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.
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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)\}...
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...
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 ...
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.
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...
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##...
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?
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...
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...
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.
$$ f(x)= x + 5 + \frac {1}{x-5}$$
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?
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...
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))...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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} +...
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...
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...
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...
The frequency chart below shows the cumulative number of Ms. Hernandez's science students
whose test scores fell within certain score ranges All test scores are whole numbers.
Cumulative number Score range of students
$\begin{array}{lll}
&65-70& 12\\
&65-80& 13\\
&65-90& 19\\
&65-100& 21...
[Mentor Note -- Thread moved from the technical forums, so no Homework Template is shown]
Hi all,
Recently I 'did' (a virtual lab) a drag laboraty experiment that used a wind tunnel to measure drag coefficient of 3 different shapes (cylinder, airfoil, triangular prism) and I'm not convinced...
I get one of the ranges by calculating:
sin(90°) = 1
d·sin(θ) = d × 1 = d = n·λ
d = 6 × 550-nm = 3,300 nm = 3.3 microns = 3.3 × 10⁻⁶ m
But, how can I get the other range of 2.2 × 10⁻⁶ m
Could anyone explain it to me? Thanks
Consider only the Earth-Moon system, where both the Earth and Moon are spheres. A horizontal line joins the centres of the Earth and Moon. Consider a point P that lies on the surface of the Earth. The line joining P and the centre of the Earth meets the horizontal line joining the centres of the...
I sketch a diagram for the problem and show it to the right.
My approach is going to be along the following lines : (1) Use the equation of motion in the ##x## direction to express the total time of flight ##T## as a function of the range and initial angle ##T = T(R, \theta_0)##. (2) Plug this...
Hi. I have a collection of points in 3D space. I'm using MATLAB to find all pairs of points within a certain range from one another. Right now I'm using rangesearch(X,X,r), where X is the collection of points and r is the range.
These points are the locations of atoms and I am attempting to...
At 02:08, this video shows a function that grows from exactly 0 at input x = 0+, up to 1 at ##x=\infty##.
Its value and all its derivatives approach 0 as x -> 0. The function is Exp(-1 / x^2).
www.youtube.com/watch?v=Wwg_15a0DJo&t=146s
Q. : What function would have its value and all...
Hi,
Here is the question.
Answer given is d. But i don't understand how is that computed? I am working on this question. Meanwhile any member knowing the correct answer may help me in finding out correct answer.
Hey Everyone, my physics teacher has assigned us a task which involves predicting the range of a ball falling down an inclined plane into a free-fall, the equation for the final velocity of the ball down the ramp, accounting for rotational velocity has been provided, this is the initial velocity...
First and foremost, I've studied voltmeters and ammeters on my own, and online there aren't many resources to do so... forgive me in advance for eventual silly questions/doubts :)
I managed to calculate(intuitively) a tension of ##30.0V## per resistor, with basic procedures.
However, I'm...
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...
Scary and Cool e-wheel tech:
- upto 45mph
- upto 128 miles driving range (170 lb person at 20mph)
- battery charge 8hrs or with dual chargers 4 hrs
- $2850
https://www.ewheels.com/product/new-veteran-sherman-18-100v-3200wh-battery-2500w-motor-1000-deposit/?affiliates=152
on youtube:
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.