Page 70 - Senior Math

Write and solve an equation for each of the following.
1) One leg of a right triangle is twice as long as the other leg and the hypotenuse is 6 meters long. Find the length of each side of the triangle.
2) A rectangle has a length that is 1 mm more than 3 times its width. One of its diagonals is 1 mm more than the length. Find the length, width, and area of the rectangle.
3) A 2 cm square is cut from each corner of a rectangular piece of cardboard that is 20 cm longer than it is wide. The four flaps are turned up to form an open box with a volume of 50 cm3. Find the dimensions of the original piece of cardboard.
4) Find the value of a if the points with the given coordinates are the given distance apart.
a. (3,−1),(𝑎,7),𝑑 = 10 b. (−4,𝑎),(4,2),𝑑 = 17
c. (𝑎,5),(−7,3),𝑑 = √29 d. (6,−3),(−3,𝑎),𝑑 = √130
Solve each of the following using the formula h = 𝑣𝑡 − 4.9𝑡2.
5) An object is shot upward from the Earth’s surface with an initial velocity of 50 m/s. When will the
height of the object be 100m?
6) If a pellet is launched straight up from the surface of the earth at an initial velocity of 75 m/s, when will the altitude of the pellet be 225 m?
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