Løsning af en bunke hardcore matematik/fysik opgaver
Jeg har brug for løsningen af følgende opgaver til en prøve jeg ved jeg ikke selv kan klare, håber i vil hjælpe mig med dem....1) A 20.0 lb piece of hot copper is dropped into 30.0 lb of water at 60 degree F (Fahrenheit). If the final temperature of the mixture is 85 degree F, what was the initial temperature of the copper?
2) For what values of x does the graph of f(x) = 2x³ – 4x² – 9x + 100 have a horizontal tangent?
3) A lighthouse is on a small island 8km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1.2km from P?
4) Find all functions g such that
g´(x) = 8 sin x – 6x^5 + 6x^¾
5) A wire takes the shape of the semicircle x² + y² = 1, y ≥ 0, and is thicker near its base than near the top. Find the center of mass of the wire if the linear density at any point is proportional to its distance from the line y = 1.
6) Find the work done by the force field F(x,y) = x sin j + yj on particle that moves along the parabola y = x² from (-1,1) to (2,4).
22) A 170lb man carries a 55 lb can of paint up a helical staircase that encircles a silo with a radius of 20ft. If the silo is 100 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top?
7) Find the area enclosed by the ellipse x²/a² + y²/b² = 1
8) Find the flux of the vector field F(x,y,z) = z i + y i + x k across the unit sphere x² + y² + z² = 1.
9) The temperature at a point in a ball with conductivity K is inversely proportional to the distance from the center of the ball. Find the rate of heat flow across a sphere S of a radius a with center at the center of the ball.
10) Find the orthogonal trajectories of the family of curves for x² - y² = k and y = kx³
11) Solve the initial value problem for 1 + y cos xy + (x cos xy)y´ = 0, y(2) = 0
12) Solve the equation y´´ - 6y´ + 20y = 0
13) Show that there is no vector field G such that
curl G = 2xi + 3yzj – xz²k
