Answer:
I am not sure if this is right but the answer is
The area of a circle with circumference 18π is 254.5
4,500 plus 15% is 5,175 minus 4% is 4,968 so your answer is 4,968.
![x+y=k\implies y=k-x](https://tex.z-dn.net/?f=x%2By%3Dk%5Cimplies%20y%3Dk-x)
Substitute this into the parabolic equation,
![k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0](https://tex.z-dn.net/?f=k-x%3D6-%28x-3%29%5E2%5Cimplies%20x%5E2-7x%2B%28k%2B3%29%3D0)
We're told the line
intersects
twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know
![(-7)^2-4(k+3)=49-4(k+3)>0\implies k](https://tex.z-dn.net/?f=%28-7%29%5E2-4%28k%2B3%29%3D49-4%28k%2B3%29%3E0%5Cimplies%20k%3C%5Cdfrac%7B37%7D4%3D9.25)
We can tell from the quadratic equation that
has its vertex at the point (3, 6). Also, note that
![-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5](https://tex.z-dn.net/?f=-1%5Cle%5Csin%20t%5Cle1%5Cimplies3%5Cle3%2B2%5Csin%20t%5Cle5%5Cimplies3%5Cle%20x%5Cle5)
and
![-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6](https://tex.z-dn.net/?f=-1%5Cle%5Ccos2t%5Cle1%5Cimplies2%5Cle4%2B2%5Ccos2t%5Cle6%5Cimplies2%5Cle%20y%5Cle6)
so the furthest to the right that
extends is the point (5, 2). The line
passes through this point for
. For any value of
, the line
passes through
either only once, or not at all.
So
; in set notation,
![\{k\mid 7\le k](https://tex.z-dn.net/?f=%5C%7Bk%5Cmid%207%5Cle%20k%3C9.25%5C%7D)
Answer:
Step-by-step explanation:
Given that a particular detection system has a 0.83 probability of detecting a missile attack.
Also each system is independent of the other to detect missile attack.
a) the probability that a single detection system will detect an attack=![0.83](https://tex.z-dn.net/?f=0.83)
b) the probability that at least one of the systems will detect the attack given two systems= 1-Prob no system detects
=![1-(1-0.83)(1-0.83)\\\\=1-0.0289\\=0.9711](https://tex.z-dn.net/?f=1-%281-0.83%29%281-0.83%29%5C%5C%5C%5C%3D1-0.0289%5C%5C%3D0.9711)
c) If three systems are installed, the probability that at least one of the systems will detect the attack
= 1- none of the three systems detect attack
![= (1-0.17^3)\\=1-0.004913\\=0.995087](https://tex.z-dn.net/?f=%3D%20%281-0.17%5E3%29%5C%5C%3D1-0.004913%5C%5C%3D0.995087)
d) We find that probability of detecting is more if we increase the system form 1 to 2 and 2 to 3.
Hence for safety and defence purpose multiple detection system is recommended.
Amber could have used cross multiplication.
Have a great day!!!!