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You have a rectangular piece of cardboard that you want to fold into a box. It occurs to you that you can cut out an equal square from each corner of the rectangle, make a crease along each side and fold them up.
Suppose that the paper is 45 cm wide and 60 cm long. Now here's the question: how much should you cut from the corners to form the box with maximum capacity, and what would be the width, length and volume of the resulting box?
Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away. How large a radio telescope would we need to detect this signal?
A checkered flag used for racing is a square flag containing 64 alternating white and black squares. How many squares on the checkered flag contain an equal number of white and black squares?
Prove the following vector calculus identity in R 3 , where f is a twice continuously dierentiable scalar eld and F is a twice continuously dierentiable vector fi eld
Name at least one situation in real life where you measure slope? What is the range of the slopes you encounter for this measurement?
The Tempcontrol company has a container that reduces the temperature of a liquid from 200 f to 110 f in 25 minutes by maintaining a constant temperature of 60 F.
A car traveling at 60 mph is brought to a stop, at constant deceleration, 88 feet from where the brakes are applied. How lond did it take for the car to stop?
If it costs 1.9 times as much money to lay pipe in the water as it does on land, how far down the shoreline from should the pipe from the island reach land in order to minimize the total construction costs?
Each,day Monday through Saturday, a baker bakes three large chocolate cakes and those not sold on the same day are given away to a food bank
Two circles of different radii touch internally at C. A tangent at P on the smaller inner circle touches the larger circle at A and B. Join ABC. Prove that CP bisects angle
State the inverse, the converse, and the contrapostive of the given statements.
If a string wound around a fixed circle is unwound while held taut in the plane of the circle, its end P traces an involute of the circle. the circle in question is x^2+y^2=1 and the tracing point starts at (1,0).
A nutrition laboratory tests 50 "reduced sodium" hot dogs, finding that the mean sodium content is 316 mg, with a standard deviation of 35 mg.
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