2) f = ((1/d.) + (1/d))!. Assume that d; is constant and d(d.)/dt = v, find...
2. A camera has a single converging lens with a fixed focal length f. (a) How far should the lens be from the film in order to focus an object that is infinitely far away (namely the incoming light rays are parallel with the principal axis of the system) (b) How far should the lens be from the film to focus an object at a distance of 2f in front of the lens? (c) What is the magnification of the...
An object of height h approaches a concave mirror of focal length f along its axis with constant speed v, from an initial distance s0 >> R away. Determine the rate of change of the image height, dy'/dt, as a function of these variables and time. (Suggestion: differentiate the lens and magnification equations implicitly, and work with s, s′, f as long as possible to get dy′/dt in terms of h, s, s′, f and ds/dt first. Then eliminate s′...
Consider the curve y = f(x) with f(x) = 2+ | V+ – 1 dt. Find the value of X > 1 so that the length of the curve between (1, 2) and (x, f(X)) is 12 Enter the value of X as a decimal that is correct to at least one decimal place.
A camera with a lens diameter D = 3 mm and a focal length of f = 4.25 mm. Assume the wavelength of light is 500 nm and the sensor in the camera is 5 mm x 5 mm and that each pixel has a size of 2μm x 2μm. A) If a vertical meter stick is located 5m from the camera and the image of the meter stick is in focus, how far from the lens is the sensor?...
Find an expression for the rate of adsorption (d theta/dt)_ads, and an expression for the rate of desorption (d theta/dt)_des, where k_a and k_d are the adsorption and desorption rate constants, respectively. Using your result found in Step 2 above, show that at equilibrium theta = Kp/Kp + 1 Where K is the equilibrium constant for the adsorption/desorption process. FYI, this is called the Langmuir isotherm.
Question 3 (2 points) This assignment is set up for sequential assessment. Complete each question and submit the answer before moving on to the next question. Correct answers for each question will be made available once the maximum number of attempts have been made for each submission. Refraction - CONVERGING and DIVERGING Lenses In these problems, you will solve for the object distance do, or focal length f, or the type of lens. Pay attention to the SIGN Convention. The...
4. (a) Show that mi = F - mw x W x D) - 2mw xi where F is the total force acting on an object of mass m as measured by an inertial observer and ï is the acceleration of the object measured in a frame rotating with constant angular velocity w. Explain briefly the significance of the centrifugal force –mw (w xr) and the Coriolis force -2mw xi. You may use the following relationship: da/dt = a +w...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
Show all steps please.
b. ASSUME the Differential Equation: dx dt :-(W2)x. 1. SOLVE. That is, determine a function x = f(t) which satisfies the above. 2. CHECK. Show that your function to the above dif. eg. is, indeed, a solution.
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint: (-1)" as ds (b) Use the above formula to compute L[t? cost].
dn (a) Show that L[i" f(t)] = (-1)" (t) for any positive integer n 2 1 dsn a d K(s, t)f(t) dt / ) est = tne-8t and assume that K(s, t)f(t) dt. Hint:...