instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is the thousands digit of 923459?\n | 3\n | ibivibiv/math_instruct | |
Expand 0*t - t + 3*t + (-1 - 3 + 2)*(0 + 0 - 2*t) + 3*t + 0*t - 5*t + (3030 + 5332 - 25 + 1830)*(2*t - 2*t + t)*(1 - 4 + 2).\n | -10163*t\n | ibivibiv/math_instruct | |
Determine g, given that g**5/3 + 13*g**4/3 - 69*g**3 + 539*g**2/3 + 206*g/3 - 184 = 0.\n | -23, -1, 1, 4, 6\n | ibivibiv/math_instruct | |
How many minutes are there between 6:37 AM and 3:04 PM?\n | 507\n | ibivibiv/math_instruct | |
Let y(z) = -4*z**3 - 3*z**2 + 2*z - 1. Let s(h) = -17*h**3 - 13*h**2 + 9*h - 5. Let m(d) = 2*d**2 - 75*d - 40. Let j be m(38). What is j*s(w) + 9*y(w)?\n | -2*w**3 - w**2 + 1\n | ibivibiv/math_instruct | |
Suppose k = 5, -2*w + 2*k + 6 = -0. Suppose 0 = -3*c - w - 31. Let o = -10 - c. Solve f + 3*g - 8 = 0, -f - 2 = -4*g - o for f.\n | 5\n | ibivibiv/math_instruct | |
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"# General Cartesian/Rectangular Equation for Polar Rose ($r=\sin(k\theta)$)
How do I convert the Polar Equation $r=\sin(k \theta)$ to Cartesian Equation?
I understand that $r^2=x^2+y^2$ and that $x=r\cos\theta$ and $y=r\sin... | Let us begin by reviewing the conversion between polar coordinates $(r, θ)$ and rectangular coordinates $(x, y)$. The relationships between these coordinate systems are given by:
1. $r^2 = x^2 + y^2$
2. $x = r \cos θ$
3. $y = r \sin θ$
These formulas allow us to switch between polar and rectangular representations o... | ibivibiv/math_instruct | |
Let u = -9371.3 + 9371. What is the second biggest value in -0.2, 5, 26, u?\n | 5\n | ibivibiv/math_instruct | |
How many kilograms are there in 7/8 of a tonne?\n | 875\n | ibivibiv/math_instruct | |
What is 547 minutes before 8:50 PM?\n | 11:43 AM\n | ibivibiv/math_instruct | |
Let z be (3 + (-84)/18)/((-3)/(-9)). Let d(i) = 45*i. Let b(o) = -15*o. Let s(j) = -11*b(j) - 4*d(j). List the prime factors of s(z).\n | 3, 5\n | ibivibiv/math_instruct | |
-0.1 times -0.2242\n | 0.02242\n | ibivibiv/math_instruct | |
Let t be 1 - (5 - 1)/4. Let i be (-1 + t)*(4 - (-78)/2). Let d = -6 - i. What is the units digit of d?\n | 7\n | ibivibiv/math_instruct | |
Four letters picked without replacement from jakakfalalklkkk. Give prob of sequence aafj.\n | 1/2730\n | ibivibiv/math_instruct | |
Solve -40 + 25 = 3*j for j.\n | -5\n | ibivibiv/math_instruct | |
Let j(z) be the second derivative of 0*z**4 + 3/2*z**3 + 0*z**2 + 0 - 18*z - 3/5*z**5. Find the second derivative of j(d) wrt d.\n | -72*d\n | ibivibiv/math_instruct | |
What is the thousands digit of (4643002/455)/(2/5)?\n | 5\n | ibivibiv/math_instruct | |
Let i be (-474)/(-10) + (-16)/40. Solve -6*z + i = 17 for z.\n | 5\n | ibivibiv/math_instruct | |
Solve -3*m - 162*q + 335*q - 195*q = 365, 40 = 2*m - 2*q for m.\n | 3\n | ibivibiv/math_instruct | |
Let m(h) = 1960498*h**2 - 2*h + 4. Let q be m(-2). What is q rounded to the nearest one million?\n | 8000000\n | ibivibiv/math_instruct | |
What is the closest to 2051 in -4, -3, 0.5, 6/7, 1/3?\n | 6/7\n | ibivibiv/math_instruct | |
Let l(i) = i**2 - 1. Let b(n) = 24*n**2 + 40*n + 6. Let h be (2 + (-36)/15)/(1/15). Let j(t) = h*l(t) - b(t). Find the second derivative of j(c) wrt c.\n | -60\n | ibivibiv/math_instruct | |
Let y(b) = -3434*b - 31190. Give y(-9).\n | -284\n | ibivibiv/math_instruct | |
What is (-60)/(7 - 3)*-52*(-60)/3120?\n | -15\n | ibivibiv/math_instruct | |
What is the third derivative of 30841*q**3 - 31416*q**2 wrt q?\n | 185046\n | ibivibiv/math_instruct | |
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. What is the sum? | Let's denote the sum as \( P \), the rate of interest as \( r \) (in percentage per annum), and the time as \( t \) (in years).
The formula for simple interest (SI) is:
\[ SI = \frac{P \cdot r \cdot t}{100} \]
The formula for true discount (TD) is:
\[ TD = \frac{P \cdot r \cdot t}{100 + (r \cdot t)} \]
Given that \(... | ibivibiv/math_instruct | |
Calculate the remainder when 43519 is divided by 1635.\n | 1009\n | ibivibiv/math_instruct | |
Let g = 78/11 + -590/77. Which is the nearest to -0.1? (a) g (b) 2 (c) 0.2\n | c\n | ibivibiv/math_instruct | |
Let s = 2.7 + -3.1. Let y = -35 + 38. What is the nearest to 1/4 in s, -5, y?\n | s\n | ibivibiv/math_instruct | |
Is 334237 composite?\n | True\n | ibivibiv/math_instruct | |
Let d = -8 + 37. Suppose 2*p - 63 + d = 0. Is 11 a factor of p?\n | False\n | ibivibiv/math_instruct | |
Let j = 12.06 + -0.06. Let h = -15 + j. Let d = h + 4. Sort -0.2, d, 0.2 in descending order.\n | d, 0.2, -0.2\n | ibivibiv/math_instruct | |
What is 50 minutes after 5:06 PM?\n | 5:56 PM\n | ibivibiv/math_instruct | |
What is the second derivative of 2*c*f**2*i + 199*c*f*i + c*f - 102*c*i + 6267159*f**2*i wrt f?\n | 4*c*i + 12534318*i\n | ibivibiv/math_instruct | |
Does 84 divide 309329534?\n | False\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {m: 1, r: 2, a: 1, q: 2, x: 10}. Give prob of sequence rx.\n | 1/12\n | ibivibiv/math_instruct | |
Sort 5, 444, -2 in decreasing order.\n | 444, 5, -2\n | ibivibiv/math_instruct | |
Let g(s) = -2*s**2 - 11*s - 25. Let u(h) = -h**2 - 3*h - 12. Let q(j) = -2*g(j) + 5*u(j). Calculate q(4).\n | 2\n | ibivibiv/math_instruct | |
What is (84/(-525))/((-2)/(-15))*795/(-1272)?\n | 3/4\n | ibivibiv/math_instruct | |
Find the common denominator of -83/10605 and -44/174225.\n | 1219575\n | ibivibiv/math_instruct | |
Let t = 69 - 63.6. Let g = -5.3 + t. What is the third biggest value in 1/3, -2/11, g, -5?\n | -2/11\n | ibivibiv/math_instruct | |
Let p(x) = 3*x**3 - 73*x**2 - 49*x - 8. Let s be p(25). Which is the closest to -7/3? (a) -2/21 (b) s (c) 2 (d) 0\n | a\n | ibivibiv/math_instruct | |
Let g = 20.1 - 20. What is the closest to g in -0.2, 5, -1/4?\n | -0.2\n | ibivibiv/math_instruct | |
Let q(z) = z**3 - 11*z**2 - 2*z - 6. Let w be q(9). Let h = 131 - w. Is h prime?\n | True\n | ibivibiv/math_instruct | |
Let t = 0.014 + 0.045. Let k = 0.281 + t. Round k to 2 decimal places.\n | 0.34\n | ibivibiv/math_instruct | |
Put 3/2, -13098, 2.8 in ascending order.\n | -13098, 3/2, 2.8\n | ibivibiv/math_instruct | |
What is 7/15 of a minute in seconds?\n | 28\n | ibivibiv/math_instruct | |
Simplify ((j/j**(2/7)*j)**(-1/16)/(((j**(2/7)/j)/j)/j*j*j**(-3/7)*j*j))/(j*((j**(2/9)*j)/j*j)/j*j*j/(j**(4/7)/j)*j*(j**0)**(-11/7)) assuming j is positive.\n | j**(-1163/252)\n | ibivibiv/math_instruct | |
What is the eighth root of 22514 to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
Rearrange 17 - 3*c + 59*c**4 - 36*c**4 - 25*c**2 - 26*c**4 + c**3 - 18 to p*c**3 + t*c**4 + a + h*c**2 + l*c and give a.\n | -1\n | ibivibiv/math_instruct | |
What is prob of picking 3 o when three letters picked without replacement from oocpoccpc?\n | 1/84\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 0.027 (b) -12 (c) -0.4 (d) 164\n | d\n | ibivibiv/math_instruct | |
How many kilograms are there in five quarters of a tonne?\n | 1250\n | ibivibiv/math_instruct | |
What comes next: 17, 26, 27, 20, 5?\n | -18\n | ibivibiv/math_instruct | |
Let j = -1.2 - -1. Let d be 10/(-35)*7/3. Which is smaller: d or j?\n | d\n | ibivibiv/math_instruct | |
What is the third derivative of -6*j**4 + 3591064*j**3 - 5571*j**2 - 24195 wrt j?\n | -144*j + 21546384\n | ibivibiv/math_instruct | |
Is ((-1)/(-2))/(9070/9068 - 1) a composite number?\n | False\n | ibivibiv/math_instruct | |
b"What is the nth term of 72498641, 72498639, 72498637, 72498635, 72498633?\n" | -2*n + 72498643\n | ibivibiv/math_instruct | |
Evaluate ((-2)/4)/((-3010)/6880).\n | 8/7\n | ibivibiv/math_instruct | |
Let t(s) = 2*s**2. Let q(l) be the second derivative of -l**3/2 + 36*l**2 - 1056*l + 3. Determine q(t(j)).\n | -6*j**2 + 72\n | ibivibiv/math_instruct | |
Which is the closest to -96? (a) 2 (b) 5 (c) -10 (d) -0.5\n | c\n | ibivibiv/math_instruct | |
Let h = -24 + 15. Let x = -336 + 189. Let j = 148 + x. Which is the nearest to 2/3? (a) -2/3 (b) j (c) h\n | b\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 13237 and 60109.\n | 217\n | ibivibiv/math_instruct | |
Calculate prob of picking 3 n when three letters picked without replacement from {n: 7, s: 3}.\n | 7/24\n | ibivibiv/math_instruct | |
Suppose -3*w + 2*w = 5*d - 4213, 0 = 2*d - 5*w - 1696. Suppose 5*i = 5*f - 1045, 4*f + 2*i = -i + d. Suppose -5*v = -f - 35. Does 17 divide v?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 433*o**2 - 11284*o**2 - 3598*o**2 + 955*o**2.\n | -13494*o**2\n | ibivibiv/math_instruct | |
Suppose -8*i + 3*s = -13*i + 82, -3*i + 62 = 5*s. Solve 2*v - 5*v = -x - i, -5*v = -15 for x.\n | -5\n | ibivibiv/math_instruct | |
Suppose -4*n = 4*y - 128, y - 6 = -y. Let u = -7 + n. Is u a multiple of 6?\n | False\n | ibivibiv/math_instruct | |
Which is smaller: 169231 or 169230?\n | 169230\n | ibivibiv/math_instruct | |
b"What is the ath term of 34, 89, 180, 307, 470?\n" | 18*a**2 + a + 15\n | ibivibiv/math_instruct | |
4875 (base 10) to base 6\n | 34323\n | ibivibiv/math_instruct | |
What is prob of picking 1 a and 1 g when two letters picked without replacement from {n: 1, y: 1, g: 1, a: 1, f: 1, u: 2}?\n | 1/21\n | ibivibiv/math_instruct | |
What is the nearest to 4 in 2, -0.04, -5, 1/37?\n | 2\n | ibivibiv/math_instruct | |
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"Home » Math Theory » Trigonometry » Law of Sines
Law of Sines
• define the Law of Sines;
• know the history of Law of Sines;
• prove the Law of Sines;
• determine the ambiguous case of triangle solutions; and
• apply the kn... | The Law of Sines is a fundamental principle in trigonometry used for solving triangles. Specifically, this theorem applies to non-right (oblique) triangles, which do not contain a right angle. To understand the significance of the Law of Sines, let's explore its definition, history, proof, applications, and potential ... | ibivibiv/math_instruct | |
Convert -2415056 (base 7) to base 13.\n | -a9790\n | ibivibiv/math_instruct | |
In base 14, what is 79dd - 10?\n | 79cd\n | ibivibiv/math_instruct | |
Sort -2, -57, -1036, 574 in decreasing order.\n | 574, -2, -57, -1036\n | ibivibiv/math_instruct | |
What is 323 minutes before 8:27 PM?\n | 3:04 PM\n | ibivibiv/math_instruct | |
Solve -9 = g - 7*s, 4*g + 642*s = 639*s + 26 for g.\n | 5\n | ibivibiv/math_instruct | |
Simplify (1*(-2*sqrt(352) + sqrt(352))*3)/(sqrt(128)*-3 - (sqrt(36)/sqrt(3))/sqrt(6)).\n | 12*sqrt(11)/25\n | ibivibiv/math_instruct | |
What are the prime factors of 796?\n | 2, 199\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-57.1446 * -79.4311 | 4539.0584 | ibivibiv/math_instruct | |
Collect the terms in -18*x - 29*x + 15*x - 44*x.\n | -76*x\n | ibivibiv/math_instruct | |
Convert -12013220 (base 5) to base 10.\n | -110435\n | ibivibiv/math_instruct | |
Suppose 0 = -2*r + n + 13, -r - 3*r = -4*n - 36. Let u(l) = -l**3 + 3*l**2 + 4*l - 1. Let o be u(r). Sort -4, o, -3.\n | -4, -3, o\n | ibivibiv/math_instruct | |
Convert -5 (base 15) to base 16.\n | -5\n | ibivibiv/math_instruct | |
Let p(l) = -2*l + 5. Let u(f) be the third derivative of f**4/12 + 764*f**2. What is u(p(s))?\n | -4*s + 10\n | ibivibiv/math_instruct | |
Express -7*f**2 - 73*f + 73*f + 2 as b*f**2 + n + o*f and give b.\n | -7\n | ibivibiv/math_instruct | |
Find the third derivative of 31138*f**4 - 67*f**3 - 1705352*f**2 - 8.\n | 747312*f - 402\n | ibivibiv/math_instruct | |
What are the prime factors of 731?\n | 17, 43\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 6038525?\n | 3\n | ibivibiv/math_instruct | |
Suppose 11*f - 59 = 6*f - 2*h, 2*f - 26 = -2*h. What is the remainder when 175 is divided by f?\n | 10\n | ibivibiv/math_instruct | |
What is the value of ((-99)/(-132))/(3/(-16))?\n | -4\n | ibivibiv/math_instruct | |
b"What is the ath term of -498, -477, -428, -339, -198, 7, 288, 657?\n" | 2*a**3 + 2*a**2 + a - 503\n | ibivibiv/math_instruct | |
b"What is the zth term of -7619, -15237, -22853, -30467?\n" | z**2 - 7621*z + 1\n | ibivibiv/math_instruct | |
Let i(t) = -1004*t**3 + 559*t**2 + 8*t. Let q(m) = -3012*m**3 + 1676*m**2 + 22*m. Let a(d) = 11*i(d) - 4*q(d). What is the third derivative of a(g) wrt g?\n | 6024\n | ibivibiv/math_instruct | |
Let h(r) = r**3 - 120*r**2 + 2*r - 1661. Determine h(0).\n | -1661\n | ibivibiv/math_instruct | |
What is the product of -1 and -22134?\n | 22134\n | ibivibiv/math_instruct | |
List the prime factors of 34352.\n | 2, 19, 113\n | ibivibiv/math_instruct | |
Is 28463 prime?\n | True\n | ibivibiv/math_instruct |
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