# Mathslover

Popular questions and responses by Mathslover
1. ## Fibonacci sequence

The Fibonacci sequence a1=1,a2=1,a3=2,a4=3,a5=5,a6=8… is defined recursively using the formulas a1=a2=1 and an+2=an+an+1 for all n≥1. Find the greatest common divisor of a484 and a2013.

2. ## Phyics Toughest question on earth

Estimate the time difference between the longest day and the shortest day of a year in seconds if you lived on the Earth's equator with the assumptions below. Note: this is not the difference between solstices as we are adjusting the earth's rotation axis

3. ## math

Let S be a set of 31 equally spaced points on a circle centered at O, and consider a uniformly random pair of distinct points A and B (A,B∈S). The probability that the perpendicular bisectors of OA and OB intersect strictly inside the circle can be

4. ## Algebra (factorial)

Evaluate gcd(19!+19,20!+19). Details and assumptions The number n!, read as n factorial, is equal to the product of all positive integers less than or equal to n. For example, 7!=7×6×5×4×3×2×1.

5. ## heeeeeeelp math

Find the sum of all primes q

6. ## heeeelp math

Find the largest possible number of distinct integer values {x_1,x_2,…,x_n}, such that for a fixed reducible degree 4 polynomial with integer coefficients, |f(x_i)| is prime for all i?

7. ## heeeeeeeeelp math

Find the largest possible number of distinct integer values {x_1,x_2,…,x_n}, such that for a fixed reducible degree 4 polynomial with integer coefficients, |f(x_i)| is prime for all i?

8. ## Physics tough

If approximately 70% of the Earth's surface is covered with water, what is the order of magnitude for the number of raindrops in the world's oceans? Hint: The order of magnitude of 2478=2.478×10^3 is 3.

ABC is an isosceles triangle with AB=BC and ∠ABC=123∘. D is the midpoint of AC, E is the foot of the perpendicular from D to BC and F is the midpoint of DE. The intersection of AE and BF is G. What is the measure (in degrees) of BGA?

10. ## Non linear equation

The real numbers x and y satisfy the nonlinear system of equations 2x^2−6xy+2y^2+43x+43y=174, x^2+y^2+5x+5y=30. Find the largest possible value of |xy|.

11. ## Geometric Progression

Integers a, b, c, d and e satisfy 50

S=1+2*(1/5)+3*(1/5)^2+4(1/5)^3...... If S=a/b, where a and b are coprime positive integers, what is the value of a+b?

13. ## Maths

Let α and β be the roots of 3x^2+4x+9=0. Then (1+α)(1+β) can be expressed in the form a/b, where a and b are coprime positive integers. Find a+b.

14. ## pls heeelp math

For each positive integer n, let H _{n} = 1/1 +1/2 +⋯+ 1/n sum_{n=4}^{∞} 1/n*H_{n}*H_{n-1}=a/b for relatively prime positive integers a and b, find a+b

15. ## Maths

The game Slice is played using a m×n rectangular piece of paper as a board. Players alternate turns, on each turn they choose a rectangle and cut it into two rectangles, each with integer side lengths. The last player who is able to cut a rectangle is the

16. ## Math

Find the smallest number N such that: The number of divisors of N is A. The number of divisors of A is B. The number of divisors of B is C. The number of divisors of C is 3. Details and assumptions The divisors include 1 and the number itself. For example,

17. ## Physics

A tunable capacitor (with variable capacitance) is charged by a U0=12 V battery and then is connected in parallel to a R=3 Ω resistor. The capacitance C(t) of the capacitor is controlled so that the current in the circuit remains constant at all times.

18. ## Physics

Many of you may have noticed the phenomenon that basketballs get flat if the weather is cold. If a basketball was inflated to a gauge pressure of 60,000 Pa when the temperature outside was 20∘C, what is the gauge pressure inside the basketball in Pa when

19. ## Help me please Maths

Calvin is playing a game of Dungeons and Dragons. In order to make it across the river, he needs to throw six 4-sided dice, and have their sum be a multiple of 5. How many different dice throws result in Calvin making it across the river? Details and

Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1. The maximum possible value of x^3*y^3+y^3*z^3+z^3*x^3 has the form a/b where a and b are positive, coprime integers. What is the value of a+b?

21. ## Exponential

What is the sum of all integer values of x such that (x^2−17x+71)^(x^2−34x+240)=1?

Suppose a,b, and c are positive integers such that a+b+c+ab+bc+ca+abc=1000.

23. ## Complex angles

There are four complex fourth roots to the number 4−43√i. These can be expressed in polar form as z1=r1(cosθ1+isinθ1) z2=r2(cosθ2+isinθ2) z3=r3(cosθ3+isinθ3) z4=r4(cosθ4+isinθ4), where ri is a real number and 0∘≤θi

24. ## math

A sphere of radius 32√ is tangent to the edges AB, AD, AA1, and the face diagonal CD1 of the cube ABCDA1B1C1D1. The volume of the cube can be written as a+bc√, where a, b are integers and c is a square-free positive integer. What is the value of a+b+c?

25. ## math

Jack has 222 lego cubes, each of side length 1. He puts them together to form a rectangular prism. If the perimeter of the base of the prism is 10, what is the height of the prism?

26. ## math

Calvin's River Crossing Attempt 180 points Calvin is playing a game of Dungeons and Dragons. In order to make it across the river, he needs to throw six 4-sided dice, and have their sum be a multiple of 5. How many different dice throws result in Calvin

How many permutations σ of the set {1,2,…,15} are there such that σ(1)=1,∣σ(n)−σ(n−1)∣≤2 for 2≤n≤15? Details and assumptions σ(n) denotes the nth position of the permutation.

28. ## math

Let ABCD be a rectangle such that AB=5 and BC=12. There exist two distinct points X1 and X2 on BC such that ∠AX1D=∠AX2D=90∘. Suppose that d is the distance from X1 to X2. What is d2?

29. ## math

Equilateral triangle ABC has a circumcircle Γ with center O and circumradius 10. Another circle Γ1 is drawn inside Γ such that it is tangential to radii OC and OB and circle Γ. The radius of Γ1 can be expressed in the form ab√−c, where a,b and c

The sequence {ak}112 (base)k=1 satisfies a1=1 and an=1337+n/an−1, for all positive integers n. Let S=⌊a10a13+a11a14+a12a15+⋯+a109a112⌋. Find the remainder when S is divided by 1000. Details and assumptions The function ⌊x⌋:R→Z refers to the

31. ## geometry help

Circle Γ with center O has diameter AB=192. C is a point outside of Γ, such that D is the foot of the perpendicular from C to AB and D lies on the line segment OB. From C, a tangent to Γ is drawn, touching Γ at E, where the foot of the perpendicular

Alex and Bella play the following game. They first choose a positive integer N, and take turns writing numbers on a blackboard. Alex starts first, and writes the number 1. After that, if the number k is on the board, the next player may write down either

Let A=a1,a2,…,ak and B=b1,b2,…,bj be sequences of positive integers such that a1≥a2≥⋯ak≥1, b1≥b2≥⋯bj≥1, ∑i=1k ai≤6, and ∑j i=1 bi≤6. For how many ordered pairs of sequences (A,B) satisfying the above conditions can we find a

How many pairs of positive integers (a,b), where a≤b satisfy 1/a+1/b=1/50?

x and y are positive real numbers that satisfy log(base)x y + log(base)y x = 17/4 and xy=288√3. If x+y=a+b√c, where a, b and c are positive integers and c is not divisible by the square of any prime, what is the value of a+b+c?

A point charge of charge 1 mC and mass 100 g is attached to a non-conducting massless rod of length 10 cm. The other end of the rod is attached to a two-dimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel

Ravi wants to trisect an angle AOB, which has measure θ. From A, he drops a perpendicular to side OB, intersecting at C. He then constructs an equilateral triangle ACD on the opposite side of AC as compared to O. He claims (without any justification) that

38. ## Math pleaaaase help

A national math contest consisted of 11 multiple choice questions, each having 11 possible answers. Suppose that 111 students actually wrote the exam, and no two students has more than one answer in common. The highest possible average mark for the

For a set of numbers T, we say that T has distinct subset sums if all distinct subsets of T have distinct sums. How many subsets of {1,2,3,4,5,6,7,8} have distinct subset sums? Details and assumptions The empty set (the set of no elements) has sum 0 by

40. ## Maths

For a set of numbers T, we say that T has distinct subset sums if all distinct subsets of T have distinct sums. How many subsets of {1,2,3,4,5,6,7,8} have distinct subset sums? Details and assumptions The empty set (the set of no elements) has sum 0 by

41. ## Probablity

Samir had prepared the problem tests for Stages 1 to 5 of Geometry and Combinatorics for next week but forgot to label which test was for which stage. Since Samir didn't label them, the computer assigned them labels 1 through 5 randomly, with each label

42. ## Math(combinations) Help

Let Pn be the set of all subsets of the set [n]={1,2,…,n}. If two elements of P5 are chosen at random, the expected number of elements (of [n]) that they have in common can be expressed as a/b where a and b are coprime positive integers. What is the

43. ## Geaometry (Graph)

A graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have?

For how many positive integers 1≤k≤1000 is the polynomial fk(x)=x^3+x+k irreducible?

Find the sum of integers c for all triples of integers (a,b,c),a≤b≤c, that satisfy the system of equations a^2−bc=91 b^2−ac=91 c^2−ab=91 Details and assumptions If a number c appears in several different triples (a,b,c), it must be counted with

Determine the last three digits of 2^5+3^5+4^5+......+10,000,000^5 + 2^7+3^7+4^7+......+10,000,000^7

What is the largest prime factor of 5^8+2^2?

posted on June 21, 2013
2. ## pls heeelp math

posted on June 7, 2013
3. ## pls heeelp math

posted on June 7, 2013
4. ## pls heeelp math

posted on June 7, 2013
5. ## math

its wrong

posted on June 4, 2013
6. ## math

posted on June 1, 2013
7. ## math

thanks

posted on June 1, 2013
8. ## math

its wrong

posted on June 1, 2013
9. ## Maths (Geometry)

20

posted on May 30, 2013
10. ## math

yes

posted on May 30, 2013
11. ## math

thanks

posted on May 30, 2013
12. ## math

meter

posted on May 28, 2013
13. ## maths

Let ABCD be a rectangle such that AB=5 and BC=12. There exist two distinct points X1 and X2 on BC such that ∠AX1D=∠AX2D=90∘. Suppose that d is the distance from X1 to X2. What is d2?

posted on May 25, 2013
14. ## heeeeeeeeeeeeeelp Physics

its not

posted on May 24, 2013