hemiiI8675

15 Questions
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Algebra

Let
f(x) = \sqrt[3]{x + \sqrt[3]{x}}
Find the largest three-digit value of x such that f(x) is an integer.

hemiiI8675 Jan 9, 2025

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Counting

There is a group of five children, where two of the children are twins. In how many ways can I distribute $8$ identical pieces of candy to the children, if the twins must get at least one piece of candy each?

hemiiI8675 Jan 9, 2025

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Counting

In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

hemiiI8675 Jan 9, 2025

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Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

hemiiI8675 Jan 9, 2025

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Algebra

Let a be a real number such that a - \frac{1}{a} = 1. Compute a^3.

hemiiI8675 Jan 8, 2025

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Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{1 + 2}}

hemiiI8675 Jan 8, 2025

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Algebra

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

hemiiI8675 Jan 8, 2025

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Algebra

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

hemiiI8675 Jan 8, 2025

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Logarithm

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

hemiiI8675 Jan 7, 2025

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Proportion

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

hemiiI8675 Jan 7, 2025

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Rate question

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

hemiiI8675 Jan 7, 2025

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Polynomials

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)?

hemiiI8675 Jan 7, 2025

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Algebra

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

hemiiI8675 Dec 28, 2024

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Algebra

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

hemiiI8675 Dec 28, 2024

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Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

hemiiI8675 Dec 28, 2024