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Answer:
125/6(In(x-25)) - 5/6(In(x+5))+C
Step-by-step explanation:
∫x2/x1−20x2−125dx
Should be
∫x²/(x²−20x−125)dx
First of all let's factorize the denominator.
x²−20x−125= x²+5x-25x-125
x²−20x−125= x(x+5) -25(x+5)
x²−20x−125= (x-25)(x+5)
∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx
x²/(x²−20x−125) =x²/((x-25)(x+5))
x²/((x-25)(x+5))= a/(x-25) +b/(x+5)
x²/= a(x+5) + b(x-25)
Let x=25
625 = a30
a= 625/30
a= 125/6
Let x= -5
25 = -30b
b= 25/-30
b= -5/6
x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)
∫x²/(x²−20x−125)dx
=∫125/6(x-25) -∫5/6(x+5) Dx
= 125/6(In(x-25)) - 5/6(In(x+5))+C
Answer:C A B
Step-by-step explanation:A:40 divided by 5=8 B:100 divided by 12 =8.33 C:180 divided by 23=7.83
Volume
cube and sphere
the diameter of the sphere=height of box=legnth of box=width of box
volume of cube=side^3
volume of sphere=(4/3)pir^3
side=d=2r
Vcube=d^3
vsphere=(4/3)pi(d/2)^3
Vsphere=(pid^3)/6
percent
basketballV/boxV=( (pid^3)/6)/(d^3)=(pid^3)/(6d^3)=pi/3=aprox 0.523599=52.3599% (round if nececary)