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The function f(x,y)={x^2y/x^4+y^2 (x,y) is not=0 0, (x,y)=0 is not continuous at (0,0)
f(x)=x2 from x=0 to x=5
A rectangular plate 12 ft long and 8 ft wide is submerged vertically with the longer edge in the surface of the water. Find the force on one side of the plate.
A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.
(a). assuming that the tank is half-filled with water.
Assume that 10 ft-lb of work is required to stretch a spring 1 ft beyond its natural length. What is the spring constant?
A spring exerts a force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m beyond its natural length?
A flat rectangular plate is submerged horizontally in water. (a) Find the force (in lb) and the pressure (in lb/ft²) on the top surface of the plate if its area is 100 ft² and the surface is at a depth of 5 ft.
(b) Find the force (in N) and the pressure (in Pa) on the top surface of the plate if its area is 25 m² and the surface is at a depth of 10 m.
Find the volume of the solid obtained by rotating the region enclosed by 𝑥=√6sin(𝑦)
and 𝑥=0
about the 𝑦-
axis over the interval 0≤𝑦≤𝜋.
The base of the solid is the triangle enclosed by𝑥+𝑦=1,
the𝑥‑axis, and the𝑦‑axis. The cross sections perpendicular to the𝑦‑axis are semicircles. Compute the volume of the solid.
A hot air balloon with a buoyancy (Upward force) of 450N is being held by two
ropes of lengths 29 and 25 metres. The ropes are pegged into the ground 36
metres apart. Calculate the tension in each rope. You will first have to find the
angle at which each force vector is being applied. (hint: use cosine law and use
the length of the ropes and the distance between the rope to find the angles first)
*Buoyancy replaces the gravitational force*
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#340153 on Dec 2023