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hellodjfos;s'ff Thank you for your help
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In the third why are we excluding both the batsman and the bowler.You must find the combinations when only the batsman is being included in the squad(1st), only the bowler is being included in the squad(2nd) and when none of them are being included(3rd).
1st: 1C1(for the batsman having a confirmed place)*6C4*4C4(bowler has been excluded here)*2C1*2C1=60
2nd: 6C5*1C1(bowler having confirmed place)*4C3*2C1*2C1=96
3rd: 6C5(batsman excluded)*4C4(bowlers excluded)*2C1*2C1=24
24+96+60=180
Because when we exclude both the batsmen and bowler, the batsman is still refusing to be in a team with a bowler but if they are not picked, they don't end up being in a team together anyways so the condition is met.In the third why are we excluding both the batsman and the bowler.
Thank youBecause when we exclude both the batsmen and bowler, the batsman is still refusing to be in a team with a bowler but if they are not picked, they don't end up being in a team together anyways so the condition is met.
Can I work the 2nd part like this....|z-10i|=2|z-4i|
(z-10i)(z+10i)=4(z-4i)(z+41) - using the concept from first equation in (i)
(z-10i)(z-10i)*=4(z-4i)(z-4i)* - now use concept from 2nd equation in (ii)
(z-10i)(z*+10i)=4(z-4i)(z*+4i)
zz*+10iz-10iz*+100=4(zz*+4iz-4iz*+16)
3zz*+6iz-6iz*-36=0
3(zz*-2iz*+2iz-12)=0 - first part proven
|z-2i|=(z-2i)(z*+2i)=zz*-2iz*+2iz+4
Now compare this with the earlier equation we have proven. If we subtract 16 from this new equation, both the equations would be equal right? So...
zz*-2iz*+2iz+4=4^2 - notice i out 4^2 not 16 because we were squaring both sides of the equation as the question had told us to do earlier.
Hence radius=4 making the equation |z-2i|=4
That works well too.Can I work the 2nd part like this....
zz*-2iz*+2iz-12=0
zz*-2iz*+2iz+4-16=0
zz*-2iz*+2iz-4i²-16=0
z*(z-2i)+2i(z-2i)=4²
(z-2i)(z*+2i)=4²
(z-2i)(z-2i)*=4²
|z-2i|²=4²
|z-2i|=4
P.s can we take z-2i as whole in place of z because the statements in (i) are for z?
Usually they tell us whether to use radians or degrees. For complex number questions, try to use radians always (since that's the conventional rule) but they do accept answers in degrees. For a question like this where it's unclear whether to use radians or degrees, just look at how reasonable the trigonometric term is... so try out different values of x in sin(x/3) in degrees and radians mode and see which is more reasonable. Since most values of x produce a value too small in degree mode and most values of x produce a value large enough in radians, we do this question in radians.hellodjfos;s'ff in these questions how do we know that we have to take x in radians or degrees?
arg(u*/u) means arg(u*)-arg(u)(iii) part plz...a bit confused about the minus sign in the argumemt of u
u is 3-i and u* 3+iarg(u*/u) means arg(u*)-arg(u)
so arg(u*/u)=arg(u*)-arg(u)
Find these arguments and you will be able to prove the equation.
-tan-¹(1/3) and tan-¹(-1/3) are the same so tan-¹(1/3)-tan-¹(-1/3) becomes tan-¹(1/3)+tan-¹(1/3) hence 2tan-¹(1/3)u is 3-i and u* 3+i
The problem is when it would be written as arg(u*)-arg(u), which would be tan-¹(1/3)-tan-¹(-1/3), what would be done to the minus sign in arg(u)?
Thank u sooo much!!!-tan-¹(1/3) and tan-¹(-1/3) are the same so tan-¹(1/3)-tan-¹(-1/3) becomes tan-¹(1/3)+tan-¹(1/3) hence 2tan-¹(1/3)
-tan-¹(1/3) and tan-¹(-1/3) are the same so tan-¹(1/3)-tan-¹(-1/3) becomes tan-¹(1/3)+tan-¹(1/3) hence 2tan-¹(1/3)
Yes they're the same. You can even put the values in your calculator and clarify that.Will tan-¹(1/-3) also equal -tan-¹(1/3)?
So if a complex number is -5+2i so how will its argument be written in a presentable way? And it won't be equal to -tan-¹(2/5) right?Yes they're the same. You can even put the values in your calculator and clarify that.
To find standard deviation, you need the value of either Σx and Σx^2 or Σ(x-50) and Σ(x-50)^2. Since we only have the latter, we have to solve the question using them.Can someone help me with the second part why are we subtracting 50 from 72?
Nov 2010 62View attachment 64597
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