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Questions (43)

If approximately 70% of the Earth's surface is covered with water, what is the order of magnitude for the number of raindrops in
1. 2 answers
2. 568 views
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
1. 3 answers
2. 649 views
The real numbers x and y satisfy the nonlinear system of equations2x^2−6xy+2y^2+43x+43y=174, x^2+y^2+5x+5y=30. Find the
1. 1 answer
2. 501 views
Integers a, b, c, d and e satisfy 50<a<b<c<d<e<500, and a,b,c,d,e form a geometric sequence. What is the sum of all possible
1. 1 answer
2. 436 views
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?
1. 0 answers
2. 447 views
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
1. 0 answers
2. 435 views
Estimate the time difference between the longest day and the shortest day of a year in seconds if you lived on the Earth's
1. 3 answers
2. 808 views
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
1. 4 answers
2. 690 views
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
1. 3 answers
2. 576 views
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
1. 0 answers
2. 530 views
Many of you may have noticed the phenomenon that basketballs get flat if the weather is cold. If a basketball was inflated to a
1. 1 answer
2. 719 views
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
1. 1 answer
2. 626 views
Let x,y,z be non-negative real numbers satisfying the condition x+y+z=1. The maximum possible value ofx^3*y^3+y^3*z^3+z^3*x^3
1. 0 answers
2. 433 views
What is the sum of all integer values of x such that(x^2−17x+71)^(x^2−34x+240)=1?
1. 2 answers
2. 562 views
The Fibonacci sequencea1=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
1. 1 answer
2. 1,228 views
Suppose a,b, and c are positive integers such thata+b+c+ab+bc+ca+abc=1000.
1. 1 answer
2. 413 views
There are four complex fourth roots to the number 4−43√i. These can be expressed in polar form asz1=r1(cosθ1+isinθ1)
1. 2 answers
2. 1,222 views
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
1. 3 answers
2. 1,020 views
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
1. 9 answers
2. 520 views
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
1. 5 answers
2. 593 views
Calvin's River Crossing Attempt180 points Calvin is playing a game of Dungeons and Dragons. In order to make it across the
1. 4 answers
2. 589 views
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
1. 0 answers
2. 414 views
Let ABCD be a rectangle such that AB=5 and BC=12. There exist two distinct points X1 and X2 on BC such that
1. 0 answers
2. 366 views
Equilateral triangle ABC has a circumcircle Γ with center O and circumradius 10. Another circle Γ1 is drawn inside Γ such
1. 0 answers
2. 571 views
The sequence {ak}112 (base)k=1 satisfies a1=1 and an=1337+n/an−1, for all positive integers n. LetS=⌊a10a13+a11a14+a12a15+�
1. 0 answers
2. 514 views
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
1. 5 answers
2. 1,147 views
Alex and Bella play the following game. They first choose a positive integer N, and take turns writing numbers on a blackboard.
1. 1 answer
2. 595 views
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,
1. 0 answers
2. 569 views
How many pairs of positive integers (a,b), where a≤b satisfy 1/a+1/b=1/50?
1. 3 answers
2. 875 views
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
1. 1 answer
2. 505 views
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
1. 1 answer
2. 714 views
Ravi wants to trisect an angle AOB, which has measure θ. From A, he drops a perpendicular to side OB, intersecting at C. He
1. 1 answer
2. 506 views
A national math contest consisted of 11 multiple choice questions, each having 11 possible answers. Suppose that 111 students
1. 0 answers
2. 483 views
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
1. 0 answers
2. 560 views
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
1. 0 answers
2. 512 views
Samir had prepared the problem tests for Stages 1 to 5 of Geometry and Combinatorics for next week but forgot to label which
1. 0 answers
2. 1,323 views
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
1. 1 answer
2. 511 views
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
1. 4 answers
2. 483 views
For how many positive integers 1≤k≤1000 is the polynomial fk(x)=x^3+x+k irreducible?
1. 0 answers
2. 341 views
Find the sum of integers c for all triples of integers (a,b,c),a≤b≤c, that satisfy the system of equationsa^2−bc=91
1. 1 answer
2. 502 views
Evaluate gcd(19!+19,20!+19).Details and assumptions The number n!, read as n factorial, is equal to the product of all positive
1. 3 answers
2. 1,292 views
Determine the last three digitsof 2^5+3^5+4^5+......+10,000,000^5 + 2^7+3^7+4^7+......+10,000,000^7
1. 1 answer
2. 316 views
What is the largest prime factor of 5^8+2^2?
1. 1 answer
2. 373 views

Answers (11)

please give me solution!!!!! Please
its wrong
plesse tell me write answer
thanks
its wrong
20
yes
thanks
meter
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?
its not

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