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heureka

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 #4
avatar+26396 
+6

When the fraction 1/288 is expressed in base 12,

is it terminating or repeating? Explain.

 

1288=a121+b122+c123+d124+e125|1212288=124=a+b121+c122+d123+e124decimal places=124integer(124)=aa=0124a=b121+c122+d123+e1241240=b121+c122+d123+e124124=b121+c122+d123+e124|121224=12=b+c121+d122+e123decimal places=12integer(12)=bb=012b=c121+d122+e123120=c121+d122+e12312=c121+d122+e123|12122=6.0000000=c+d121+e122decimal places=0integer(6.0000000)=cc=61288=0.00612

 

laugh

19.10.2016
 #1
avatar+26396 
0

f(t)=4cost+2sin2t, [0,pi/2]

What is ABSOLUTE MAX?

 

 

f(t)=4cos(t)+2sin(2t)0tπ2f(t)=4[sin(t)]+2cos(2t)2f(t)=4sin(t)+4cos(2t)|find min/max f(t)=00=4sin(t)+4cos(2t)|:40=sin(t)+cos(2t)cos(2t)sin(t)=0|cos(2t)=cos2(t)sin2(t)|=1sin2(t)sin2(t)|=12sin2(t)cos(2t)sin(t)=0|cos(2t)=12sin2(t)12sin2(t)sin(t)=0|(1)1+2sin2(t)+sin(t)=02sin2(t)+sin(t)1=0|substitute: u=sin(t)2u2+u1=0u1,2=1±(1)242(1)22u1,2=1±1+84u1,2=1±94u1,2=1±34u1=1+34u1=12u2=134u2=1t1=arcsin(u1)t1=arcsin(12)t1=30 or t1=π6t2=arcsin(u2)t2=arcsin(1)t2=90 or t2=π2|no solution because 0tπ2

 

f(t)=4cos(t)+2sin(2t)f(30)=4cos(30)+2sin(230)f(30)=4cos(30)+2sin(60)f(30)=432+232f(30)=23+3f(30)=33f(30)=5.19615242271

 

Max or min at t=30(=π6)f(30)=5.196?
y"(t)=4cos(t)4sin(2t)2y"(t)=4cos(t)8sin(2t)y"(30)=4cos(30)8sin(230)y"(30)=4cos(30)8sin(60)y"(30)=432832y"(30)=1232y"(30)=63|maximum because y(30)<0

 

Max at t=30(=π6)f(30)=5.196

 

laugh

18.10.2016
 #1
avatar+26396 
0

(a + a^2 + a^3)^4=a^12+4 a^11+10 a^10+16 a^9+19 a^8+16 a^7+10 a^6+4 a^5+a^4
In the expanded part, the term "19a^8", how is the coefficient 19 arrived at? Thanks for any help.

 

Formula trinomial:

 

We have:

 

We need the coefficient of :

So

 

 

laugh

17.10.2016