член: HumanBemg

47 Questions
5 Answers

+199

Geometry

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

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HumanBemg 20 февр. 2026 г.

+199

Geometry

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

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HumanBemg 20 февр. 2026 г.

+199

Help me CPhill Now

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

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HumanBemg 16 авг. 2025 г.

+199

help math

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.

HumanBemg 22 июл. 2025 г.

+199

help me

Let \omega be a nonreal root of x^3 = 1. Compute
(1 - \omega + \omega^2)^6 + (1 + \omega - \omega^2)^6.

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HumanBemg 21 июл. 2025 г.

+199

Geometry

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

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HumanBemg 28 мая 2025 г.

+199

Counting

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

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HumanBemg 23 мая 2025 г.

+199

Counting

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

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HumanBemg 22 мая 2025 г.

+199

Counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

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HumanBemg 9 апр. 2025 г.

+199

Counting

In how many ways can 5 balls be placed in 4 boxes, if 2$balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

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HumanBemg 9 апр. 2025 г.

+199

Counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

HumanBemg 8 апр. 2025 г.

+199

Counting

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

HumanBemg 8 апр. 2025 г.

-1

+199

Geometry

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

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HumanBemg 5 апр. 2025 г.

+199

Geometry

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

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HumanBemg 5 апр. 2025 г.

+199

Geometry

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

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HumanBemg 5 апр. 2025 г.

+199

Algebra

The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
xf(x) + f(1 - x)/x = x^3 + 3x^2 + 14x - 13
for all real x. Find f(x).

HumanBemg 1 апр. 2025 г.

+199

Algebra

Find all x such that
(2x)^{\log_{10} 2} = (9x)*{\log_{10} 9} + (5x)^{\log_{10} 9} + \log_x 243

HumanBemg 29 мар. 2025 г.

+199

The answer is 8. Hope this helps!

HumanBemg9 апр. 2025 г.

+199

The range is [-5,infty).

HumanBemg21 мар. 2025 г.

+199

(A) k > 0 and a > 1

(B) k < 0 and a < 1

(D) k > 0 and a < 1

HumanBemg8 мар. 2025 г.

Имя пользователя	HumanBemg
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