e the second derivative of k(a). Suppose t(u) = 0. Calculate u.
0, 2, 3
Let u(r) be the second derivative of -r**4/4 - 1573*r**3/6 + 525*r**2 + 2*r + 9772. Factor u(z).
-(z + 525)*(3*z - 2)
Let d(u) be the third derivative of u**5/60 - 51*u**4/8 + 76*u**3/3 + 1373*u**2. Determine g, given that d(g) = 0.
1, 152
Let s(i) = i**2 + 13*i + 15. Let p be s(-12). Factor -3*f**4 + 21*f**5 - 11*f**3 - 9*f**2 - 18*f**5 - 4*f**p.
3*f**2*(f - 3)*(f + 1)**2
Solve -1/7*l**2 - 198/7 + 39/7*l = 0 for l.
6, 33
Let t be (16/6)/((-600)/(-900)). Let v(j) be the first derivative of 0*j**2 + 1/6*j**3 + 0*j + 1/10*j**5 - 1/4*j**t - 20. Factor v(z).
z**2*(z - 1)**2/2
Let y(f) = f**2 + 18*f + 86. Let j be y(-13). Let z be (32/(-56))/((-54)/j). Factor 2/9*q**3 + z + 2/3*q + 2/3*q**2.
2*(q + 1)**3/9
Let h(b) be the third derivative of -b**7/140 + 5*b**6/4 - 573*b**5/10 - 650*b**4 - 2704*b**3 + b**2 + 379*b. Suppose h(o) = 0. Calculate o.
-2, 52
Let t(r) be the second derivative of r**7/2520 - 23*r**6/2160 - r**5/45 + r**4/12 - 3*r**2/2 - 30*r - 1. Let a(l) be the third derivative of t(l). Factor a(w).
(w - 8)*(3*w + 1)/3
Let i(v) be the first derivative of v**5/480 + 5*v**4/192 - 6*v**2 - 2*v + 140. Let c(x) be the second derivative of i(x). Solve c(m) = 0 for m.
-5, 0
Factor 420*j - 68334*j**2 - 612 + 68331*j**2 + 195.
-3*(j - 139)*(j - 1)
Let h be (13800/(-315))/46*42/(-45). Suppose 20/9*u**4 - 4/9*u**3 + h*u**5 - 28/9*u**2 + 8/9 - 4/9*u = 0. Calculate u.
-2, -1, 1/2, 1
Let g(f) = -4*f + 44. Let r be g(10). Suppose 2*j + 21*j**5 + 760*j**r - 782*j**4 + 24*j**2 - j - 22*j**3 - 2 = 0. What is j?
-1, -2/7, 1/3, 1
Let v(u) = 1080*u - 11825. Let h be v(11). Solve 5*d**3 - 15 - h*d**2 - 235/4*d = 0.
-1/2, 12
Let m = -937/7326 - -285/814. What is x in 1352/9 + m*x**2 - 104/9*x = 0?
26
Let y(g) be the second derivative of 1/100*g**5 + 3 - 1/30*g**3 - 10*g + 1/5*g**2 + 1/150*g**6 - 1/20*g**4. Suppose y(s) = 0. What is s?
-2, -1, 1
Let j(k) be the second derivative of 3/2*k**2 + 111*k - 17/80*k**5 - 1/40*k**6 + 1/168*k**7 - 3/16*k**4 + 0 + 2/3*k**3. Find p such that j(p) = 0.
-2, -1, 1, 6
Suppose 24*h - 30 = 29*h. Let j(m) = -27*m**3 - 54*m**2 - 3*m + 12. Let v(i) = 2*i**2. Let r(q) = h*v(q) - j(q). Solve r(w) = 0.
-1, 4/9
Let w(x) be the third derivative of -5/18*x**3 + 55*x**2 + 1/12*x**4 - 1/180*x**5 + 0 + 0*x. Factor w(k).
-(k - 5)*(k - 1)/3
Let u(q) be the first derivative of q**4/84 + 29*q**3/21 - 3*q - 32. Let h(t) be the first derivative of u(t). Solve h(g) = 0 for g.
-58, 0
Suppose -6*c - 6 = -9*c. Let x(j) = 38*j - j**c - 62*j + 5 - 2*j**2. Let n(t) = -2*t**2 - 12*t + 2. Let y(p) = -11*n(p) + 6*x(p). Solve y(v) = 0.
1, 2
Suppose -5*q = -3*h, 27*h - 5*q = 30*h. Let k(v) be the third derivative of 1/15*v**5 + 1/60*v**6 + 0 - 20*v**2 + h*v + 0*v**3 - 1/4*v**4. Factor k(z).
2*z*(z - 1)*(z + 3)
Factor 32/5*s - 78/5 - 2/5*s**2.
-2*(s - 13)*(s - 3)/5
Suppose -r + 3*w + 22 = 0, -5*r + 3*r = 3*w - 17. Suppose -5*q + r - 3 = 0. Factor k**3 - 3*k**4 + 0*k**2 + 3*k**5 - 4*k**3 + 4*k**2 - k**q.
3*k**2*(k - 1)**2*(k + 1)
Factor 48/7*x**2 + 0*x + 32/7*x**3 + 0 + 4/7*x**4.
4*x**2*(x + 2)*(x + 6)/7
Let x(d) = d**3 + 4*d**2 - 10*d. Let f be x(-5). Let 13*s + f*s**4 - 7*s - 3*s**2 + 3*s**5 - 22*s**4 - 9*s**3 = 0. Calculate s.
-2, -1, 0, 1
Let b(k) be the first derivative of -4*k**5/5 + 4*k**3/3 + 2547. Suppose b(a) = 0. Calculate a.
-1, 0, 1
Let f(c) be the first derivative of -c**2/2 - 5*c + 3. Let i be f(-7). Let 40*g - 20*g + 22*g**2 + 23*g**i + 5*g**3 + 55*g - 125 = 0. What is g?
-5, 1
Suppose 0 = 18*d - 42 - 12. Find k, given that 12*k**2 - 44*k**5 + 16*k - 23*k**2 - 19*k**2 - 10*k**2 - 190*k**4 - 228*k**d = 0.
-2, -1/2, 0, 2/11
Let a(b) be the first derivative of b**6/135 - b**4/54 - 173*b - 74. Let g(p) be the first derivative of a(p). Determine y, given that g(y) = 0.
-1, 0, 1
Let o(d) be the third derivative of -d**5/540 + 137*d**4/216 - 5*d**3 + 59*d**2 + 5. Factor o(q).
-(q - 135)*(q - 2)/9
Let c(a) be the second derivative of -1/96*a**4 + 0 - 16*a**2 + 20*a - 2/3*a**3. Factor c(w).
-(w + 16)**2/8
Suppose -389*x = 581*x - 1940. Let 12*o**x + 28/3 - 20*o - 4/3*o**3 = 0. What is o?
1, 7
Let z(p) be the first derivative of -2*p**5/35 + 201*p**4/14 - 796*p**3/21 + 8971. Factor z(x).
-2*x**2*(x - 199)*(x - 2)/7
Let a(f) = -67*f**2 - 10176*f - 359537. Let p(g) = -100*g**2 - 15264*g - 539304. Let x(i) = -8*a(i) + 5*p(i). Factor x(b).
4*(3*b + 212)**2
Let j be (-28981)/(-1679) - (-2 - -19). Let p(h) be the first derivative of j*h**2 - 2/69*h**3 + 25 - 18/23*h. Factor p(q).
-2*(q - 3)**2/23
Let a = -7179 + 7181. Let m(x) be the first derivative of -1/2*x**3 + 3/2*x + a + 0*x**2. Solve m(b) = 0 for b.
-1, 1
Let j(w) be the second derivative of -2 - 5/38*w**4 - 49/19*w**2 + 21/19*w**3 + 1/190*w**5 + 3*w. Factor j(k).
2*(k - 7)**2*(k - 1)/19
Factor 25/2 + 15/4*s**3 - 10*s**2 - 5/4*s.
5*(s - 2)*(s + 1)*(3*s - 5)/4
Let p = -57/43 - -5515/4128. Let t(o) be the third derivative of 0*o**3 - 14*o**2 - 1/240*o**5 + 0*o + 0 - p*o**4. Factor t(a).
-a*(a + 1)/4
Solve 1/4*c**5 + 108*c + 0 - 35/4*c**4 + 69*c**2 - 11*c**3 = 0.
-2, 0, 3, 36
Let b = -28686 - -28688. Factor 3/2*m + 45/4 - 3/4*m**b.
-3*(m - 5)*(m + 3)/4
Let t be (-1 - -4)/(4/124). Factor 5*l**2 + 5*l**3 - t*l + 93*l.
5*l**2*(l + 1)
Let g be ((-3591)/(-1470) - (-4)/70)*(-8)/(-250). Let a(t) be the first derivative of 0*t - 3/5*t**2 - 1/10*t**4 - 2/3*t**3 - 7 + g*t**5. What is p in a(p) = 0?
-1, 0, 3
Let k(t) be the third derivative of 1849*t**6/24 - 3053*t**5/4 - 715*t**4/8 - 25*t**3/6 + t**2 + 1794*t + 2. Let k(b) = 0. Calculate b.
-1/43, 5
Suppose -4*s = -3*s - 2. Let -10*v + 19*v**2 + 9*v**3 - 10*v**s - 5*v**3 + 9*v**2 = 0. Calculate v.
-5, 0, 1/2
Factor -176*g - 4500*g + 300*g + 4*g**2 + 1196836.
4*(g - 547)**2
Let v(a) be the first derivative of a**6/5 - 96*a**5/25 + 117*a**4/5 - 224*a**3/5 + 147*a**2/5 + 689. Factor v(p).
6*p*(p - 7)**2*(p - 1)**2/5
Suppose 0 + 244/23*n - 2/23*n**3 + 242/23*n**2 = 0. Calculate n.
-1, 0, 122
Let y(a) be the third derivative of 0 + 0*a + 169/36*a**4 + 1/540*a**6 + 13/90*a**5 - 5/3*a**3 + 2*a**2. Let v(r) be the first derivative of y(r). Factor v(q).
2*(q + 13)**2/3
Let m(r) = -14*r**4 - 7*r**3 + 140*r**2 + 73*r - 30. Let v(j) = -15*j**4 - 5*j**3 + 140*j**2 + 75*j - 30. Let h(l) = 5*m(l) - 6*v(l). Find q such that h(q) = 0.
-2, -1, 1/4, 3
Let i(p) = 5*p - 39. Let q be i(14). Let g be 0 + (q - (4 + 0)). Factor -40*h + 14*h**5 + 4 - 5*h**4 - 2*h**3 + g*h**3 + 16 - 19*h**5 + 5*h**2.
-5*(h - 1)**3*(h + 2)**2
Let q(u) = -3*u**2 - 443*u - 9772. Let y be q(-27). Let k = 26/7 + -253/70. Solve 0 - k*z**4 - 4/5*z**y - 7/10*z**3 + 8/5*z = 0 for z.
-4, 0, 1
Let u(z) = -13*z**3 + 43*z**2 + 475*z + 452. Let g(n) = -n**3 - n**2 + n + 4. Let t(f) = -22*g(f) + 2*u(f). What is h in t(h) = 0?
-6, -1, 34
Let p be (24 - 7) + -1 - 1. Suppose 5 = -14*q + p*q. Find d such that 0 - 5/6*d**q + 0*d + 0*d**3 + 0*d**2 - 5/6*d**4 = 0.
-1, 0
Let j(h) be the first derivative of -h**4/2 + 52*h**3/3 - 109*h**2 + 168*h + 2818. Factor j(d).
-2*(d - 21)*(d - 4)*(d - 1)
Let -32610*q**3 - 49265*q + 320 + 14145*q - 207195*q**3 + 967980*q**2 = 0. Calculate q.
4/219, 4
Let v(s) = -s**5 - 14*s**4 + 39*s**3 + 24*s**2 - 132*s + 80. Let i(q) = -2*q**4 - q**3 + 2*q**2. Let j(m) = 4*i(m) - v(m). Let j(p) = 0. Calculate p.
-10, -2, 1, 4
Let t(l) = -68*l**3 - 61*l**2 - 1294*l - 1229. Let k(w) = 228*w**3 + 182*w**2 + 3880*w + 3686. Let p(d) = -3*k(d) - 10*t(d). Factor p(m).
-4*(m - 28)*(m + 1)*(m + 11)
Let g(o) be the third derivative of -o**6/120 - 219*o**5/20 - 4510*o**4 - 53792*o**3/3 - 2678*o**2 + 1. Determine s, given that g(s) = 0.
-328, -1
Let f be (-2 - (-12)/42)*574/(-1845). Factor 0 + 32/15*c - 48/5*c**2 - f*c**4 + 22/5*c**3.
-2*c*(c - 4)**2*(4*c - 1)/15
Determine h, given that 525/4*h + 387/4 + 141/4*h**2 + 3/4*h**3 = 0.
-43, -3, -1
Suppose 0 = 4*t - 4*v + 4, -5*t = 18*v - 19*v - 15. Let d be (t/13)/((-780)/(-1014)). Let 0 + 2/15*p**5 + 0*p**2 + 0*p - d*p**3 - 4/15*p**4 = 0. What is p?
-1, 0, 3
Let y = 717 - 717. Let n be y/((-25)/(-8 + 13)). Solve -2/7*t**2 + n - 4/7*t = 0 for t.
-2, 0
Suppose -2*t = -k - 1, -4*t = -9*k + 4*k + 1. Let n(m) = -m**3 - m - 2. Let r(q) = q**3 + 21*q**2 + 31*q + 11. Let z(c) = t*r(c) - 2*n(c). Factor z(l).
3