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^{+0}
233554 Questions
0
3
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+1234
Algebra
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 ..
blackpanther
Jul 8, 2024
0
3
0
+1234
Algebra
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 ..
blackpanther
Jul 8, 2024
0
3
1
+4
Help
solve the equation cos^2(x)-sin^2(x)=sin(x) given the domain (0,2pi]
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Gus123456
Jul 8, 2024
0
1
1
+1420
Algebra
In an arithmetic sequence, the 23rd term is $\frac{1}{4},$ and the $33$rd term is $-\frac{1}{5}$. What is the $43$rd term?
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ABJeIIy
Jul 8, 2024
+1
2
1
+1420
Algebra
A geometric sequence has 400 terms. The first term is 1000 and the common ratio is -\frac{8}{9}$ How many terms of this sequence are greater than 1?
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ABJeIIy
Jul 8, 2024
0
2
0
+1420
Algebra
If x and y are positive integers for which 3x + 2y + xy = 115 + 11x + 2y, then what is x + y?
ABJeIIy
Jul 8, 2024
0
3
0
+1420
Algebra
Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.
ABJeIIy
Jul 8, 2024
0
1
0
+1230
Algebra
Let x and y be complex numbers. If x + y = 2 and xy = 5 - x^2 - y^2, then what is x^2 + y^2?
kittykat
Jul 8, 2024
0
2
1
+1230
Algebra
Let a and b be complex numbers. If a + b = 4 and a^2 + b^2 = 6 + ab, then what is a^3 + b^3?
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kittykat
Jul 8, 2024
0
3
1
+1230
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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kittykat
Jul 8, 2024
0
3
1
+1230
Algebra
Compute
\frac{1}{1 \times 4} + \frac{1}{7 \times 10}
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kittykat
Jul 8, 2024
0
2
1
+174
Counting
Catherine rolls a standard $3$-sided die six times. If the product of her rolls is $600,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)
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cooIcooIcooI17
Jul 8, 2024
0
2
0
+174
Counting
In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving at least four pieces each?
cooIcooIcooI17
Jul 8, 2024
0
1
0
+174
Counting
In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?
cooIcooIcooI17
Jul 8, 2024
0
3
0
+1230
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}.
kittykat
Jul 8, 2024
0
3
1
+1230
Algebra
Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)
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kittykat
Jul 8, 2024
0
3
1
+1230
Algebra
Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$
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kittykat
Jul 8, 2024
0
2
0
+1230
Algebra
Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.
kittykat
Jul 8, 2024
Jul 7, 2024
0
2
0
+174
Number Theory
Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim
read more ..
cooIcooIcooI17
Jul 7, 2024
0
2
0
+174
Number Theory
What are the first $5$ digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{17}$ is written in base $16$?
(Express your answer as a five digit hexadecimal number. You do not need to
read more ..
cooIcooIcooI17
Jul 7, 2024
0
1
1
+174
Number Theory
Jon teaches a fourth grade class at an elementary school where class sizes are always at least $20$ students and at most $60$. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately
read more ..
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cooIcooIcooI17
Jul 7, 2024
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