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The base of an aquarium with volume V = 440 is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
What is the difference between prime numbers and composite numbers? How are prime numbers and composite numbers related? Prime numbers are often used in cryptography.
A boat travels 72 miles upstream in the same time that it takes to travel 120 miles downstream. The speed of the boat in still water is 32 mph. Find the speed of the current.
College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 95% confident that the sample percentage has a margin of error of 2 per..
What are the dimensions of this rectangle?
Amy paid $81.11 for a pair of shoes during a 40% off sale. What was the original price?
An isosceles triangle whose base is the interval from (0,0) to (c,0) has its vertex on the graph of f, where f(x)=12-x^2 for x is greater than or equal to 0 and f(x) is greater than or equal to 0.
Find the rate at which velocity of expelled air is changing with respect to the trachea's radius during a cough. Is the velocity of airflow increasing or decreasing when r=1/2R? Why? Show all your work.
the length of a rectangular pool is 6 meters less than twice the width. if the pool's perimeter is 126 meters, find the surface area of the pool.
find the person's weight 800 miles above the surface of the Earth. Assume that the radius of the Earth is 4000 miles. Round your answer to the nearest whole pound. Show work.
If F is a field, prove that the field of fractions of F[[x]] is the ring F((x)) of formal Laurent series. Show that the field of fractions of the power series ring Z[[x]] is properly contained in the field of Laurent series Q((x)).
You have a wire that is 38 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What i..
Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
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