bIueb3rry

113 Questions
13 Answers

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Algebra

Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}

bIueb3rry 3 hours ago

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Algebra

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

bIueb3rry 8 hours ago

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24

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Geometry

Two runners start at vertices A and B simultaneously and run clockwise around the perimeter of square ABCD at the same speed. A drone flies so that it is always at the midpoint of the two runners. What is the minimum distance between the two runners? прочитайте больше ..

bIueb3rry 27 мая 2025 г.

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3

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Counting

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

bIueb3rry 19 мая 2025 г.

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2

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Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds прочитайте больше ..

bIueb3rry 10 мая 2025 г.

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1

1

+474

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that прочитайте больше ..

bIueb3rry 10 мая 2025 г.

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2

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Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is less than 20. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry 19 апр. 2025 г.

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5

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Counting

Find the number of subsets of
S = \{1, 3, 8, 17, 30, 36, 47, 58\},
so that the sum of the elements in the subset is a multiple of 5. (Note that for the empty subset, we take the sum of the elements as 0.)

bIueb3rry 19 апр. 2025 г.

0

5

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+474

Counting

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with прочитайте больше ..

bIueb3rry 17 апр. 2025 г.

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8

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+474

Counting

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

bIueb3rry 17 апр. 2025 г.

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6

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Counting

How many ordered pairs of positive integers (m,n) satisfy \text{lcm}[m,n] = 360 and \gcd(m,n) = 360?

bIueb3rry 17 апр. 2025 г.

0

9

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+474

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that прочитайте больше ..

bIueb3rry 17 апр. 2025 г.

0

3

0

+474

Geometry

Find sin B.
BD = 15, CD = 10, AC = 6

bIueb3rry 4 апр. 2025 г.