why the a and b in dot product can be cancelled out while the a and b in absolute value do not?
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why the a and b in dot product can be cancelled out while the a and b in absolute value do not?
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- A vertical right circular cylindrical tank measures 32 ft high and 18 ft in diameter. It is full of liquid weighing 64.4 lb/ft³. How much work does it take to pump the liquid to the level of the top of the tank? The amount of work required is ft-lb. (Round to the nearest whole number as needed.)A 10 m chain is hanging from a tall building. The chain has a density of 1.5 kg/m. At the bottom of the chain is a 50 kg stone. How much work does it take to wind up the chain and stone to the top of the buildingA bathtub in the shape of a hemispherical bowl of diameter 6 feet is filled with water. How much work is required to empty the tub by pumping all of the water to the height of the top of the tub?
- A man pushes a lawn mower on a level lawn with a force of 191 N. If 25% of this force is directed forward, how much work is done by the man in the pushing mower 7.1 m?How much work is done by a person lifting a 4.1 kg object from the bottom of a well at a contact speed of 2.2 m/s for 11s? Write your answer In joules?A man pushes a lawn mower on a level lawn with a force of 192 N. If 45% of this force is directed forward, how much work is done by the man in pushing the mower 6.5 m?
- One vector has magnitude 18 units and another 5.5 units. Find their scalar product if the angle between them is 25 degrees, and then if the angle between them is 82 degrees.An aquarium 12m long, 2m wide, and 7m deep is full of water. The density of water is 1000kg/m^3 and the force of gravity is 9.8m/s^2 a) Find the work needed to pump all of the water out of the aquarium.Work = Joules. b) Find the work needed to pump half of the water out of the aquarium.Work = Joules.Find the dot product of two vectors shown in the figure. The magnitude of the vectors are A=6 andB=6 130.0° 53.0 O 7.0 O 4 O 3.2 O there is no answer O 8.1
- A tank in the shape of a hemispherical bowl of radius 4 m is completely filled with water. How much work is required to pump all the water to a height 5 m above the tank? (The density of water is 1000 kg/m3 .Assume g = 9.8 m/s2) Answer in exact form and decimal.In recent years, there has been a large push for an increase in the use of renewable resources to produce the energy we need to power our vehicles. One of the newer fuels that has become more widely available is E85, a mixture of 85% ethanol and 15% gasoline. Despite being more environmentally friendly, one of the potential drawbacks of E85 fuel is that it produces less energy than conventional gasoline. Assume a car gets 27.5 mi gal using gasoline at $3.50/gal and 21.5 mi gal using E85 at $2.85/gal. How much will it cost to drive 700. miles using conventional gasoline fuel? How much will it cost to drive 700. miles using E85 fuel?A coal power plant has a rated output of 150 MW and a first law efficiency of 41%. Coal has an energy density of 24 MJ/kg. How many metric tons of coal are wasted by the power plant per hour while running at full capacity (that is, how much of the coal that was burned did not actually contribute to generating electricity)? Express your answer in metric tons of coal.