instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let h be ((-30)/(-25))/((-1)/10). Let k(r) = -9*r - 13. Is k(h) prime?\n | False\n | ibivibiv/math_instruct | |
Simplify 3*(1*sqrt(2448) + 2 + sqrt(2448) + (0 + 1*sqrt(2448) - sqrt(2448))**2 + sqrt(2448)) + (1 + sqrt(612) + 1 + 1)*6.\n | 24 + 144*sqrt(17)\n | ibivibiv/math_instruct | |
If the area of a square plot of land is 325 square meters, what is the perimeter of the square in simplest radical form, measured in meters? | If the area of a square is 325 square meters, then the length of each side is $\sqrt{325}=5\sqrt{13}$
The perimeter of a square is four times the length of one side, so the perimeter of this square is $4(5\sqrt{13})=\boxed{20\sqrt{13}}$ meters.
The answer is: 20\sqrt{13} | ibivibiv/math_instruct | |
Add together 0.088864 and 1713.\n | 1713.088864\n | ibivibiv/math_instruct | |
Calculate -0.3248991 - 25280.\n | -25280.3248991\n | ibivibiv/math_instruct | |
Let i be 1/2 - (-987)/14. Suppose -2*f + 169 + i = 0. What are the prime factors of (2/6)/(10/f)?\n | 2\n | ibivibiv/math_instruct | |
Which is the closest to 171? (a) -3/4 (b) 0 (c) -2811\n | b\n | ibivibiv/math_instruct | |
Let y be (2 + -2 - -61) + 4. Let k be (-2)/(-5)*y/26. What is the remainder when (-4)/(-12)*k*39 is divided by 4?\n | 1\n | ibivibiv/math_instruct | |
Sort 49, 5, 19, -13461 in ascending order.\n | -13461, 5, 19, 49\n | ibivibiv/math_instruct | |
Sort 31, -671, 23, 12 in descending order.\n | 31, 23, 12, -671\n | ibivibiv/math_instruct | |
Calculate 65632 divided by 6.\n | 32816/3\n | ibivibiv/math_instruct | |
What is the next term in -14, -2, 24, 70, 142, 246?\n | 388\n | ibivibiv/math_instruct | |
What is the next term in 0, 11, 12, -9, -64?\n | -165\n | ibivibiv/math_instruct | |
Calculate -4 - (12 + -16 - -1).\n | -1\n | ibivibiv/math_instruct | |
Which is the closest to -0.59? (a) -117146 (b) 4 (c) -0.3\n | c\n | ibivibiv/math_instruct | |
4569 divided by -4569\n | -1\n | ibivibiv/math_instruct | |
Let v(i) = -i**2 - 6*i + 2. Let a be 4/6*-3*3. Let p be v(a). Suppose 0 = -2*q + 3*k + p*k + 26, 0 = -q - 2*k - 5. List the prime factors of q.\n | 3\n | ibivibiv/math_instruct | |
Solve -z - 5*s = -8, -7 = 4*z - 2*s + 5 for z.\n | -2\n | ibivibiv/math_instruct | |
Suppose 0 = 2*u, -14 = -b - b + u. Calculate the remainder when 20 is divided by b.\n | 6\n | ibivibiv/math_instruct | |
Let s = -81537/10 + 8150. Find the common denominator of -68/9 and s.\n | 90\n | ibivibiv/math_instruct | |
Suppose -w + 0 = -2. Let k(s) = -4*s**w + 27*s - 27*s. Let p(i) = 5*i**2. Determine p(k(l)).\n | 80*l**4\n | ibivibiv/math_instruct | |
Solve -113*p - 735 = -8*p for p.\n | -7\n | ibivibiv/math_instruct | |
Put -296/7, -2, 1/11, 1291, -4/5 in ascending order.\n | -296/7, -2, -4/5, 1/11, 1291\n | ibivibiv/math_instruct | |
Let u(r) = -r**3 + 14*r**2 - 18*r + 50. Let p be u(13). Let b(c) = -c**2 + 7*c + 10. Let x be b(8). Sort p, x, 0, -1.\n | p, -1, 0, x\n | ibivibiv/math_instruct | |
Suppose 2*p = -2*p. Let f(g) be the second derivative of 2/3*g**3 + 2*g**2 + 4*g + 1/12*g**4 + p. Solve f(u) = 0.\n | -2\n | ibivibiv/math_instruct | |
What is 704 minutes before 5:50 PM?\n | 6:06 AM\n | ibivibiv/math_instruct | |
Let l = 17 + -27. Let u = l - -14. Let w be (20/(-6))/(u/12). Is -11 at most as big as w?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = 5*l + 4*p - p - 944, -4*l = -2*p - 764. Let c = l - 14. What are the prime factors of c?\n | 2, 11\n | ibivibiv/math_instruct | |
List the prime factors of 3202822.\n | 2, 7, 228773\n | ibivibiv/math_instruct | |
Let x = 2 + -3. Suppose -5*r + 7 + 8 = -5*b, 3*r - 4*b = 8. Let w(v) = v**3 - 5*v**2 - 6*v + 1. Let a be w(6). What is the smallest value in x, r, a?\n | x\n | ibivibiv/math_instruct | |
Let j(m) be the first derivative of m**2/2 - 13*m - 14. Give j(6).\n | -7\n | ibivibiv/math_instruct | |
Expand (3 - 2*y**2 - 3)*(-4*y**2 + 3*y**2 - y**2) + 39*y**4 - 33*y**4 + 69*y**4.\n | 79*y**4\n | ibivibiv/math_instruct | |
Let m = 5 - 0. Let p(d) = 2*d - 5. Calculate the least common multiple of p(3) and m.\n | 5\n | ibivibiv/math_instruct | |
Round -0.000008202233 to 6 decimal places.\n | -0.000008\n | ibivibiv/math_instruct | |
Find the third derivative of 34*q**2 - 6*q**2 - 768*q**4 + 20*q - 213*q**4 - 6*q**2 wrt q.\n | -23544*q\n | ibivibiv/math_instruct | |
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"# Fourier Series with Complex Exponentials
In my Signals and Systems class, we learned that the Fourier Series of a signal $x(t)$ is given by
$$x(t) = \sum_{k = -\infty}^{\infty} X_k e^{ik\omega_0t}$$
where $\omega_0 = 2\p... | Let's delve into your questions regarding the Fourier Series with Complex Exponentials. I will provide detailed explanations for better comprehension.
Firstly, you may wonder why the summation in the Fourier Series includes both positive and negative values (from k=−∞ to k=∞), instead of only non-negative values (fro... | ibivibiv/math_instruct | |
Let v = 19 - -24. What is the tens digit of (-1)/(v/(-14) + 3)?\n | 1\n | ibivibiv/math_instruct | |
Let d = 0.0541 + -0.0539642. What is d rounded to 5 decimal places?\n | 0.00014\n | ibivibiv/math_instruct | |
Solve 103*g = 1586 + 1504 for g.\n | 30\n | ibivibiv/math_instruct | |
Simplify x**(-2/7)/x**(-4/17)*(x/x**(7/10))/((x*x**(-24))/x) assuming x is positive.\n | x**(28857/1190)\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 270 and 5990.\n | 10\n | ibivibiv/math_instruct | |
Let n be ((-6)/5)/(6*7/(-20)). Is -3/7 smaller than n?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common factor of 4146 and 16350?\n | 6\n | ibivibiv/math_instruct | |
11.697 times -1\n | -11.697\n | ibivibiv/math_instruct | |
What is prob of sequence ob when two letters picked without replacement from {i: 3, b: 5, o: 3, a: 6}?\n | 15/272\n | ibivibiv/math_instruct | |
What is the smallest value in -781/4, -1/2, -9923?\n | -9923\n | ibivibiv/math_instruct | |
Collect the terms in -c**2 - c**2 + 29 - 51 + 23 + 27*c + 7*c**2.\n | 5*c**2 + 27*c + 1\n | ibivibiv/math_instruct | |
What is 20335658.5 rounded to the nearest 10000?\n | 20340000\n | ibivibiv/math_instruct | |
Let a be (-6)/(-24) + 94/8. Let o be (-6501)/2*(-8)/a. Suppose 3*n = -4*p + o, -2684 = -5*p - 5*n + 26. Is p a prime number?\n | True\n | ibivibiv/math_instruct | |
What is the nearest to 158.07 in -10/3, 2/7, 4, 1/3?\n | 4\n | ibivibiv/math_instruct | |
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"Lemma 4.18.3. Let $\mathcal{C}$ be a category. The following are equivalent:
1. Nonempty finite limits exist in $\mathcal{C}$.
2. Products of pairs and equalizers exist in $\mathcal{C}$.
3. Products of pairs and fibre prod... | Category theory is a branch of mathematics that deals with abstract structure and relationships between mathematical objects. One important concept in category theory is the idea of a limit, which generalizes familiar ideas from set theory such as products and intersections. This lemma discusses three different condit... | ibivibiv/math_instruct | |
Let g be (-4)/18*-6*9/2. Sort -3, g, -4, -5 in decreasing order.\n | g, -3, -4, -5\n | ibivibiv/math_instruct | |
Put 1, -3, 303, -1 in descending order.\n | 303, 1, -1, -3\n | ibivibiv/math_instruct | |
Let p(k) = -2*k + 12. Let j(q) be the second derivative of -43*q**4/12 - 5*q - 280. Calculate j(p(b)).\n | -172*b**2 + 2064*b - 6192\n | ibivibiv/math_instruct | |
35+-584348601983\n | -584348601948\n | ibivibiv/math_instruct | |
What is the thousands digit of 28514 - (7/14*-6 + 4)?\n | 8\n | ibivibiv/math_instruct | |
Four letters picked without replacement from xxaxaxxaxa. What is prob of sequence xaaa?\n | 1/35\n | ibivibiv/math_instruct | |
Simplify -2*-2*(sqrt(1216)*2 + 3) - (sqrt(2299) - 4*((sqrt(2299) + -1 + sqrt(2299) - sqrt(2299)) + sqrt(2299)) - (sqrt(2299) + 0 + 5))**2.\n | -147125 - 112*sqrt(19)\n | ibivibiv/math_instruct | |
What is (1 - 7 - 4) + (-356 + 341 - (0 - -1))?\n | -26\n | ibivibiv/math_instruct | |
What is the value of (1 - -11)*(-13 + 324/24)?\n | 6\n | ibivibiv/math_instruct | |
How many minutes are there between 5:14 PM and 10:45 PM?\n | 331\n | ibivibiv/math_instruct | |
Total of -219.6348638 and 3914.6.\n | 3694.9651362\n | ibivibiv/math_instruct | |
What is the units digit of 41845?\n | 5\n | ibivibiv/math_instruct | |
How many millilitres are there in 51/5 of a litre?\n | 10200\n | ibivibiv/math_instruct | |
Express n**2 - 2*n**2 + 2*n**2 + (13 + 4*n - 13 - 6*n + 2*n + 3*n + (n - 3 + 3)*(-3 + 4 + 1) + n + 2*n - 2*n)*(29 - 64 + n + 31) as z*n + i + s*n**2 and give s.\n | 7\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 880 and 19277060.\n | 220\n | ibivibiv/math_instruct | |
What is the hundred millions digit of 274559087?\n | 2\n | ibivibiv/math_instruct | |
List the prime factors of 1811155777.\n | 1811155777\n | ibivibiv/math_instruct | |
Let w = -63 - -193. What is the hundreds digit of w?\n | 1\n | ibivibiv/math_instruct | |
What is the smallest number of states a Deterministic Finite Automata (DFA) must have to accept the language given by the regular expression (a + b)*abb? | The smallest number of states a Deterministic Finite Automata (DFA) must have to accept the language given by the regular expression (a + b)*abb is 5 states.
Here's an explanation:
1. The initial state (q0) represents that no characters have been read yet. From this state, if an 'a' is read, the DFA moves to state q1... | ibivibiv/math_instruct | |
Let h(p) = -p**2. Let l(k) = 2*k**2 - 8*k + 4. Let g(b) = -3*h(b) - l(b). Let n be g(-9). Put n, 3, 0 in descending order.\n | n, 3, 0\n | ibivibiv/math_instruct | |
Let t be 9/6*(-16)/6. Let k be 0 + (-737)/t - (-24)/32. Let q = 321 - k. What is the hundreds digit of q?\n | 1\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 11300 and 26000.\n | 100\n | ibivibiv/math_instruct | |
Suppose -4*v = -94 + 14. Suppose -s - s = -v. What is the lowest common multiple of s and 34/5 + (-2)/(-10)?\n | 70\n | ibivibiv/math_instruct | |
Let d(n) = -2*n**3 + 26*n**2 - 4*n + 53. What is d(13)?\n | 1\n | ibivibiv/math_instruct | |
Let b(w) = w - 1. Suppose 0*s + 10 = 2*s + 2*t, -t = -5*s + 19. Let r(m) = 3*m - 5. Suppose -6*l = -1 + 7. Let x = -2 - l. What is s*b(z) + x*r(z)?\n | z + 1\n | ibivibiv/math_instruct | |
Simplify (sqrt(38)/(-2*sqrt(2)))**2 + 0.\n | 19/4\n | ibivibiv/math_instruct | |
What are the prime factors of 1904080338?\n | 2, 3, 35260747\n | ibivibiv/math_instruct | |
Let d(f) = -f**2 + 87*f + 458. What is d(92)?\n | -2\n | ibivibiv/math_instruct | |
Let t(q) be the second derivative of q**9/252 + q**5/60 + q**2/2 - 5*q. Let n(h) be the first derivative of t(h). Find the third derivative of n(p) wrt p.\n | 240*p**3\n | ibivibiv/math_instruct | |
Let w = -0.04 - 1.96. Let p = w - -2.01. Let i = -39889 - -39892. Which is the nearest to 2? (a) i (b) p (c) 0.3\n | a\n | ibivibiv/math_instruct | |
Expand (-4*p + 5 + 8*p - 3*p)*(-1 + 1 - p)*(-4*p + p + 0*p).\n | 3*p**3 + 15*p**2\n | ibivibiv/math_instruct | |
Express (s**2 - 2*s**2 + 2*s**2 + (2 - 5 + 1)*(2*s**2 + s - s))*(5212 + 33*s - 5212) in the form o*s**3 + m*s + z + q*s**2 and give o.\n | -99\n | ibivibiv/math_instruct | |
Is 4273343 composite?\n | False\n | ibivibiv/math_instruct | |
Suppose 73 = 5*s - 152. Suppose -s = -3*l + 54. What is the units digit of l?\n | 3\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) -1 (b) 2/13 (c) 4 (d) 0.4\n | a\n | ibivibiv/math_instruct | |
What is 5938353 to the power of 1/3, to the nearest integer?\n | 181\n | ibivibiv/math_instruct | |
Expand 4*k - 5*k + 0*k + (-2*k + 2 - 2)*(-5 + 4 + 3).\n | -5*k\n | ibivibiv/math_instruct | |
Suppose 0 = c - 5 + 2. Suppose 13*m - c*m = 4*m. Solve -25 = -m*s + 5*s for s.\n | -5\n | ibivibiv/math_instruct | |
Simplify s**11*s/s**(-6)*((s/s**1*s)/s*s)**(-25) assuming s is positive.\n | s**(-7)\n | ibivibiv/math_instruct | |
Let z(c) = 3*c**3 + 18. Let x be z(0). Let l(u) = 6*u - 13. What is the tens digit of l(x)?\n | 9\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 1, w: 3, m: 11}. What is prob of sequence ywm?\n | 11/910\n | ibivibiv/math_instruct | |
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"# How to find the number of real roots for a polynomial?
How can you find of real roots for $$P(x) = x^4 - 4x^3 + 4x^2 - 10$$?
Using the Descartes' rule of signs:
The polynomial $$P(x) = x^4 - 4x^3 + 4x^2 - 10$$ has three ... | The Descartes' Rule of Signs is a useful tool in finding the maximum possible numbers of positive and negative real roots of a polynomial equation. However, there are some nuances to the rule that must be taken into account in order to avoid misinterpretations, as demonstrated in the provided example. This discussion ... | ibivibiv/math_instruct | |
Let u be 2/7 - 4104/(-532). Solve 4*c + 2*i + 6 = -4, 0 = c - 5*i + u for c.\n | -3\n | ibivibiv/math_instruct | |
What is 5126241 to the power of 1/2, to the nearest integer?\n | 2264\n | ibivibiv/math_instruct | |
What is the closest to -0.057 in -1, -1.2, -149?\n | -1\n | ibivibiv/math_instruct | |
Let j = 293 - 94. What are the prime factors of j?\n | 199\n | ibivibiv/math_instruct | |
Let d = 146 + -67. Suppose 4 + 38 = 2*w. What is the remainder when d is divided by w?\n | 16\n | ibivibiv/math_instruct | |
Let h = 40/317 - -79752/11095. Let y be 234/(-30) - 2/(-10). Let m = h + y. Which is greater: m or 1?\n | 1\n | ibivibiv/math_instruct | |
Divide 295991 by 1111.\n | 295991/1111\n | ibivibiv/math_instruct |
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