Mathslover
Popular questions and responses by Mathslover
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.
asked on May 30, 2013 
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
asked on June 4, 2013 
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
asked on May 27, 2013 
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.
asked on May 13, 2013 
heeeeeeelp math
Find the sum of all primes q
asked on June 26, 2013 
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?
asked on June 23, 2013 
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?
asked on June 20, 2013 
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.
asked on June 19, 2013 
Please help in triangle
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?
asked on June 19, 2013 
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.
asked on June 19, 2013 
Geometric Progression
Integers a, b, c, d and e satisfy 50
asked on June 19, 2013 
Maths Please Helppp
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?
asked on June 19, 2013 
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.
asked on June 19, 2013 
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_{n1}=a/b for relatively prime positive integers a and b, find a+b
asked on June 7, 2013 
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
asked on June 4, 2013 
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,
asked on June 4, 2013 
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.
asked on May 31, 2013 
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
asked on May 30, 2013 
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 4sided 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
asked on May 30, 2013 
Please Help
Let x,y,z be nonnegative 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?
asked on May 30, 2013 
Exponential
What is the sum of all integer values of x such that (x^2−17x+71)^(x^2−34x+240)=1?
asked on May 30, 2013 
Maths Please Help
Suppose a,b, and c are positive integers such that a+b+c+ab+bc+ca+abc=1000.
asked on May 30, 2013 
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
asked on May 29, 2013 
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 squarefree positive integer. What is the value of a+b+c?
asked on May 27, 2013 
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?
asked on May 27, 2013 
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 4sided dice, and have their sum be a multiple of 5. How many different dice throws result in Calvin
asked on May 27, 2013 
Please help me
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.
asked on May 27, 2013 
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?
asked on May 25, 2013 
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
asked on May 25, 2013 
Maths Help Please
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
asked on May 24, 2013 
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
asked on May 22, 2013 
Maths Please Help
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
asked on May 22, 2013 
Maths Please Help
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
asked on May 22, 2013 
Mayhs Please Help
How many pairs of positive integers (a,b), where a≤b satisfy 1/a+1/b=1/50?
asked on May 22, 2013 
Logarithm Please Help
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?
asked on May 22, 2013 
Physics Please Help
A point charge of charge 1 mC and mass 100 g is attached to a nonconducting massless rod of length 10 cm. The other end of the rod is attached to a twodimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel
asked on May 18, 2013 
Geometry please help
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
asked on May 14, 2013 
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
asked on May 14, 2013 
math please helppppppp
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
asked on May 14, 2013 
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
asked on May 14, 2013 
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
asked on May 14, 2013 
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
asked on May 13, 2013 
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?
asked on May 13, 2013 
Algebra PleaseHelppppppppp
For how many positive integers 1≤k≤1000 is the polynomial fk(x)=x^3+x+k irreducible?
asked on May 13, 2013 
Algebra Please Help
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
asked on May 13, 2013 
Algebra Please Help
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
asked on May 13, 2013 
Algebra Please Help
What is the largest prime factor of 5^8+2^2?
asked on May 13, 2013

Please help in triangle
please give me solution!!!!! Please
posted on June 21, 2013 
pls heeelp math
i have got the answer
posted on June 7, 2013 
pls heeelp math
answer===========
posted on June 7, 2013 
pls heeelp math
answer=????????
posted on June 7, 2013 
math
its wrong
posted on June 4, 2013 
math
plesse tell me write answer
posted on June 1, 2013 
math
thanks
posted on June 1, 2013 
math
its wrong
posted on June 1, 2013 
Maths (Geometry)
20
posted on May 30, 2013 
math
yes
posted on May 30, 2013 
math
thanks
posted on May 30, 2013 
math
meter
posted on May 28, 2013 
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 
heeeeeeeeeeeeeelp Physics
its not
posted on May 24, 2013 
math
its wrong mr. steve please give the correct answer
posted on May 1, 2013