrow at 45 degrees with initial velocity measured horizontally is of course reduced by air resistance. BUT initial velocity at 45 is reduced because propulsive force is constant and gravity reduces velocity by about 3m/sec. So not all distance loss is drag. Authors...
23. ### A Recalculate a range by variable 'Median'?

Hello everyone :) I'm struggling to wrap my head around recalculating a data set based upon median. The data set represents a fixed distribution pattern of population to income group. There is no data available for 'population to income group' at differing medians, hence we accept the...
24. ### Max initial angle so that the projectile range keeps increasing

Can I get a hint on how to start with this problem ? Thanks in advance I can't really think of anything...
25. ### Codomain and Range of Linear Transformation

Standard matrix for T is: $$P=\begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & -1 \end{bmatrix}$$ (i) Since matrix P is already in reduced row echelon form and each row has a pivot point, ##T## is onto mapping of ##\mathbb R^3 \rightarrow \mathbb R^2## (ii) Since there is free variable in matrix P, T is...
26. M

### Using ffmpeg to extract every n frames from a given range of an m2ts video

Hi PF! I have a video titled myvideo.m2ts that is 2 hours long at 60 fps. I would like to extract every second from 54 min to 55 min via ffmpeg. It looks like I would execute something similar to this: ffmpeg -i myvideo.m2ts -r 1 output_%04d.png except this will run the entire video. Any help...
27. ### Maximize Range of Projectile Launched from Cliff

I found the function of the range of the projectile launched from a cliff. R = vcos(x)((vsin(x))+sqrt(v^2sin^2(x)+2gh))/g I stopped here because I feel like taking the derivative and optimizing for maximum would spiral out of control. Is there another approach to this problem?
28. ### The correct way to write the range of a linear transformation

We have a transformation ##T : V_2 \to V_2## such that: $$T (x,y)= (x,x)$$ Prove that the transformation is linear and find its range. We can prove that the transformation is Linear quite easily. But the range ##T(V_2)## is the the line ##y=x## in a two dimensional (geometrically) space...
29. ### Amplify ferrite core solenoid electromagnetic range

Hello all, I'm playing around with a PIC + LCC Tank to send - at a 5MHz frecuency - some numeric data via BPSK. The receiver is a loop antenna placed in the ground. The sender antena (L) is a ferrite core solenoid (N=10). As having a larger core, or increasing the Number of coils around the...
30. ### Find the range of ##k## for which ##\omega## is imaginary

Out of the given information I see no way of solving neither of the two sections. So I did some reading and it turns out that the given relation is a solution of the following function (I won't prove it here) \epsilon (k, \omega) = 1 - \frac 1 2 \left[ \frac{\omega_p^2}{(\omega-kv_0)^2} +...
31. ### Operating Range Clarification

I have this doubt suppose a i have a board (B1) which operates in the range from 36V - 90V and the nominal operating range is 72V. I have another requirement (R1) with operating range 36V - 56V and with nominal operating range of 48V but functionally same as B1. So, can i use the board B1 for R1...
32. ### B Beam of air: Extending the range of a fan

If one Googles for "laminar flow nozzle", one finds many interesting tutorials on creating a nozzle for a laminar water jet; a stream of water that remains coherent over a long distance without breaking up. These typically consist of a large-diameter tube with regions inside (like sponges and...
33. ### Relationship between horizontal range and angle of launch

I would like to conduct an experiment asking the question "how does the angle at which a projectile is launched vary with respect to the horizontal range it covers?" Ultimately, I'd like to prove that the horizontal range is directly proportional to sin(2(theta)). This will be done with the aid...

50. ### Ipho 1987, thermodynamics problem: Moist air ascending over a mountain range

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.