maximum

256 Questions
127 Answers

-2

90

1

+818

help plz

Help this is a problem
Point $P$ is chosen at random inside triangle $ABC$. If $AB = \sqrt{2}$, $BC = 1$, and $CA = 1$, then what is the probability that $P$ is closer to $C$ than it is to $A$? mehr ..

maximum 13.08.2023

-2

42

5

+818

A quadratic equation

Help plz!
The equation $18+5x^2=20x + 20$ has two distinct solutions. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

●●●●●

maximum 10.08.2023

-2

82

1

+818

A special quadratic

Which quadratic is this?
Let $p(x) = x^2 + ax + b,$ where $a$ and $b$ are real numbers. Find the number of ordered pairs $(a,b)$ such that $p(a) = p(b) = 1.$

maximum 10.08.2023

-2

91

2

+818

ordering numbers

Arrange the following numbers in increasing order (smallest first, biggest last)
A = 2^(1/2)*4^(1/6)
B = (128)^(1/12)/64^(1/3)
C = (8^(1/5))^(2^2) mehr ..

maximum 10.08.2023

-2

103

1

+818

help plz

I need help with a function problem:
Find the range of the function $f(x) = \sqrt{x + 5} + \sqrt{20 + x}.$

maximum 10.08.2023

-2

49

1

+818

Circle

The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by
\[r = \sqrt{ab + ac + bc}.\]
What is the value of $r$ when $a = 4$, $b = 9$ and $c = 36$?

maximum 09.08.2023

-1

26

2

+818

proper divisors

The proper divisors of $12$ are $1,$ $2,$ $3,$ $4$ and $6$. A proper divisor of an integer $N$ is a positive divisor of $N$ that is less than $N$. What is the sum of the proper divisors of the sum of the proper divisors of $256$?

maximum 09.08.2023

-2

93

2

+818

Complex numbers

Solve for $z$ in the following equation: $2-3iz = 3 + 2z$.

maximum 08.08.2023

-2

52

1

+818

integral solutions

Find the largest integral value of $x$ which solves: $\frac{1}{3}<{\frac{x}{5}}<{\frac{7}{8}}$

maximum 08.08.2023

-2

62

4

+818

rectangle question

A non-square rectangle has integer dimensions. The number of square units in its area is four times the number of units in its perimeter. What is the smallest possible perimeter of the rectangle?

maximum 08.08.2023

+818

-1

Do not post AoPS homework.

maximum20.01.2025