43. Determine t, given that -14*t + p*t**2 + 196 = 0.
28
Let u(q) be the second derivative of -q**6/180 + q**5/12 + 7*q**4/6 - 14*q**3 + 128*q. Let l(b) be the second derivative of u(b). Let l(c) = 0. Calculate c.
-2, 7
Suppose 0 = 5*w - j - 29, -13*j - 36 = -4*w - 9*j. Let r be (w - 392/72)*(0 + -3). Determine g so that 0 - 2/3*g**2 - r*g = 0.
-2, 0
Let j(g) = -g**3 - 183*g**2 - 2040*g + 24274. Let s(t) = -183*t**2 - 2040*t + 24273. Let c(l) = 3*j(l) - 2*s(l). Factor c(k).
-3*(k - 7)*(k + 34)**2
Suppose 8*o = 384 - 368. Factor -15*r**2 + 12 + 9*r - 34*r + 11*r**o - 35*r + 79*r**2.
3*(5*r - 2)**2
Suppose 1 = -36*y + 73. Find c such that 5*c**2 + c**3 - 6*c**y + 4*c**2 + c**2 = 0.
-4, 0
Let c = 82369/18 - 4576. Let v(n) be the third derivative of -1/6*n**6 + 5/36*n**4 - c*n**7 + 0 + 0*n + 0*n**3 - 1/12*n**5 + 2*n**2. Factor v(b).
-5*b*(b + 1)**2*(7*b - 2)/3
Let a(x) be the first derivative of -2*x**3/15 + 5322*x**2/5 - 14161842*x/5 + 1840. Solve a(y) = 0.
2661
Let g(f) = 43*f**2 + 5*f - 3. Suppose -m - m - 8 = -5*d, 0 = 5*m - 5. Let j(a) = 44*a**2 + 2*a - 2. Let r(x) = d*g(x) - 3*j(x). Factor r(i).
-2*i*(23*i - 2)
Factor 105*p - 63*p**4 - 25*p**3 + 83 + 7 + 58*p**4 - 5*p**2.
-5*(p - 2)*(p + 1)*(p + 3)**2
Let h = -22 - 118. Let z be ((-12)/(-10))/((-6)/h). Solve 25*q**5 - 18*q**3 - 3*q - z*q**5 + 12*q**4 + 7*q**2 + 5*q**2 = 0 for q.
0, 1
Solve 728/5 + 1/5*f**2 - 729/5*f = 0.
1, 728
Let l(y) = y**2 + 35*y**2 + 34*y + 0*y + 8*y**3 + 18. Let a(g) = -15 - 8*g**3 - 36*g**2 - 269*g - 2 + 234*g. Let r(i) = 6*a(i) + 5*l(i). What is j in r(j) = 0?
-3, -1, -1/2
Let l(m) be the third derivative of -81*m**6/280 + 522*m**5/35 + 467*m**4/56 + 13*m**3/7 - 269*m**2. Find k such that l(k) = 0.
-1/9, 26
Let g(l) = -l**3 - 2. Let b(a) be the second derivative of a**5/10 + a**4/3 + a**3/3 + 2*a**2 + 188*a. Let v(h) = -b(h) - 4*g(h). Find i, given that v(i) = 0.
-1, 1, 2
Suppose -30 = y + 2*y - 5*g, 40 = -4*y - 2*g. Let z be (y/(-8) - 3/(-12))*6. Factor -3 + 0*p - z*p**2 - 67*p**3 + 64*p**3 - 11*p + 2*p.
-3*(p + 1)**3
Let b(s) be the second derivative of -s**7/168 + s**6/15 - 3*s**5/16 - s**4/6 + 2*s**3/3 + 78*s + 12. Let b(j) = 0. Calculate j.
-1, 0, 1, 4
Let r(o) be the third derivative of o**8/336 + o**7/35 + 13*o**6/120 + o**5/5 + o**4/6 + 16*o**2 + 4. Factor r(y).
y*(y + 1)**2*(y + 2)**2
Suppose 0 = -2*p - 12, 125 = 4*w - 15*p + 19*p + 137. Determine f, given that 0 + 10/7*f**w - 32/7*f**2 + 6/7*f = 0.
0, 1/5, 3
Let q(l) be the first derivative of -l**5/60 - l**4/18 + l**3/18 + l**2/3 + 28*l + 11. Let p(r) be the first derivative of q(r). Let p(v) = 0. Calculate v.
-2, -1, 1
Let c(m) be the third derivative of -9*m**8/112 + 479*m**7/70 + 1379*m**6/40 + 1173*m**5/20 + 85*m**4/4 - 56*m**3 - 2*m**2 + 259*m. Let c(k) = 0. What is k?
-1, 2/9, 56
Let n be (-155)/((-281945)/(-232404)) - -128. Let f be (-2)/8 - 25/(-68). Let 4/17*p + 0 + f*p**2 - n*p**3 - 2/17*p**4 = 0. What is p?
-2, -1, 0, 1
Let n = -47244 + 47284. Suppose n + 2/5*p**2 + 8*p = 0. What is p?
-10
Let c(u) be the first derivative of 4*u**5/15 + u**4/4 - 17*u**3/9 - 2*u**2 + 4*u/3 - 5110. Suppose c(s) = 0. What is s?
-2, -1, 1/4, 2
Let l = 408 - 406. Let m be l/(-3)*7 - (-1 + -5). Factor 3*h - 5/3 - m*h**2.
-(h - 1)*(4*h - 5)/3
Let m(n) be the first derivative of -n**9/9072 - n**8/840 - n**7/280 + 5*n**3/3 + 5*n**2/2 + 72. Let t(k) be the third derivative of m(k). Solve t(r) = 0 for r.
-3, 0
Let w(q) be the first derivative of -q**4/3 + 220*q**3/9 + 76*q**2 - 3693. Factor w(i).
-4*i*(i - 57)*(i + 2)/3
Let m(d) = -d**3 + d**2 + 5*d + 3. Let c be m(-5). Suppose 12 = c*u - 122*u. Factor 1/2*q + 0 - 2*q**u.
-q*(4*q - 1)/2
Let w be (3 - -7) + (-78)/9. Suppose -z = 5*z - 48. Factor w + 11/3*i**2 - z*i.
(i - 2)*(11*i - 2)/3
Let w(n) = 5 - 15*n**2 - 2 - 6*n - 6. Let p(u) = -u**3 + u**2 - u + 1. Let t(v) = -3*p(v) - w(v). Factor t(b).
3*b*(b + 1)*(b + 3)
Suppose r - 3*r = -5*k + 155, -k = r - 31. Suppose 0 = v - 5*w + 1, -2*w + 18 = 35*v - k*v. Factor 1/3*z**2 + 1/3*z - 1/3*z**v + 0 - 1/3*z**3.
-z*(z - 1)*(z + 1)**2/3
Suppose -g - 13 = 2*h, 2*h - 2*g = 5*h + 18. Let i be (-4)/6*(h - -5). Determine k so that -2*k**3 - i*k**3 + 2*k**3 + 8*k - 52*k**2 + 48*k**2 + 16 = 0.
-2, 2
Suppose -37 = -11*n - 21 + 39. Let t(w) be the third derivative of 0 - 1/30*w**6 + 0*w + 1/3*w**4 + 8*w**2 + 0*w**3 - 1/15*w**n. What is q in t(q) = 0?
-2, 0, 1
Let z be (-672)/160 - 1415/(-325). Let 6/13 + z*i - 12/13*i**2 + 2/13*i**5 - 4/13*i**3 + 6/13*i**4 = 0. What is i?
-3, -1, 1
Suppose 0 = -2*t + 5*g - 26 - 5, -g = 1. Let h be (20/(-6))/((-42)/t - 3). Factor 5*w**5 - h*w**4 - 55*w - 30*w**3 + 70*w**2 + 2 - 4 + 17.
5*(w - 1)**4*(w + 3)
Suppose -29265*a + 4962*a**2 - 15000 + 9*a**4 - 1739*a**2 - 519*a**3 + 1401*a**2 + 4427*a**2 - 12660*a = 0. What is a?
-1/3, 8, 25
Let d(b) = -3*b**3 + 7*b**2 + 43*b + 53. Let t(v) = 5*v**3 - 9*v**2 - 62*v - 80. Let x(p) = -8*d(p) - 5*t(p). Solve x(w) = 0 for w.
-6, -4, -1
Suppose 5*s - 2*r + 2762 = -4*r, -3*s + r = 1655. Let o = 555 + s. Find p, given that 3/4*p**4 + 3 - 3*p + 3/2*p**o - 9/4*p**2 = 0.
-2, 1
Factor -1012/17*j + 0 + 2/17*j**2.
2*j*(j - 506)/17
Let z be 3/(-1)*170/15. Let t = z - -106/3. Factor -2/3*h**2 + t - 2/3*h.
-2*(h - 1)*(h + 2)/3
Let h(n) = 7*n**2 - 30*n + 144. Suppose -2*z + 4*v = 22, 37*v - 41*v - 69 = 5*z. Let m(g) = 15*g**2 - 61*g + 288. Let b(y) = z*h(y) + 6*m(y). Factor b(k).
-(k - 12)**2
Let t(n) = n**3 + n**2 + n. Let h = 18 + 24. Let i(c) = 42 - 3*c - h - 3*c**2. Let s(g) = -i(g) - 3*t(g). Suppose s(u) = 0. What is u?
0
Let p(g) be the third derivative of -1/20*g**5 - 86*g**2 + 0 - g - 1/40*g**6 + 1/4*g**4 + 0*g**3. Factor p(v).
-3*v*(v - 1)*(v + 2)
Let n = 1441 + -1443. Let m be 3/3*n*(7 + -8). Solve 3*o**m - 6*o**3 + 0*o**4 + 9/2*o + 3/2*o**5 - 3 = 0 for o.
-2, -1, 1
Let f(c) = 2*c**3 - 6*c**2 + 13*c - 9. Let h be f(4). Suppose 0*x = -5*x + h. Solve -x*m**3 - 30*m**3 + 2*m**5 - 7*m**5 + 35*m**2 + 25*m**4 - 10*m = 0.
0, 1, 2
Suppose u + 90 = 94. Suppose -u*r**3 - 14*r**2 + 4 - 28 - 4*r**4 + 42*r**2 + 4*r = 0. What is r?
-3, -1, 1, 2
Suppose -187 - 225 = 4*f + 3*l, -3*l - 206 = 2*f. Let p = f + 106. Factor p*b**2 + 16*b**2 + b - 9*b**2 - b**3 - 10.
-(b - 10)*(b - 1)*(b + 1)
Let f(z) be the first derivative of -z**5/5 - 29*z**4/2 - 365*z**3/3 - 196*z**2 + 816*z + 4276. Suppose f(i) = 0. What is i?
-51, -4, 1
Factor 1404/7 + 136/7*v**2 - 2/7*v**3 - 1538/7*v.
-2*(v - 54)*(v - 13)*(v - 1)/7
Let 12/5*z**4 - 2/5*z**5 + 0 - 8*z**2 + 24/5*z + 6/5*z**3 = 0. Calculate z.
-2, 0, 1, 6
Let h be (-30)/3 - 39696/(-3840). Let w(s) be the third derivative of 0 + 17*s**2 + 1/6*s**3 + 3/8*s**4 + 0*s + h*s**5. Determine z, given that w(z) = 0.
-2/9
Let g(v) = 3481920*v**2 + 14916*v + 24. Let d(w) = -9*w**2 - 3*w + 2. Let c(x) = 4*d(x) - g(x). Let c(r) = 0. What is r?
-2/933
Let p(f) be the third derivative of f**7/1260 - 13*f**6/144 + 83*f**5/120 - 307*f**4/144 + 61*f**3/18 - 2*f**2 + 2*f - 129. Factor p(r).
(r - 61)*(r - 2)*(r - 1)**2/6
Let c(f) be the third derivative of f**6/30 + 10*f**5/3 + 389*f**4/6 - 880*f**3/3 + 8*f**2 + 18. Factor c(v).
4*(v - 1)*(v + 11)*(v + 40)
Find i, given that -1/3 + 1/6*i**3 - 2/3*i**2 + 5/6*i = 0.
1, 2
Let c(r) be the second derivative of r**5/15 - 2*r**4/3 + 57*r**2/2 - r - 4. Let y(f) be the first derivative of c(f). Factor y(u).
4*u*(u - 4)
Let x(o) be the third derivative of -o**7/525 - o**6/150 + 14*o**5/75 + 26*o**4/15 + 32*o**3/5 + 4*o**2 - 9*o. Determine l so that x(l) = 0.
-4, -2, 6
Let f(k) = k**3 - 42*k**2 + 39*k + 86. Let o be f(41). Suppose 12*v**2 - 5*v**2 - 11*v**2 - o - 172*v + 180 = 0. What is v?
-44, 1
Let q be 15/156 - (6021/(-351) + 17). Factor -q*z**5 - 9/4*z - 3/2*z**4 - 1/2 - 4*z**2 - 7/2*z**3.
-(z + 1)**4*(z + 2)/4
Let s(m) be the third derivative of m**7/1155 - m**6/60 - 7*m**5/66 + 129*m**4/44 + 270*m**3/11 - 2*m**2 + 130*m + 3. What is r in s(r) = 0?
-5, -2, 9
Factor -9 - 32*g**2 - 4*g**3 + 91 + 236*g - 178 - 216.
-4*(g - 3)*(g - 2)*(g + 13)
What is u in -117/2*u + 230 + 1/4*u**2 = 0?
4, 230
Suppose 3*h + h - l - 29 = 0, 0 = -2*h - 2*l + 12. Suppose 0 = -51*d + 107 + 148. Suppose -6*x**3 - h*x**4 + 3*x**3 + 4 + 8*x - d*x**3 + 3*x**4 = 0. What is x?
-1, 1
Let v = 11216 - 33623/3. Let p(r) be the second derivative of 0 - 5*r**2 - 2