hat is k?
31
Let b(a) be the first derivative of -5*a**6/12 + 83*a**5/40 - 35*a**4/16 + a**3/24 + 3*a**2/8 + 1580. What is v in b(v) = 0?
-1/4, 0, 2/5, 1, 3
Let q = 2/33815 + 338144/101445. Let d(v) be the second derivative of v**5 + 32*v - 1/15*v**6 + 0*v**2 - q*v**3 + 1/6*v**4 + 0. Factor d(s).
-2*s*(s - 10)*(s - 1)*(s + 1)
Let c be (-568)/(-11360) - 2*(-1)/10. Let y be (-1 + 2/4)/(-1). Solve -y - 1/4*s**4 - c*s**3 + 1/4*s + 3/4*s**2 = 0 for s.
-2, -1, 1
Factor -52*x**2 + 2079*x + 1/3*x**3 - 11858/3.
(x - 77)**2*(x - 2)/3
Let z = 84 - 86. Let s be (-17 - -15)/(0 - (3 + z)). Factor 3/8*c**s - 3/8*c**3 + 3/8*c - 3/8.
-3*(c - 1)**2*(c + 1)/8
Let c(p) be the third derivative of p**6/280 + 3*p**5/70 - 9*p**4/14 + 20*p**3/7 - 220*p**2 - p. What is j in c(j) = 0?
-10, 2
Let t(s) be the second derivative of 0*s**3 - 7/100*s**5 - 1/30*s**6 - 1/210*s**7 + 0 + 0*s**2 + 88*s - 1/20*s**4. Factor t(z).
-z**2*(z + 1)**2*(z + 3)/5
Let -5 + 14 + 12*b - 24*b**3 + 6*b**2 - 163*b**5 + 6*b**4 + 166*b**5 + 9*b - 21 = 0. What is b?
-4, -1, 1
Suppose -24*k + 5 = 4*j - 23*k, -3*j + k = -30. Let 14/3*y + j - 1/3*y**2 = 0. What is y?
-1, 15
Let x(l) be the second derivative of l**5/5 + 40*l**4/3 + 248*l**3 + 2016*l**2 - l + 694. Determine a, given that x(a) = 0.
-28, -6
Let y(m) be the third derivative of 1/4*m**3 - 1/720*m**6 + 28*m**2 - 1/360*m**5 + 0*m + 1/16*m**4 + 0. Solve y(a) = 0 for a.
-3, -1, 3
Suppose -d - 4*n = -2, d - 5*n - 15 = -13. Factor -2*s**d + 228*s - 2708 - 1900 - 36*s.
-2*(s - 48)**2
Let m = -509634 + 509638. Solve 81/7*s**m - 198/7*s**3 - 32/7 + 40*s - 572/7*s**2 = 0 for s.
-2, 2/9, 4
Suppose 3*w = -4*o + 313, -5*o - 17*w + 420 = -19*w. Factor -116*r**4 + 64*r**4 + 55*r**4 - 65*r - o*r - 57*r**3 + 48 + 153*r**2.
3*(r - 16)*(r - 1)**3
Let p(b) = -19*b - 74. Let o be p(-4). Factor -12*u**3 - 13*u**o + 20*u**3 + 4*u**4 - 32*u - 3*u**2.
4*u*(u - 2)*(u + 2)**2
Let u = 3723 + -3706. Let q(k) be the third derivative of -1/84*k**8 + u*k**2 + 0*k - 1/15*k**5 + 0*k**4 + 0*k**3 + 1/30*k**6 + 2/105*k**7 + 0. Factor q(v).
-4*v**2*(v - 1)**2*(v + 1)
Suppose -1 + 37 = 12*p. What is h in -h**2 + 3*h - 2*h**4 + 9*h**p + 7 + 19*h**2 + 24*h + 13*h**2 = 0?
-1, -1/2, 7
Let s(c) be the third derivative of c**8/336 + 11*c**7/525 + c**6/40 - 3*c**5/50 + 266*c**2 - 5. Let s(f) = 0. Calculate f.
-3, -2, 0, 3/5
Suppose -3*v + 2*v = -16*v. Let b(h) be the third derivative of 0 + 0*h - 9*h**2 - 1/420*h**7 + v*h**3 - 1/48*h**6 - 1/12*h**4 - 1/15*h**5. Factor b(l).
-l*(l + 1)*(l + 2)**2/2
Suppose -8 = k - 2*q - 19, 28 = -4*k - 10*q. Suppose 2/5*p**4 - 36/5*p**2 - 8*p - 8/5*p**k - 14/5 = 0. What is p?
-1, 7
Let m(b) be the first derivative of -2268*b - 508/21*b**3 + 1170*b**2 + 1/7*b**4 - 28. Let m(u) = 0. What is u?
1, 63
Let h = -58951 - -58953. Find i such that -33/2*i - 3/4*i**h + 69/4 = 0.
-23, 1
Let a(b) be the first derivative of -2*b**5/5 - 11*b**4 - 82*b**3/3 - 20*b**2 + 772. Factor a(g).
-2*g*(g + 1)**2*(g + 20)
Let d = -226 + 130. Let w be (-152)/d - (-10)/15. Determine o so that -w*o**4 + 3/4*o**5 + 0 + 9/4*o**2 + 3/4*o**3 - 3/2*o = 0.
-1, 0, 1, 2
Let a = 15363 - 261099/17. Let u = -33/68 + a. Find w such that -9/4 - 7/4*w**2 + u*w + 1/4*w**3 = 0.
1, 3
Determine s so that 757/4*s**2 + 1/4*s**3 + 142883/4*s - 143641/4 = 0.
-379, 1
Let d be 9/12 - 27/72 - (-7089)/136. Determine p, given that -42*p + d*p**3 - 49/6*p**4 - 149/3*p**2 - 20/3 = 0.
-2/7, 2, 5
Let j be 603/67 - (-1*1)/1. Let z(y) = 7*y**3 - y**2 - y - 5. Let a(t) = -3*t**3 + t**2 + 2. Let h(m) = j*a(m) + 4*z(m). Factor h(k).
-2*k*(k - 2)*(k - 1)
Let a(d) be the second derivative of 2 - 7/3*d**3 - 62*d - 49/2*d**2 - 1/12*d**4. Determine q, given that a(q) = 0.
-7
Let w = 121/19 - 529/95. Factor 2/5*j**5 + 2/5*j**4 + 2/5 - 4/5*j**3 + 2/5*j - w*j**2.
2*(j - 1)**2*(j + 1)**3/5
Let a = 70 + -69. Suppose 24 = -3*c + 9. Let h(b) = -b**2 - b - 1. Let v(n) = -3*n**2 + 35*n + 195. Let q(o) = a*v(o) + c*h(o). Factor q(m).
2*(m + 10)**2
Let p be ((-2)/14)/((-52)/(17472/72)). Let o(d) be the second derivative of -22*d - 1/15*d**6 + p*d**4 - 3*d**2 + 2/3*d**3 + 0 - 1/5*d**5. Factor o(c).
-2*(c - 1)**2*(c + 1)*(c + 3)
Let i be (-63)/((-81)/(-9)) - -4. Let c be i/15 + -3*219/(-135). Factor -c*u - 4 - 2/3*u**2.
-2*(u + 1)*(u + 6)/3
Let z(v) be the third derivative of -343*v**6/60 + 4067*v**5/20 - 48223*v**4/16 + 571787*v**3/24 - 2*v**2 - 2*v + 50. Determine i, given that z(i) = 0.
83/14
Let d(t) = 28*t**2 - 824*t + 3780. Let u(g) = 10*g**2 - 275*g + 1260. Let x(h) = -3*d(h) + 8*u(h). Factor x(w).
-4*(w - 63)*(w - 5)
Let l(f) be the second derivative of 35/6*f**3 - 69*f + 0 + 5/12*f**4 - 45*f**2. Factor l(q).
5*(q - 2)*(q + 9)
Suppose 12*m - 4*v + 56 = 16*m, 5*v = -21 + 81. Solve 2/7*w**3 - 4/7*w**m + 0 + 2/7*w = 0 for w.
0, 1
Let j = 55193/10 - 5519. Let f(u) be the second derivative of -j*u**3 + 3/5*u**2 + 1/20*u**4 + 0 - 9*u. Factor f(l).
3*(l - 2)*(l - 1)/5
Let t(j) be the third derivative of -j**5/80 + 167*j**4/32 + 868*j**2. Solve t(c) = 0.
0, 167
Let n(o) be the third derivative of -3/5*o**5 - 4*o**2 + 1 + 13/3*o**4 + 0*o - 16*o**3 + 1/30*o**6. Suppose n(i) = 0. Calculate i.
2, 3, 4
Let 0 - 271/2*b**4 + b + 271/2*b**2 + 267/2*b**3 - 269/2*b**5 = 0. What is b?
-1, -2/269, 0, 1
Let f(r) be the first derivative of -r**3/3 + 37*r**2/2 + 258*r - 6866. Let f(o) = 0. Calculate o.
-6, 43
Factor -816*m - 697 - 574 - 16*m**3 - 198 + 244*m**2 + 713.
-4*(m - 9)*(m - 7)*(4*m + 3)
Let l(h) be the second derivative of 2*h**7/21 + 2*h**6/5 - 18*h**5/5 - 18*h**4 + 54*h**3 + 486*h**2 - 3540*h. Factor l(b).
4*(b - 3)**2*(b + 3)**3
Suppose 2*h - 89 + 85 = 0. Let u be h/(-4) + 21/18. Factor -u*y + 0 - 1/6*y**2.
-y*(y + 4)/6
Let g(a) be the third derivative of 0 + 3/35*a**7 + 33/4*a**4 - 19/20*a**5 + 70*a**2 - 18*a**3 + 0*a - 33/80*a**6 - 1/224*a**8. Let g(i) = 0. Calculate i.
-2, 1, 6
Suppose 6*t - 5 = 7. Suppose 0 = -2*a - u + 2, -5*a = -t*a - 4*u - 14. Suppose 6 - a*v - 7 + 4*v - v**2 = 0. What is v?
1
Let h(p) = p**3 - 10*p**2 + 20*p + 15. Suppose -v + 0*d + 5 = -2*d, -4*v = 3*d - 31. Let z be h(v). Find l such that 1/2*l**3 - z + 4*l + 7/2*l**2 = 0.
-4, 1
Let y(n) be the first derivative of 0*n + 5/6*n**3 - 216 - 5/2*n**4 + 15/2*n**2 + 1/2*n**5. Determine d, given that y(d) = 0.
-1, 0, 2, 3
Let g(t) be the first derivative of 1/2*t**4 + 12/55*t**5 - 16/11*t + 1/33*t**6 + 4/33*t**3 - 24 - 12/11*t**2. Suppose g(i) = 0. What is i?
-2, -1, 1
Let j(l) = 22*l**3 + 499*l**2 + 523*l - 1107. Let m(r) = 5*r**3 + 126*r**2 + 131*r - 276. Let c(n) = 2*j(n) - 9*m(n). Factor c(o).
-(o - 1)*(o + 2)*(o + 135)
Let m(f) = 22*f**2 - 9902*f + 12330568. Let h(a) = -46*a**2 + 19801*a - 24661135. Let y(i) = -10*h(i) - 21*m(i). Let y(g) = 0. Calculate g.
2483
Let m(v) = v**3 - 13*v**2 + 19*v + 36. Let d be m(11). Let i(f) be the second derivative of 8/9*f**2 + 0 + 7*f - 8/27*f**d + 1/27*f**4. Factor i(l).
4*(l - 2)**2/9
What is j in 72*j**2 - 7960 - 76*j**2 - 3990*j - j**2 = 0?
-796, -2
Let s be (-24)/72*1/(-1). Let c(y) be the second derivative of 2*y**2 + 0 + 0*y**3 - 5*y - s*y**4. Find m such that c(m) = 0.
-1, 1
Let -313632/19 - 160/19*s**3 - 4784/19*s**2 - 63360/19*s - 2/19*s**4 = 0. What is s?
-22, -18
Let q(d) be the second derivative of d**7/1680 + d**6/90 + d**5/15 - 55*d**3/6 + 58*d. Let x(b) be the second derivative of q(b). Suppose x(i) = 0. What is i?
-4, 0
Let b(c) = -c - 5. Let a be b(-9). Suppose -4*l + a*j + 44 = 0, 8*l + 5*j - 25 = 3*l. Factor -w**3 + 4*w**2 + 0*w**3 - 4*w**4 + 9*w**3 - l*w.
-4*w*(w - 2)*(w - 1)*(w + 1)
Let n(r) be the third derivative of 1/21*r**4 + 0*r + 1/210*r**5 + r**2 - 5/21*r**3 - 5. Factor n(m).
2*(m - 1)*(m + 5)/7
Let y(c) be the first derivative of -c**4/2 - 43*c**3/2 - 120*c**2 - 56*c + 356. Factor y(z).
-(z + 4)*(z + 28)*(4*z + 1)/2
Suppose 2*r - h = -6*h + 16, -4 = 7*h - 5*h. Factor -r*n**2 - 11/3*n**3 - 14/3 - 41/3*n + 1/3*n**4.
(n - 14)*(n + 1)**3/3
Let x(v) be the first derivative of 676*v**3 + 6*v**5 - 819/8*v**4 - 1/8*v**6 - 6591/8*v**2 - 20 + 0*v. What is w in x(w) = 0?
0, 1, 13
Let l(s) = -26*s + 2137. Let h be l(82). Let o(p) be the first derivative of 8/9*p**4 + 20/3*p**3 + 25 + 200/9*p**2 + 250/9*p + 2/45*p**h. Factor o(v).
2*(v + 1)*(v + 5)**3/9
Let p = 413159/10 - 82315/2. Factor 968/5*n**4 + 16/