Maximum Definition and 1000 Threads

Homework Statement An object is moving in the xy-plane according to the equations x(t) = 3sin(3t) and y(t) = 4cos(3t). What is the maximum magnitude of the particle's acceleration? 1) 5 m/s22) 15 m/s23) 30 m/s24) 36 m/s2 [the accepted answer]5) 45 m/s2 Homework Equations x(t) =...

Homework Statement Homework Equations Torque = Force x Distance Shear stress = Force/Area 3. The Attempt at a Solution I know how to do this question as I've seen the mark scheme. However, initially I did it wrong. What I did was as follows: Torque = Force x Distance therefore...

Homework Statement Magna is traveling at 110 kph, and realizes Commodore in front of him is traveling at 80kph. To avoid a collision, what is the max speed the Magna can have as it reaches the commodore? Homework EquationsThe Attempt at a Solution I am not sure how to approach this.

Homework Statement Hi everybody! Here is another problem about contraction and Banach fixed-point theorem that I don't get: The function ƒ: C([0,½]) → C([0,½]) is defined by: [f(x)](t) := 1 + \int_{0}^{t} x(s) ds ∀ t∈[0,\frac{1}{2}]. Is ƒ a contraction with respect to the norm || ⋅ ||∞? If...

$f(x)=12x-32+24\sqrt {9-3x}, x\leq 3$ find $max f(x)$

Homework Statement Hi everybody! I have a math problem to solve, I'd like to check if I understand well the Banach fixed-point theorem in the case of Euclidean norm and how to deal with maximum norm. Check if the following functions ƒ: ℝ2 → ℝ2 are strictly contractive in relation to the given...

Homework Statement A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy? Homework Equations Δ[/B]dv = v1Δt + 1/2aΔt2The Attempt at a Solution [/B] Calculate time: Δt = 2.3 m/s / 9.8m/s2 = 0.23 s Now...

Homework Statement Light of wavelength λ = 535 nm shines through two narrow slits which are 670 μm apart. What is the maximum number of interference maxima which could conceivably be observed (assuming that diffraction minima do not extinguish them and the screen is arbitrarily large)?Your...

Homework Statement Consider a closed rectangular box with a square base of side 3cm and height 5cm. If the side is measured with an error at most 0.02cm and the height is measured with an error at most 0.01cm, use differentials to estimate the maximum possible error in computing the volume of...

Homework Statement A student siphons water over a 8.5 m high wall at sea level. She then climbs to the summit of a mountain (elevation 4390 m , atmospheric pressure =58.5 kPa) and attempts the same experiment. Comment on her prospects for success. Homework Equations Bernoulli's equation...

Homework Statement If an engine operates between 250°C and 25°C, what is its maximum thermodynamic efficiency?Homework Equations Ec=1-Tc/Th The Attempt at a Solution 1-25/250 =90% or 1-(25+273)/(250+273) =43% In this question,which one should I use K or ºC ? thank you

Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...

Homework Statement If w = 74 kN/m , determine the absolute maximum bending stress in the beam in MPa. Homework Equations I'm not too sure how to go about my calculations. Please help! The Attempt at a Solution I = [(1/12)*(200*256^3)] - [(1/12)*(192*250^3)] = 29.62*10^6 F = 74*24*1000? [/B]

Homework Statement In the very long wire conductor as shown on the picture , flows a current magnitude I. Near the wire there is a square shaped contour , with length a ,which rotates around its axis a constant angular velocity. Axis of square contour and a straight line conductor are...

Homework Statement A spring with a spring constant of 5.0 N/m has a 0.25 kg box attached to one end such that the box is hanging down from the string at rest. The box is then pulled down another 14 cm from its rest position. Calculate the maximum height, the maximum speed, and the maximum...

Homework Statement Let f: ℝ→ℝ be continuous function such that f(x) approaches 0 when x---> -∞ and f(0)=2. In addition, f is decreasing when x≥3. Prove f has a maximum (greatest value) in ℝ. Homework Equations Theorem: If function f is continuous on a closed interval [a, b], then f has maximum...

Planck length is ~ 1.6\times 10^{-35} meters. Does this mean that this may be a lower limit on meaningful wavelength and therefore upper limit on energy?

Homework Statement Hi everybody! It's kind of the first time that I try to solve this type of problem, so I'd like to see what you guys think about it and if I am heading in the right direction: Examine if the set {(x2 + x + 1)/(x2 + 1) : x∈ℝ} has a maximum and/or a minimum, and calculate...

If I had a turbine roughly 2 inches in diameter (4-5 blades), where the housing for the blades is about one inch wide (meaning the axle is 1"), what would be the estimated voltage I could produce if I were to use my lung power in one complete exhale through the input? That is, if there were...

If both $a$ and $\sqrt{a^2+204a}$ are positive integers, find the maximum value of $a$.

this should be easy. suppose i have a very large spaceship holding a tremendous volume of air at 14.7psi with a density of .0023769 slug/ft^3. i put a hole in the side of my spaceship that is 6" in diameter which vents to the vacuum of outer space. what is the velocity of the escaping air? i did...

I have a hydraulic cylinder that can lift up to 3 metric tons and I want to attach it to an arm. The bracket is in a rigid U shape (right angles only, no round corners), with a round pin going through it. At first I thought it'd be a simple bending stress calculation, but there is a giant hole...

Homework Statement Part 1: I've worked out part 1 already. The answer is 4650m/s^2 A ball travels vertically downwards until it hits a concrete floor with speed 22.7-m/s. It then bounces vertically upwards at 10.8-m/s. Examination of a high speed video shows that the collision took 7.2-ms...

Homework Statement Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation? Homework Equations |ET|≤ (K(b-a)^3)/(12n^2) The Attempt at a Solution So I know how to find the error of the trapezoidal...

Homework Statement A capacitor with two parallel plates of area 88.5 cm2 and nylon (dielectric strength 14 MV/m) inserted between them breaks down when a potential difference of 5.80 kV is applied. What is the maximum charge the plates will hold when the nylon is removed and the space filled...

Homework Statement 2 adjacent sides of a parallelogram measure 15ft and 10ft w/ max errors of ±0.1ft angle is 45° w/ max error of ±0.5° What is the maximum error in the calculated value of the area or the parallelogram? Homework Equations A = area = xysinθThe Attempt at a Solution x = 15ft...

dear all , My question is what is the maximum load taken by beam of UB 610 x 229 x 125Kg/m for a span of 5 mtr? its supported on both side by anchoring on concrete beam.

What is the Largest possible value of n such that there is a multiple of 4 less than n^2 but greater than n^2 + 2016/n^2 ?

Finding the maximum kinetic energy in a simple parabolic projectile motion requires us to find the maximum velocity. I know that the velocity will be maximum at two points, the point of projection and point of return. So there must be two points where the kinetic energy is maximum. But my...

Hi All, What is the maximum number of layers of immiscible fluids in nature. Is seems intuitive to me that this limit exists. for the sake of definiteness, let' s consider usual laboratory"s condition of temperature and pressure. Best wishes, DaTario

I read this in Gordon's book "Structures or why things don't fall down". I read that the maximum length of lintel should be a maximum of 2.5 metres. Why? What if its more?

Homework Statement H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s. The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground. Homework Equations The...

Homework Statement The binding energy of the ion H2+ is -16.3 eV at the equilibrium separation 0.106 nm. The Hellman-Feynman theorem states taht the force between the nuclei in a molecule can be calculated from the electrostatic repulsion between the nuclei and the electrostatic attraction of...

Is the maximum bending moment and maximum shear stress an absolute value? For example, when drawing out a bending moment diagram say if I get -400 kNm at one point and 300 kNm at a different point. If these values are the maximum/minimum points on my diagram would 400 kNm be considered as a...

I recently plotted a piecewise function: Plot[Piecewise[{{1 - Exp[-.002*t], 0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)], 120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}] I then defined the function which I am calling q[t_] as follows: q[t_] := Piecewise[{{1 -...

Homework Statement Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with each other and emit their beams uniformly in a horizontal plane. A receiver is taken 0.500...

In a --specifically uniform electric field-- (I may be wrong here) my understanding is that the dipoles will result in no net dipole force (due to cancelling out) but there will actually be a net torque experienced about the center. This torque will be trying to turn the dipole so the moment, p...

Homework Statement A German U2 rocket from WW2 had a range of 300km, reaching a maximum height of 100km. Determine the rocket's maximum intial velocity. X component variables: di=0, df=300, a=0, time=9, vi=? Y component variables: a=-9.8, vf=0, vi=?, di=0, df=100, displacement=100, Note: For...

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...

Homework Statement Let X1, X2,...Xn be a random sample from pdf, f(x|θ) = θx-2 where 0 < θ ≤ x < ∞ Find the MLE of θMy attempt: Likelihood fxn: L(θ|x) = ∏θx-2 = θn∏ θx-2 And to find MLE, I take Log of that function and partial derivative (w.r.t θ, of log L(θ|x) and set that = 0, and get...

Hi guys, The imagine the picture attached is a cross section of a cylinder. How would I work out the maximum amount of pressure this can be exposed to before the metal shears off at the location labelled "2mm thick"? Lets say the following material is used: T6 Aluminium Ultimate Tensile...

Hello! (Wave) We are given the function $g: \mathbb{R}^{2016} \to \mathbb{R}$ with $g(y)=\sqrt{10 y_1^2 + 10^2 y_2^2+ \dots+ 10^{2016} y_{2016}^2} where y=(y_1, \dots, y_{2016})$. I have found that the maximum of this function over the set $\{ y=(y_1, \dots, y_{2016}) \in \mathbb{R}^{2016}...

Homework Statement Homework Equations number of alpha hydrogens= number of no bond resonating structures The Attempt at a Solution option 1: 3 option 2: 6 option 3: 8 option 4: 9 So the answer should be 4, right?

Homework Statement 2 boxes containing the same number of moles of 2 ideal identical gases with the same adiabatic index (this is given as gamma), at the same initial temperature Ti but with different volumes, V1 and V2 are brought together. Find the maximum mechanical work that can be obtained...

Homework Statement Find the maximal power on resistor R. Homework Equations [/B] The Attempt at a Solution I used Thevenin theorem. I found that Z_t=5+j10 , and U_t= 10-j10. The maximum power happens in this case when $$R=|Z_t| = 5 \sqrt{5}$$ , and I get that P=6.18, while the answer is...

Hi - Can anyone help me out with a question. The answer seems obvious, but maybe so obvious that I'm jumping to wrong conclusions! Just been reading Guy Martin's book "When your dead, your dead" (good read by the way) and one of his stories is about breaking the world speed record for a wall of...

Homework Statement Determine the maximum kinetic energy of a uniform rod of mass 0.5Kg and length 0.75 that has an angular displacement of 5 degrees. Homework Equations y = rsin (x) where x is the angular displacement The Attempt at a Solution Using conservation of energy ETotal = EMech +...

I would like to know the maximum voltage that a metal sphere can hold from applying negative charge to it. My thoughts are that the maximum voltage is the breakdown voltage of the surrounding medium (air in this case). I assume that at that voltage, electrons would arc from the sphere to the...

Homework Statement A 5V battery rated at 1800mAh has a soucre resistance of 10 Ohms. What is the maximum power that can be extracted from the battery? Homework EquationsThe Attempt at a Solution I understand that had the battery not had any source resistance then the power out would have been...

Homework Statement After happily working my way through the earlier parts of this question, I'm pretty much at the end of my tether with the last two parts. Please find the diagram attached: A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a...