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Suppose that f:D+Tis a surjection and let to € T. Define Y =Z-F {{to}) CZ. (1) Show that the function g:Y+T - {to}, given by g(t)= f(t) for t e Y, is a well- defined function. (2) Show that g is a surjection.
Consider a mass oscillating on a horizontal spring on a frictionless surface about the origin If at t = 0 the mass is moving through the origin in the positive x direction, which of the following could be the v(t) for the mass? vi m/s) vi m/s) tis) 0.5 101.5 2.0 2.0 t( s) ti s) 2.0 ti s) tf s) 0.51.0 1.52 -2
7) Let f(t) = u(t - Ta) - ut - 27.) a) Sketch f(t) with proper amplitude vs. time labels b) Now rewrite f(t) in terms of (8) "delta" functions 8) Suppose F(s) *+1) What is the value of f(t) at time t = 0-?
Consider the following. Tis the reflection through the origin in R2: T(x, y) = (-x, -y), v = (2,5). (a) Find the standard matrix A for the linear transformation T. A= 1 (b) Use A to find the image of the vector v. T(v) = (c) Sketch the graph of v and its image. у 6 у 6 V 5: 5 41 4 3 3 T(v) 2 2 11 1 X 1 -6 -5 -4 -3 -2 -1 -A 2...
Let A, B be an n × n matrices. Prove that [10%] ABt = B tA t
Find L(f) if f (t) equals ta sin (2t). Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin (2 * x) or (a - b)/(1+n). Use an asterisk, *, to indicate multiplication. For example, 2* f (x), a* * (x+b) * (c*x+d), b* tan (a * ) or ea*r) * b. L (f) (s) QC
The line of action of force F passes through point B. Find the moment due to force F about axis AC, given: F̄ = <10, 70, -10> lbs, AX = 6 ft, AY = 3 ft, AZ = 7 ft, BX = 7 ft, BY= 5 ft, BZ = 9 ft, CX = 5 ft, CY = 5 ft, CZ = 1 ft MAC = lb·ft M̄AC= < , , > lb·ft Find the moment about points A, B, C,...
1 (15 poie) Acconding so Newson's law of ceeling if n obiect t sonee Ta innonel in a medm having the comstat smpeae M. then the ate of chnge of Ts ppol to the derece of temperatre M T This gives the dfferentil ouution M-T dr (a) Solve the diferential eqtion for 7 (b) A thermometer reading 100 F is placed in a medium having a comstant tmpee of 70'F. Ater 6 min the thermometer reads 80F. What is the...
Force F = 1.99 N i -3.18 N k acts on a pebble with position vector T = 0.48 m J -2.20 m k relative to the origin What is the resulting torque on the pebble about the origin? Enter i, j, and k component. What is the resulting torque on the pebble about the point (2.12 m, 0, -3.32 m)? Enter i, j, and k component.