Math Is Fun Forum

These questions are a compilation of physics-related mathematics problems. Enjoy!

1. In bobbym's lavish home, he has a triangular grandstand shown by Diagram 1.0:
(A and a are the same length.)
Find where the center of mass is with calculus.

2. Bobbym is riding a sled on a gargantuan hill, and his speed is given by 29 - t^2 + t. How far will the valiant bobbym travel from t(time) =0 to when he stops at v =0?

3. What is the least positive integer with the property that the product of its digits is 5! ?

4.Find the sum of all the integers N > 1 with the properties that the each prime
factor of N is either 2, 3, or 5, and N is not divisible by any perfect cube greater
than 1.

5.If you roll six fair dice, let p be the probability that exactly three different numbers
appear on the upper faces of the six dice. If p = m/n where m and n are

relatively prime positive integers, find m + n.
5a. Say p is the probability that exactly four different numbers appear on the upper faces of the dice. How much smaller or larger is this probability?

6.Find the sum of all the digits in the decimal representations of all the positive
integers less than 10000.
7 Bobbym has some square tiles. Some of the tiles have side length 5 cm while
the others have side length 3 cm. The total area that can be covered by the
tiles is exactly 20124 cm squared.
. Find the least number of tiles that Bobbym can have.
8.Bobbym needed to address a letter to 27432 Mathematica Road. He remembered the
digits of the address, but he forgot the correct order of the digits, so he wrote
them down in random order. The probability that Bobbym got exactly two of the
four digits in their correct positions is m/n
, where m and n are relatively prime
positive integers. Find m + n.
9.Find the number of subsets of {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 22} where the
elements in the subset add to 49.
10. There is a triangle where all sides of the triangle is 1, and Bobbym picks 3 points from the triangle's area. What is the probability that the area of the three points is greater than .4? All three points are distinct.

1. The sum of the first 2 terms of an geometric series is 7. The sum of the first 6, however, is 91. What is the sum of the first 4 terms?

2. Find the sum of .(Please put your solution in fractional forme.)

3. By adding the same constant A to 20, 50 and 100, a geometric progression results. Find the common ratio and the constant A.

4. The first three numbers of a set A form a arithmetic progression. The last three form a geometric progression. The sum of the first and last elements of A is 16. The sum of the middle two numbers is 12.Find these 4 elements, but be warned that there is more than one solution. BONUS to anyone who finds both of them.
All elements of A are integers.

5. The sum of the first 2011 terms of a GEOMETRIC PROGRESSION is 200. The sum of the first 4022, however, is 380, Find the sum of the first 6033 terms.

6. Find the coefficient of the term that contains x^4 in the expansion of

7. Find the least positive integer whose digits add to a multiple of 27 yet the number itself is not a multiple
of 27. For example, 87999921 is one such number.

8.How many non-congruent isosceles triangles (including equilateral triangles) have positive integer side
lengths and perimeter less than 20?

9. The Bobbym Lizard Garden Store sells grass seed in ten-pound bags and fifteen-pound bags. Yesterday half
of the grass seed they had was in ten-pound bags. This morning the store received a shipment of 27 more
ten-pound bags, and now they have twice as many ten-pound bags as fifteen-pound bags. Find the total
weight in pounds of grass seed the store now has.
10. The zeros of the function f(x) = x^2-ax+3a are integers. What is the sum of the possible values of a. If there are NONE, respond with NONE.

16. A sphere has radius 6 inches. What is the volume, in cubic inches, of the smallest cube that contains the ENTIRE sphere?
Is it 1728?