alculate j.
1
Let p(r) be the second derivative of -r**4/30 + 52*r**3/5 + 316*r**2/5 - 252*r. Factor p(b).
-2*(b - 158)*(b + 2)/5
Let p(q) be the second derivative of -q**4/18 - 14*q**3 + 127*q**2/3 - 6109*q. Factor p(x).
-2*(x - 1)*(x + 127)/3
Let a = 56629/3 - 282929/15. Factor 1536/5*f - 576/5*f**2 + 0 + a*f**3 - 3/5*f**4.
-3*f*(f - 8)**3/5
Let a(k) be the second derivative of -k**4/8 + 1099*k**3/4 - 1647*k**2/2 + 4099*k. Factor a(r).
-3*(r - 1098)*(r - 1)/2
Let -20*v**2 - 9*v**4 + 32/3 - 56/3*v + 42*v**3 = 0. What is v?
-2/3, 2/3, 4
Suppose -3*s - 3*t = 444, -s - 4*t + 437 = -4*s. Let j be 6 + 8/(280/s). Let -3/5*i**4 - 12/5*i + 12/5*i**3 - j*i**2 + 12/5 = 0. Calculate i.
-1, 1, 2
Let z(s) be the first derivative of 6*s**2 + 0*s**3 + 3/20*s**5 - 3/4*s**4 - 22*s - 4. Let n(h) be the first derivative of z(h). Suppose n(q) = 0. Calculate q.
-1, 2
Find b such that -447/4*b**2 + 63/2*b**4 + 51/4*b**3 + 9 - 84*b = 0.
-3/2, -1, 2/21, 2
Let d(r) be the second derivative of 0*r**2 + 11/6*r**3 + 1/6*r**5 + 0 + 23*r + 0*r**4 - 1/90*r**6. Let n(x) be the second derivative of d(x). Factor n(c).
-4*c*(c - 5)
Let f(z) be the second derivative of z**6/120 - 11*z**5/80 - 43*z**4/24 + 4*z**3 + 3*z - 550. Find j such that f(j) = 0.
-6, 0, 1, 16
Factor -68/9*y**2 + 2450/9 + 1/9*y**3 + 1085/9*y.
(y - 35)**2*(y + 2)/9
Let c(r) = -r**5 + r**3 - r**2 - 5*r + 1. Let x(n) = 10*n**5 + 28*n**4 - 158*n**3 + 348*n**2 - 228*n - 12. Let q(b) = -12*c(b) - x(b). Factor q(t).
2*t*(t - 4)**2*(t - 3)**2
Let d(v) = v**3 - 11*v**2 - 5*v + 23. Let u be d(8). Let l = 211 + u. Factor 4/3*a - 1/3*a**l - 1.
-(a - 3)*(a - 1)/3
Let t(d) be the second derivative of 3/2*d**2 - 1/10*d**6 + 5 + 0*d**4 - d**3 + 3/10*d**5 + 5*d. Determine a, given that t(a) = 0.
-1, 1
Factor 0*d + 0 + 0*d**2 + 10/3*d**3 + 4/9*d**4 - 2/9*d**5.
-2*d**3*(d - 5)*(d + 3)/9
Let -3*u**2 - 1/3*u**3 + 46/3*u + 40 = 0. Calculate u.
-12, -2, 5
Let x = -14/107 - -256/321. Let v(f) be the second derivative of -1/10*f**5 + x*f**3 + 0 - 1/6*f**4 + 0*f**2 + 17*f. Factor v(b).
-2*b*(b - 1)*(b + 2)
Let h(g) = -400*g - 44. Let r be h(1). Let q be (r/925)/((-2)/10). Suppose -12/5*o**2 + q*o + 3/5*o**3 + 0 = 0. What is o?
0, 2
Let r = -234 + 240. Solve r*y**5 - 3*y**5 - 36 - 30*y + 32*y**2 - 12*y**4 + 12*y**3 - y**5 = 0.
-1, 2, 3
Suppose 3*n - 4*m + 1184 = 0, 2*m - 651 = -4*n - 2215. Let b = -388 - n. Solve -3/4*i + 3/4*i**b - 9/4*i**2 + 3/2 + 3/4*i**3 = 0.
-2, -1, 1
Let y = 6 + -2. Let a be (-2)/(-3)*(2 + y). Factor -24*k**a - 3*k**2 + 15*k**4 - 4*k**3 + 13*k**4 - k**2 + 4*k.
4*k*(k - 1)**2*(k + 1)
Suppose 12*n = -6 + 30. What is y in 12*y - 12*y**2 - 3*y**2 + 6*y**3 - 2*y**2 - 4 + 4*y**n - y**4 = 0?
1, 2
Let s(g) be the third derivative of -g**8/672 - 83*g**7/420 + 17*g**6/24 - g**5/60 - 169*g**4/48 + 85*g**3/12 - g**2 - 2*g - 924. Find i such that s(i) = 0.
-85, -1, 1
Factor 384 + 90*j**2 - 4*j**3 + 21*j**2 - 30*j**2 + 34*j**2 - 524*j + 29*j**2.
-4*(j - 32)*(j - 3)*(j - 1)
Let b(p) be the second derivative of 0*p**2 + 2/15*p**6 + 6*p**3 - 20 - p + 7/5*p**5 + 5*p**4. Factor b(g).
4*g*(g + 1)*(g + 3)**2
Suppose 6*l + 790 = 2086. Factor -l*q - q**4 + 216*q.
-q**4
Let t be 3 - (-1974)/(-252) - -5. Solve 5/3 + 17/6*n + t*n**3 + 4/3*n**2 = 0.
-5, -2, -1
Let d(f) be the first derivative of -108 + 39/4*f**2 - 1/2*f**3 + 45*f. Let d(b) = 0. Calculate b.
-2, 15
Let z(t) be the first derivative of 2*t**3/15 - 508*t**2 + 645160*t - 104. Factor z(q).
2*(q - 1270)**2/5
Let b be 27/(-117) - 270/(-156). Factor 0*j + b*j**5 + 0 - 24*j**2 + 36*j**3 - 27/2*j**4.
3*j**2*(j - 4)**2*(j - 1)/2
Let a(y) = -y - 14. Let f be a(-12). Let z be 3/((-3)/(-7)) - f. Factor 25*i + 3*i**2 - z*i + 2*i + 24.
3*(i + 2)*(i + 4)
Let t(l) be the second derivative of l**6/30 - 2*l**5/5 - 7*l**4/6 + 45*l**2 + 79*l. Let y(h) be the first derivative of t(h). What is j in y(j) = 0?
-1, 0, 7
Let z(c) be the first derivative of 13/5*c**2 - 1/10*c**4 + 4/3*c**3 - 57 - 44/5*c. Factor z(r).
-2*(r - 11)*(r - 1)*(r + 2)/5
Let f = -936 + 930. Let p be f*(-24)/(-56)*(-7)/4. Let 4 - p*k**2 - 17*k = 0. What is k?
-4, 2/9
Let l(h) be the second derivative of -h**7/42 + h**6/30 + h**5/2 + 2*h**4/3 - 3188*h. Solve l(d) = 0 for d.
-2, -1, 0, 4
Factor -1700/3*g**2 + 5*g**3 + 0 + 5/3*g**4 + 0*g.
5*g**2*(g - 17)*(g + 20)/3
Let m = 19/2 - 33/4. Let w be 2/(-4) - (-2015)/130 - 12. Factor 1/4*j + 1/2 - 2*j**2 + m*j**w.
(j - 1)**2*(5*j + 2)/4
Let w(a) be the first derivative of a**4/38 + 2264*a**3/19 + 3844272*a**2/19 + 2901143936*a/19 - 8667. Find b, given that w(b) = 0.
-1132
Let d = -11/23820 - -357377/166740. Determine c, given that 1440/7*c**2 + 246/7*c**3 + 375 + 3450/7*c + d*c**4 = 0.
-5, -7/5
Let f(w) be the third derivative of -w**6/1260 + w**5/60 + 2*w**4/21 + 21*w**3/2 + 43*w**2. Let x(k) be the first derivative of f(k). Factor x(o).
-2*(o - 8)*(o + 1)/7
Let x(k) = 33*k**3 + 137*k**2 - 32*k - 373. Let a(y) = 8*y**3 + 34*y**2 - 8*y - 94. Let f(s) = 25*a(s) - 6*x(s). Find p, given that f(p) = 0.
-14, -2, 2
Let o(y) be the third derivative of 63*y**2 + 0*y + 0 + 1/480*y**6 + 1/15*y**5 + 2/3*y**4 + 0*y**3. Factor o(r).
r*(r + 8)**2/4
Let m(k) = 5*k**2 - 273*k - 12. Let l(d) = 10*d**2 - 545*d - 20. Suppose 141*p - 138*p + 15 = 0. Let g(c) = p*m(c) + 3*l(c). Find r, given that g(r) = 0.
0, 54
Let y(q) be the second derivative of 250*q**7/3 + 20*q**6/9 - 82*q**5/3 + 8*q**4/3 + 34*q**3/9 - 4*q**2/3 - 286*q. Solve y(g) = 0 for g.
-1/3, -2/7, 1/5
Let s be 55/200 - (-36)/288. Let u(t) be the second derivative of 17*t + s*t**2 + 1/150*t**5 + 1/45*t**3 - 2/45*t**4 + 0. Determine r, given that u(r) = 0.
-1, 2, 3
Let g = -3 - -6. Suppose -4*o + 5*i = -41, 5*o - 47 = 4*i - 7. Solve -4*z + 12*z - 2*z**2 - 8*z**g - 28*z**o + 35*z**2 - 5*z**2 = 0 for z.
-1, -2/7, 0, 1
Let z(u) = -20*u**2 - 1167*u - 6600. Let l be z(-52). Suppose 2*r - 1/2*r**3 - r**2 + l = 0. Calculate r.
-2, 2
Let m(j) be the third derivative of -j**5/19 + 37*j**4/228 + 4*j**3/57 - 1957*j**2. Determine p so that m(p) = 0.
-1/10, 4/3
Let x be (2448/85)/((-9)/(-210)). Let a be ((x/(-98))/16)/((-1)/2). What is f in 0*f**2 + 0 + 0*f + a*f**4 - 4/7*f**3 = 0?
0, 2/3
Let h(n) = 14*n + 216. Let k be h(-15). Let g(t) = -t**2 + 8*t - 7. Let s be g(6). Solve -9*j**s + j**3 + j**3 - j**3 - 2*j**4 + k*j**5 = 0 for j.
-1, 0, 1/3
Find d, given that -120*d**2 - 72*d**2 - 36*d + 11473*d**3 - 5*d**4 - 11534*d**3 = 0.
-6, -1/5, 0
Let v be ((-60)/(-168))/((-8)/206). Let w = v - -67/7. Factor -w*t + 3/8 - 3/8*t**2 + 3/8*t**3.
3*(t - 1)**2*(t + 1)/8
Let 10*t - 2/15*t**2 + 152/15 = 0. Calculate t.
-1, 76
Let k(d) = 503*d + 38731. Let a be k(-77). Suppose 0*q - 3/8*q**4 - 3/4*q**3 + a - 3/8*q**2 = 0. Calculate q.
-1, 0
Let x(j) be the first derivative of -10*j**6/9 - 164*j**5/15 - 35*j**4/3 + 100*j**3 - 10297. Factor x(d).
-4*d**2*(d + 5)**2*(5*d - 9)/3
Let q(v) = v**2 - 88*v + 3481. Let r(h) = h**2 - 85*h + 3481. Let z(l) = -11*q(l) + 10*r(l). What is x in z(x) = 0?
59
Let v = -4037591/352188 - 319/9783. Let z = 1/324 - v. Let z*d**3 + 27/4 + 81/4*d + 1/4*d**5 + 45/2*d**2 + 11/4*d**4 = 0. Calculate d.
-3, -1
Let w = -1131448/3 - -377152. Let 64/3*r + 230/3*r**3 + 100/3*r**4 + w + 62*r**2 = 0. What is r?
-1, -1/2, -2/5
Suppose 8 - 2*s**2 + s - 1/4*s**3 = 0. What is s?
-8, -2, 2
Let p = -10489/6 - -1749. Let j(d) be the second derivative of -4*d + 0 + 0*d**2 - p*d**3 - 5/12*d**4. Factor j(m).
-5*m*(m + 1)
Let j = -91/395 - -96167/790. What is f in 189/2*f**2 - j*f + 51/2*f**3 + 3/2*f**4 + 0 = 0?
-9, 0, 1
Let u(k) be the third derivative of -k**6/120 - 3*k**5/20 - 5*k**4/8 + 7*k**3/2 - 105*k**2. Let m be u(-6). Solve 4/3*l**2 + 0 - 2*l + 2/3*l**m = 0.
-3, 0, 1
Suppose -1050 = -2*a + 5*a. Let r = a + 614. Factor r*c**2 - 3 + 3 - 3*c**3 - 258*c**2.
-3*c**2*(c - 2)
Let w(q) be the first derivative of q**9/5040 + q**8/1400 - 3*q**7/1400 + 4*q**3/3 + 3*q**2 + 58. Let b(c) be the third derivative of w(c). Factor b(x).
3*x**3*(x - 1)*(x + 3)/5
Suppose -h + 11 = -199*k + 196*k, 2*h + 3*k = -5. Let b = 1/10 + 11/10. Factor 8/15*u**h + 4/15 - b*u.
2*(u - 2)*(4*u - 1)/15
What is k in 15/2*k - 1/4*k**2 + 99/4 = 0?
-3, 33
Let s(g) be the second derivative of -g**5/25 + 4*g**4/15 + 8*g**3/3 - 96*g**2/5 + 2*g - 677. Find u, given that s(u) = 0.
-4, 2, 6
Let q(s) be 