Problem+of+the+Week

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After being dropped from the top of a tall building, the height of an object is described by //y = 400 − 16t^ 2  //, where // y // is measured in feet and // t // is measured in seconds. (a) How many seconds did it take for the object to reach the ground, where // y // = 0? (b) How high is the projectile when // t // = 2, and (approximately) how fast is it falling?
 * Week 1 - 1/20-1/23**

Find the area of enclosed by the graph of |x| + |y| = 20.
 * Week 2 - 1/26 - 1/30**

An integer is defined as upright if the sum of its first two digits equals its third digit. For example, 145 is upright because 1 + 4 = 5. How many positive three-digit integers are upright?
 * Week 3 - 2/2 - 2/6**

The parabola with the equation //y = ax^2// passes through three vertices of a square that has two of its vertices along the y-axis (one of them is at the origin). If the area of the square is 18, find the value of //a//.
 * Week 4 - 2/9 - 2/13**

By using only the five digits 1, 2, 3, 4, and 5, a sequence is created as follows: one 1, two 2's, three 3's, four 4's, five 5's, six 1's, seven 2's, etc. Thsequence appears ast this: 1, 2, 2, 3, 3 ,3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 2... What is the 100th digit in this sequence?
 * Week 5 - 2/16 - 2/20**

The sequence 24, //x, y, z//, 60 is arithmetic. What is the value of //x + y + z//?
 * Week 6 - 2/23 - 2/27**