Range Definition and 979 Threads

Homework Statement f(x) = x , 0 <x<1/2 1/2 , 1/2 < x <1 in this question , I am not convinced that a_ 0 = 0 for half range sine series , because i found that but , thoerically , for half rang sine series , a_ 0 must be = 0 , ,am i right ? why the value of A- 0 that i got is not = 0 ...

Hello, all! I am involved in a discussion where the topic is the heat of fusion for hydrogen. From what I've found, the heat of fusion for H2 is around 22.5 million °F and the average house fire is no more than 1,800 °F or so. So, what I'm trying to find is, how far from 0.10 grams of a...

Homework Statement Let ##f:S\to T## be a given function. Show the following statements are equivalent: a) ##f## is 1-1 b) ##f(A\cap B) = f(A) \cap f(B),\; \forall A,B \in S## c) ##f^{-1}(f(A)) = A,\; \forall A \subseteq S.## Homework Equations Definition: ##f## is 1-1 of ##A## into ##B##...

Homework Statement If f: [0,1] \rightarrow \mathbb{R} is continuous, show that (n+1) \int_0^1 x^n f(x) \mathrm{d}x is in the range of f Homework Equations (n+1) \int_0^1 x^n f(x) \mathrm{d}x=\int_0^1 (x^{n+1})' f(x) \mathrm{d}x The Attempt at a Solution I tried integration by parts, but that...

Homework Statement FIGURE 2 shows an adjustable voltage regulator using the LT1083 .The LT1083 develops a 1.25V reference voltage between the output and the adjust terminal. By placing a resistor R1 between these two terminals, a constant current is caused to flow through R1 and down through...

This is actually a straightforward question, but I'm struggling to find answers because I don't know very much about lasers. I want to use a nonlinear crystal for frequency doubling in an infrared laser (1480 nm) so that the output is half @ 740 nm. I know that nonlinear crystals like KTP are...

Homework Statement An object is thrown with velocity v from the edge of a cliff above level ground. Neglect air resistance. In order for he object to travel a maximum horizontal distance from the cliff before hitting the ground, the throw should be at an angle theta with respect to the...

So I've been working at a steel mill where we deal with billets cooling from temperatures around 1200 C to between 10-25 C. I have access to average thermal expansion coefficients over this temperature range. First question: Over a large temperature range as aforementioned am I correct in...

Hello! (Wave) How can we find what section of the cylinder $x^2+y^2=1$ corresponds to cylindrical points $(1,\theta,z)$ in the range $\theta$ in $[0,\pi]$ and $z$ in $[ -1,1]$ ? We have that the cylindrical points are of the form $(r, \theta, z)$ where the following relations hold: $$x=r...

1. Homework Statement I've found the dimension of V to be 3. According to the solutions, it seems that the basis can be written straight away, { (1,1,1,2), (1,2,-3,1), (3,4,-1,5) } (which is also the basis for the column space of the matrix), without verifying the vectors are linearly...

Hello, Sorry if this is in the incorrect forum. I've come across a discussion that has made the following argument, but I'm unable reconcile the views. I've searched within and without and have come across no answer that addresses this specific claim. To begin, from my understanding gravity...

Homework Statement A standing archer can fire an arrow from a bow with a maximum speed of 40.0 m/s. The archer rides a horse that can run at 12.0 m/s. The archer shoots an arrow at the maximum speed while riding the horse in the direction the horse is running and 10 degrees above horizontal...

Homework Statement A ball is thrown at angles 45° and 30° above the horizontal with the same initial speed. What multiple of the horizontal range at angle 30° is that at angle 45°? Homework Equations Trigonometry formula The Attempt at a Solution I think that first step is to divide the...

Homework Statement ##P=A(A^*A)^{-1}A^*## where A is a mxn real/complex matrix and ##A^*A## is invertible. ##A^*## means the conjugate transpose of A. Homework EquationsThe Attempt at a Solution Let y be in the range(A), such that ##y = Ax## for some ##x##. We can see that ##PA =...

I went through my Physics textbook where we have a chapter on Communication systems. There's a certain section where they show us the formula for the LOS max. range for a tower with a given height (say h) but I, unsatisfied with it, set out to derive it myself at home and wasn't convinced with...

Hi all, So the (hypothetical) question I have is about the range of the Earth's length of orbit (number of days) within the Sun's habitable zone which could sustain human life. I.e. what would the length of the shortest 'habitable' year be, and the longest (in days)? What would our living...

Homework Statement Find the sum of the numbers between 200 and 800 inclusive, which are multiples of 6, but not multiples of 9. Homework EquationsThe Attempt at a Solution Numbers that are multiples of 6 should be: a = 6n, n ∈ ℤ and a is any multiple of six. 200 = 6n → n1 = ##\frac{200}{6}## =...

Homework Statement A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below...

Why is "black noise" 1/(f^B) where B>2 associated with "persistence" and "long range dependence"? This book I'm reading uses the level of the Nile river as an example... I can understand what the Rescaled Range is saying but i don't get the implications w/respect to those terms or phrases. Is...

Hi! I was reading this article about the possibility of detecting removals of "double-use" fissile materials from a known reactor using an antineutrino detector deployed in a truck "that uses 20 tons or less of scintillator material (and) could be fit into a 6-meter shipping container and parked...

Hello. On a german wiki article I have found the operation principle of a range finder: https://de.wikipedia.org/wiki/Abstandsmessung_(optisch)#Lasertriangulation Here are two pictures for illustration: The Laser, the CCD sensor, and the lens are in a fixed relation to each other, inside a...

Homework Statement ##4^{x} - 7*2^{(x-3)/2} = 2^{-x} ## Set of real solutions of this equation is found in which following range: a) (-9, -2) b) (0, 3) c) (-3, 0] d) (3, 7] Homework Equations 3. The Attempt at a Solution [/B] I simplified to ##2^{3x} - 7*2^{(3x - 3)/2} = 1## ##2^{3x} -...

I think I am in a misconception concerning laser beams: Even the best lasers have a small line width. The spectral line is gauss-shaped. therefore the wave in position-pace is also a gauss-shaped wave packet, that travels with a certain group velocity. But this gauss shaped wave packet has a...

Homework Statement A random sample of size n = 81 is taken from an infinite population with the mean μ = 128 and the standard deviation σ = 6.3. With what probability can we assert that the value we obtain for the sample mean X will fall between 126.6 and 129.4?The Attempt at a Solution z =...

Homework Statement Given a Uniform Distribution (0,1) and Z = X/Y Find F(z) and f(z) Homework EquationsThe Attempt at a Solution So I'm just trying to make sure i have the range correct on this one... I'm honestly lost from beginning to end with it. R(z) = {0,∞} because as y is very small, Z...

Homework Statement Let p: x and y satisfy inequality x2 + y2 + 4x - 8y + c < 0 where c is real number q: x and y satisfy x - y + 8 > 0 ; 4x + 3y - 24 < 0 ; y < 0 Find the range of c so that: a. p is sufficient condition for q b. p is necessary condition for q Homework Equations Circle...

I am looking to find a 5v to ≈70v dc-dc converter in the 1w range or the equivalent transformer + diodes. This is for a bio stimulation device and I need a high voltage and low amperage. However, not having spent years researching and buying electrical components, I'm a little uncertain where...

Homework Statement If we neglect air resistance, then the range of a ball (or any projectile) shot at an angle θ with respect to the x-axis and with an initial velocity v0, is given by R(θ)=v_0^2/g sin(2θ) for 0 ≤ θ ≤ π/2 where g is the acceleration due to gravity (9.8 meters per second per...

Homework Statement Homework Equations kinematics. a=F/m The Attempt at a Solution 100cos(70)=342 100sin(70)=393.7 X=1/2(-9.8)t^2+100t; t=0. t=20.4

Here is the problem: If -1 is a range value for the function f(x) = -6x + 11, find the domain value. thank you for your help

Homework Statement At 0.5 of its maximum height, the speed of a projectile is 0.75 of its initial speed. What was its launch angle? Homework Equations Not sure here, but: v^2 - vo^2 = 2as [maximum height] Ay = Asin(theta) [y-component] The Attempt at a Solution I didn't get very far...

Homework Statement [/B] The problem on where the photon will hit a screen, after passing through a single horizontal slit. I know the wavelength, slit width, magnitude of momentum of incoming photon (calculated), and distance between screen and slit. Homework Equations I just don't...

Homework Statement Let X∼Geometric(1/3), and let Y=|X−5|. Find the range and PMF of Y. Homework Equations Px(k) = p(1-p)^(k-1) for x=1,2,3... 3. My attempt at a solution I set up the PMF for Px Px(k) = 1/3(2/3)^(k-1) for k = 1,2,3,... However I don't know how to convert this to Y

Homework Statement Uploaded Homework Equations x(t)=xo+v0xT+1/2axt^2 The Attempt at a Solution (2Vo)costheta(t)=R, How would I get rid of T?

Homework Statement Find the domain and range of the following function: f(x, y) = ln(x+y) Homework EquationsThe Attempt at a Solution I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive...

1. Homework Statement The problem and all known information is attached. Homework Equations The kinematic equations are attached. The Attempt at a Solution My attempt is attached. I did part (a), (b), and (c), right. How do I do part (d)? I tried distance/ time .

Hello All! I was wondering about how to find the range of motion of specific joints with the only given "hints" being degrees and time (in seconds) of the ankle, hip, and knee joints. Also a scatter plot. I am aware that I have to use the degrees of each joint (perhaps finding , however I do not...

Homework Statement question: State two different functions that have same range but different domain. Then tell me what is the range of those two functions. The attempt at a solution Y = x/2 Y= x/2 +1 I don't know if that is correct or not. Any suggestion will help.

Homework Statement Let T:V→V be a linear operator on a vector space V over C: (a) Give an example of an operator T:C^2→C^2 such that R(T)∩N(T)={0} but T is not a projection (b) Find a formula for a linear operator T:C^3→C^3 over C such that T is a projection with R(T)=span{(1,1,1)} and...

Homework Statement So I'm currently modifying an example Symbolic Regression program that uses genetic programming, a type of evolutionary algorithm. I'm using the python deap library. Not sure if anyone on here is familiar with it, but I think that the error is more general to a misuse of...

Sources A and B are on the horizontal x-axis and both emit a long-range radio wave of wavelength 400m, with the phase of emission from A ahead of that from source B by 90 degrees. The distance r(A) from Source A to the detector (D) in the y-axis is greater than the distance of r(B) by 100m. What...

Hey everyone... so I understand that an alpha particle, being a helium nucleus, is quite a large particle compared to, for example, a beta particle. Due to this, it will encounter a lot more collisions and impart its momentum to other particles of air at a much more rapid rate. Is there...

Find the Range of Uniform convergence of $ \zeta\left(x\right) = \sum_{n=1}^{\infty}\frac{1}{{n}^{x}} $ Using the Weierstrass-M test, I get this converges for $ 1 \lt x \lt \infty $ But the book's answer is $ 1 \lt s \le x \lt \infty $? I have scoured the book but can't see why they say it...

Hi, hope this is not too dumb: Is it possible to create paint or clothes whose color is outside of the visible range (of course, we need to then store them in receptacles within the visible range )? Is a substance/object's "natural color" (I guess this is the color in which it either appears in...

Hi all, the question which I'd like to share is the following: if you look at the formal theory of any random optics book for FP interferometer you will get to the formula of the FSR (Free Spectral Range), defined as "The wavelength separation between adjacent transmission peaks" (Wikipedia)...

Homework Statement A locust jumps at an angle of 43.8 degrees and lands 1.0 m from where it jumped. If it jumps with the same initial speed at an angle of 62.4 degrees, how far would it jump then? X-component knowns: Initial velocity = v(cos(43.8)) displacement = 1m angle = 43.8 degrees...

Homework Statement If one can approximate NOvA detectors being built out of hundreds of "sandwiches" or PVC plastic of 1cm thickness and a "plane" of oil of 5.6 cm, what is the range of muon of energy 200MeV, 500MeV, 1GeV, and 1.8GeV in the detector? Homework Equations \frac{dE}{dρ*x} =...

Homework Statement Let G be any group and a in G, define f: Z → G by f(n) = a^n Apply any isomorphism theorem to show that range of f is isomorphic to a quotient group of Z Homework EquationsThe Attempt at a Solution The range of f is a^n , then quotient group of Z is Z/nZ Apply the first...

I need to do this graph "graphic locking range and stability laser" that equations are used to make the graph thanks

Homework Statement A greasy spud is launched off of the top of an infinitely large frictionless wedge. The angle that the wedge slopes down at is 30 degrees. Find the launch angle that maximizes the horizontal range of the spud.Homework Equations [/B] x = x0 + vxt + (1/2)at2 The Attempt at a...