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A window with a 20-foot perimeter (frame) is to be comprised of a semi-circular stained glass pane above a rectangular clear pane as shown in the accompanying figure. Clear glass costs $3 per square foot and stained glass costs $10 per square foot. Express the cost of the window as a function of the radius of the stained glass pane.
A two-person game is played in which a fair coin is tossed until either the sequence HT (heads, tails) or the sequence TT (tails, tails) appears.
Find the interior, the closure, the accumulation points, the isolated point and the boundary points of the following sets.
You decide to start your article with a math example that the readers can understand. Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing.
The dimensions of a closed rectangular box are measured as 90 cm, 65 cm, and 34 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
ABCD is a cross-section of a uniform rectangular block of mass 20kg. AB is 0.75m and BC is 1m. The block rests with A on rough horizontal ground with AB at 20 degrees to the horizontal.
You follow the same pattern for every fourth, fifth locker and so on up to every thousandth locker. Which locker doors will be open when the process is complete?
Verify that 18^3 - 1^3 = 17* 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates.
When a mass of 4 kilograms is tied to the middle of the clothesline, it sags a distance of 1 meters. What is the magnitude of the tensions at the end of the clothesline?
What alternative would be chosen according to expected value?
the selling price s(c) after 45% markup of an item as a function of the stores' cost c.
Solve the following problem by simplex method
A submarine dives at an angle of 12 degrees to the surface of the water. The submarine travels at a speed of 740 feet per minute. About how deep is the submarine after 5 minutes?
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