All Questions ⁺⁰236340 Questions

0

16

3

+911

Algebra

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

magenta Jun 24, 2024

0

19

1

+911

Algebra

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

magenta Jun 24, 2024

-1

16

1

+331

Number Theory

Determine all positive integers that have exactly 8 positive divisors.

Stanry Jun 24, 2024

-1

19

1

+331

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $7$ pieces of candy per scoop to the vat, and another machine that can remove exactly $6$ pieces of candy with a different scoop from read more ..

Stanry Jun 24, 2024

-1

19

1

+331

Number Theory

As shown in class, the Euclidean algorithm can be used to find solutions to equations of the form
\[ax + by = c.\]
Use the Euclidean algorithm to find integers $x$ and $y$ such that $5x + 2y = 1,$ with the smallest possible positive read more ..

Stanry Jun 24, 2024

-1

16

1

+331

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.
When read more ..

Stanry Jun 24, 2024

-1

12

1

+331

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

NotThatSmart ●

Stanry Jun 24, 2024

0

24

1

+1379

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $10$ positive divisors, $n$ has exactly $16$ positive divisors, and $mn$ has exactly $21$ positive divisors. How many divisors does $m^2 n^2$ have?

learnmgcat Jun 24, 2024

0

17

1

+1379

Number Theory

Let $M$ be the least common multiple of $1,$ $2,$ $\dots,$ $12$, $13$, $14$, $15$, $16$. How many positive divisors does $M$ have?

learnmgcat Jun 24, 2024

0

15

0

+1379

Number Theory

Let $m$ and $n$ be positive integers. If $m$ has exactly $10$ positive divisors, $n$ has exactly $16$ positive divisors, and $mn$ has exactly $21$ positive divisors. How many divisors does $m^2 n^2$ have?

learnmgcat Jun 24, 2024

0

12

2

+1379

Number Theory

Let $m$ be a positive integer. If $m$ has exactly $18$ positive divisors, then how many positive divisors does $m^2$ have?

learnmgcat Jun 24, 2024

0

18

1

+1839

Counting

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

ABJeIIy Jun 24, 2024

0

15

0

+1379

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

learnmgcat Jun 24, 2024

0

26

0

+1379

Counting

In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable boxes, if at least three of the boxes must be empty?

learnmgcat Jun 24, 2024

0

32

0

+1379

Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

learnmgcat Jun 24, 2024

0

21

0

+1839

Number Theory

Let $m$ and $n$ be positive integers such that $m$ has exactly $8$ positive divisors, $n$ has exactly $6$ positive divisors, and $mn$ has exactly $12$ positive divisors. What is the smallest possible value of $mn?$

ABJeIIy Jun 24, 2024

0

26

0

+1839

Number Theory

Let $m$ be a positive integer such that $m$ has exactly $8$ positive divisors. How many distinct prime factors does $m$ have?

ABJeIIy Jun 24, 2024

0

17

0

+1577

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

parmen Jun 24, 2024

0

35

0

+1577

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

parmen Jun 24, 2024

0

29

0

+1577

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

parmen Jun 24, 2024

0

33

0

+1577

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

parmen Jun 24, 2024

0

16

2

+63

Polynomial Problem!

The polynomial

has one integer root. What is it?

MeldHunter Jun 24, 2024

0

18

0

+2653

Algebra

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$

LiIIiam0216 Jun 24, 2024

0

11

1

+2653

Algebra

All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

LiIIiam0216 Jun 24, 2024

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