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A swimming pool will be 30' wide by 100' long, being a total of 4' deep throughout. Each wall of the pool (plus the bottom) must be covered by one coat of paint and two coats of waterproof lacquer. A gallon of paint covers 80 square feet and costs $22. A gallon of lacquer covers 25 square feet and costs $35.
Determine
*how many gallons of paint and lacquer will be required to coat the pool, using the above specifications, and
*how much will be spent on the paint and lacquer.
Height x width 430, Height x length 4100, Length x width 100*30
120, 400, 3000
120, 400
240 sq.ft + 800 sq.ft + 3000 sq.ft = 4,040 sq.ft
A gallon of paint covers 80 sq. ft. So divide 80 into 4,040 sq. ft. to find that you will need 50.5 cans of paint or 51 cans of paint. The cost of one coat of paint will be 51 cans of paint times $22 per can to reach the cost of $1,122.
You will then need to divide 25 into 4,040 sq. ft. to find that you will need 161.6 cans (this number must then be multiplied by two, because the pool needs to have two coats of waterproof lacquer). So, you will need 324 cans of lacquer at $35 per can. The total amount of lacquer will be $11,340. The final step is to add $11,340 to $1,122 to get a total of $12,462.
Chart A shows the total budget for Smalltown, broken down by four departments. Chart B shows the the division of each department's funds.
CONSTRUCTED- RESPONSE ASSIGNMENT #2
1. For each of the below proposed budget cuts, calculate by what percentage it will reduce the total budget. Then order the cuts from the least cut to the greatest.
Cut #1: A 35% reduction on Parks equipment.
Cut #2: An 80% reduction on Sports equipment.
Cut #3: A 25% reduction in all salaries except for Park salaries.
Cut #4: A 20% reduction on equipment for Gardens, Sports, and Parks.
2. There is no cut to Smalltown's total budget, but the total budget is re-apportioned. Sports is reduced by 90% of its total, and Parks is reduced by 10% of its total, and these funds are instead allocated to Gardens and Pool. If Gardens and Pool are given equal dollar increases, then what percentage of Smalltown's total budget will Gardens now receive?
. Park Equipment is reduced by 35%. This would be 40% 50% 35% = 7%
Sport Equipment is reduced by 80%. This would be 30% 50% 80 = 12%
All salaries except Park Salaries by 25%. This would be 15% (Garden) + 15% (Pool) + 30% (Sport) = 60%. Then you would multiply 60% 50% 25% = 7.5%
Equipment for Garden, Sports, & Parks is reduced by 20%. This would be 15% (Garden) + 30% (Sports) + 40% (Parks) = 85%. Then you would multiply 85% 50% 20% = 8.5%
The order of the cuts from least to greatest would be Parks at 7%, then all salaries except Parks salaries at 7.5%, then Equipment for garden, sports, & parks at 8.5%. And finally, Sports Equipment at 12%.
2. If Sports is reduced by 90% : 30% * 90% = 27%. Then, 30% - 27% = 3%
If Parks is reduced by 10%: 40% * 10% = 4%. Then, 40% - 4% = 36%
Next, you would add 27% + 4% = 31%
Since we are asked to give equal dollar increases to both Gardens and Pool, we would divide by two: 31% / 2 = 15.5% and add 15% (Garden) + 15.5% (Equal re-apportioned) = 30.5%
To check: 3% (Sports) + 36% (Parks) + 30.5% (Garden) + 30.5(Pool) = 100%
CONSTRUCTED-RESPONSE ASSIGNMENT #3
The Earth is less than 1/300,000th the mass of the Sun it orbits. Yet the moon (smaller still) remains in the Earth's orbit, rather than being taken in by the enormous pull of the Sun. Explain how these respective orbits are possible, citing the law of gravity and the role of centrifugal force.
Every mass exerts a gravitational force on every other mass. The force of gravity = GmM / r*r, where G is the gravitational constant (a very small number), m and M are the two masses, and r is the distance between the masses. Gravity is a weak force. So, a large mass is needed to create a significant force. For example, the gravitational force between my body and my computer is so small as to be insignificant. But the Earth is very large and exerts a noticeable force.
There is gravity in space.
The Sun's gravitational pull on the moon is greater than Earth's gravitational pull. But both the Earth and the moon are rotating around the Sun. (As a side note: it's helpful to differentiate between the revolution one body makes around a larger body versus the rotation it makes while spinning on its axis).
The Earth and the moon are not pulled into the Sun due to inertia. The term centrifugal force does not refer to a true force; rather, it is the tendency of an object to follow a straight path while a force is causing the object to turn. The result appears to be a force pushing the object away from the center of its rotation.
That is, the Earth is being pulled toward the Sun, but it is also travelling in a direction perpendicular to the sun. The combination of these factors means that the Earth remains in a stable orbit, neither falling into the Sun, nor continuing in a straight line tangentially away from the Sun.
Likewise, the moon is orbiting the Sun while it rotates around the Earth. The moon's path would take it away from the Earth, but the Earth's gravitational pull deflects the moon from its path, so the moon is continually falling over the horizon. The net effect is that the moon remains the same distance from the earth.
CONSTRUCTED-RESPONSE ASSIGNMENT #4
In the course of a day's work, a farmer chops wood, shovels snow, picks and pries large stones from the ground, and rides a bicycle to pick up the mail. All of these actions involve work which is made more efficient through the use of simple machines. List the different simple machines used by the farmer, and describe how they enable work that might not otherwise be possible.
Riding a bicycle is an example of a wheel and axle. This simple machine makes traveling over distances easier and less strenuous. A farmer chopping wood is an example of a wedge. The head of the axe, as it makes contact with the wood, acts as a wedge to split the wood in half.
An axe works on the same principle as the inclined plane and is, in fact, two inclined planes meeting at an edge. The wedge can separate an object into pieces. Wedges can also hold objects. Other examples of wedges are knives and forks. Without an axe, the farmer would be unable to break wood into pieces.
The snow shovel combines a lever with a wedge. The handle is a lever and the sharp edge is a wedge that separates the snow from the ground. Without a snow shovel, moving snow would be a far more tedious task, and the farmer would have to move the snow less effectively by hand, which would take far longer.
The pick is being use as a wedge to get at the stones and then used as lever to remove the stones from the ground. This simple machine is first used as a wedge to break the stones into smaller pieces and then a lever to pry the stones from the ground. Without this simple machine the farmer would likely not be able to remove the stones from the ground.
There are three classes of levers. The crowbar and seesaw are examples of levers in which the fulcrum is positioned between the effort force and the resistance. Another type of lever positions the effort between the fulcrum and the resistance, such as the human arm. A third type of lever positions the resistance between the fulcrum and the effort, as in the case of a wheelbarrow.
A bicycle is a compound machine. The wheels and pedals of a bicycle are indeed examples of a wheel and axle. The gear shifts and brake handles are levers. Without a bicycle, the farmer would have to walk to wherever he was going.
Another simple machine, the pulley, can be used to redirect a force or to enhance a force. The more cable segments, the greater the mechanical advantage.
Other simple machines include the inclined plane and the screw.
