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Quadratic Equations

✔The floor of a basement game room is covered by 480 square asphalt tiles of a certain size. If 3 inches is added to the length of a side of each tile, the floor could be covered by 270 tiles. Find the length of a side of the tile on the floor.
✔If \(A\) is a cross-section area of a chimney, its so-called effective area \(E\) is the smallest root of the equation \(E^2 -2AE+A^2-0.36A =0\). Solve \(E\) interms of \(A\). From the result, find \(E\) if \(A = 30\) square feet.
✔If an object is shot vertically from the surface of the earth with an initial velocity of \(v\) feet per second, and if air resistance and other disturbing factors are neglected, it is found that \(s = vt - 0.5gt^2\), where \(s\) feet is the height of the object above the surface at the end of \(t\) seconds and \(g = 32\), approximately. (a) Solve for \(t\) in terms of \(s\) (b) If \(v=300 \text{fps}\), use (a) to find where \(s=450\) and \(s=0\).
✔If an object is shot vertically from the surface of the earth with an initial velocity of v feet per second and if the air resistance and other disturbing factors are neglected, it is found that \(s = vt -0.5gt^2\), where s feet is the height of the object above the surface at the end of t seconds and g = 32 feet per second square. (a) Solve t in terms of s. (b) If v = 300 feet per second use (a) to find when s =450 and s= 0.
✔The base of a triangle is 4 feet shorter than its altitude, and the area of the triangle is 126 square feet. Find the base and the altitude.
✔An open rectangular gutter is to be made by turning up the sides of a piece of metal 18 inches wide. If the cross-section area of the resulting gutter is 36 square inches, find the gutter's depth.
✔After plowing a border inside a rectangular field 60 rods wide and 80 rods long, a farmer finds that one half of the field remains to be plowed. How wide is the border?










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