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nathanl6656
Username
nathanl6656
Score
200
Membership
Stats
Questions
47
Answers
14
47 Questions
14 Answers
0
1
0
+200
Algebra
Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?
nathanl6656
9 hours ago
0
1
2
+200
Algebra
Let f(x) = \sqrt{x}
Find the largest three-digit value of x such that f(x) is an integer.
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nathanl6656
Aug 27, 2024
0
1
1
+200
Algebra
Compute
\frac{1}{1 \times 4} + \frac{1}{7 \times 10}
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nathanl6656
Aug 27, 2024
0
1
1
+200
Algebra
Let a be a real number such that a - \frac{1}{a} = 4 + a^2 + \frac{1}{a^2}. Compute a^3 - \frac{1}{a^3}.
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nathanl6656
Aug 27, 2024
0
2
1
+200
Probability
The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain
read more ..
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nathanl6656
Aug 9, 2024
0
3
1
+200
Counting
The entries in a certain row of Pascal's triangle are
1, n, \dots, n, 1.
The average of the entries in this row is 2. Find $n$.
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nathanl6656
Aug 9, 2024
0
4
0
+200
Number Theory
Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.
nathanl6656
Jul 5, 2024
0
7
0
+200
Number Theory
Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.
nathanl6656
Jul 5, 2024
0
8
0
+200
Number Theory
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 $a$.
nathanl6656
Jul 5, 2024
0
7
0
+200
Number Theory
How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{10}?$
nathanl6656
Jul 5, 2024
0
4
0
+200
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 ..
nathanl6656
Jul 5, 2024
0
7
0
+200
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?
nathanl6656
Jul 5, 2024
0
7
0
+200
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?
nathanl6656
Jul 5, 2024
0
8
0
+200
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?
nathanl6656
Jul 5, 2024
0
4
0
+200
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?
nathanl6656
Jul 5, 2024
0
3
1
+200
Graphing
Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.
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nathanl6656
Jun 13, 2024
0
5
1
+200
Geometry
Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.
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nathanl6656
Jun 13, 2024
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