V=13Ah
A=32⋅66=2112
h=√652−(322)2−(662)2=24√5
V=13(2112)(24√5)=16896√5
f(x)=q(x)d(x)+r(x)
deg f = 9, deg r = 3, deg d > deg r.
For maximum deg q. deg d is minimum. => deg d = 4.
O(x9)=q(x)O(x4)+O(x3)
q(x) = O(x5)
Therefore deg q = 5.
P(x)=3x3+a2x2+a1x−6
Product of roots = −−63= 2.
Possible roots = {1,-1,2,-2}.
(3√7+3√49)3=7+49+33√7⋅49(3√7+3√49)=56+21(3√7+3√49)
Therefore P(x) is x3 - 21x - 56.
Product of roots = −−561=56
Circumference=π(Diameter)Circumference=13π cm
9x2−18x−16=0(3x−8)(3x+2)=0x=83 OR x=−23
15x2+28x+12=0(3x+2)(5x+6)=0x=−23 OR x=−65
Only x = -2/3 satisfies both equations. Therefore the answer is -2/3.
(x−p)(x−q)=x2+4x+6(x−p)(x−q)=x2+bx+cComparing coefficients,(b,c)=(4,6)∴b+c=10
5)
{x+y=3x2+y2=6x4=y4+18√3(x+y)2=9x2+y2+2xy=92xy=3x=32y32y+y=32y2−6y+3=0y=6±2√34=3±√32When y=3+√32,x=3−√32When y=3−√32,x=3+√32∴(x,y)=(3+√32,3−√32) OR (3−√32,3+√32)
4)
m+n=−54mn=34(m+7)(n+7)=mn+7(m+n)+49=34+7(−54)+49=41
3)
s+t=−94st=−64=−32st+ts=(s+t)2−2stst=(−94)2−2(−32)−32=−438