It is called the slope of the line
Number of red cards including 2 red queens = 26
Number of black queens = 2
Therefore, number of red cards including 2 red queens and 2 black queens = 26 + 2 = 28
Number of cards neither a red card nor a queen = 52 - 28 = 24
![P = \frac{ Number \: of \: favourable \: outcomes}{ Total \: numer \: of \: possible \: outcomes}](https://tex.z-dn.net/?f=P%20%20%3D%20%20%5Cfrac%7B%20Number%20%5C%3A%20of%20%5C%3A%20favourable%20%5C%3A%20outcomes%7D%7B%20Total%20%5C%3A%20numer%20%5C%3A%20of%20%5C%3A%20possible%20%5C%3A%20outcomes%7D%20)
If
![f(\theta)=10\cos\theta+5\sin^2\theta](https://tex.z-dn.net/?f=f%28%5Ctheta%29%3D10%5Ccos%5Ctheta%2B5%5Csin%5E2%5Ctheta)
then the derivative is
![f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta](https://tex.z-dn.net/?f=f%27%28%5Ctheta%29%3D-10%5Csin%5Ctheta%2B10%5Csin%5Ctheta%5Ccos%5Ctheta)
Critical points occur where
. This happens for
![-10\sin\theta+10\sin\theta\cos\theta=0](https://tex.z-dn.net/?f=-10%5Csin%5Ctheta%2B10%5Csin%5Ctheta%5Ccos%5Ctheta%3D0)
![-10\sin\theta(1-\cos\theta)=0](https://tex.z-dn.net/?f=-10%5Csin%5Ctheta%281-%5Ccos%5Ctheta%29%3D0)
![\implies-10\sin\theta=0\text{ or }1-\cos\theta=0](https://tex.z-dn.net/?f=%5Cimplies-10%5Csin%5Ctheta%3D0%5Ctext%7B%20or%20%7D1-%5Ccos%5Ctheta%3D0)
In the first case, we find
![-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi](https://tex.z-dn.net/?f=-10%5Csin%5Ctheta%3D0%5Cimplies%5Csin%5Ctheta%3D0%5Cimplies%5Ctheta%3Dn%5Cpi)
In the second,
![1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi](https://tex.z-dn.net/?f=1-%5Ccos%5Ctheta%3D0%5Cimplies%5Ccos%5Ctheta%3D1%5Cimplies%5Ctheta%3D2n%5Cpi)
So all the critical points occur at multiples of
, or
. (This includes all the even multiples of
.)
Answer:
Step-by-step explanation:
In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.
Hence <1 = <3
Given < 1 = 3x-1 and <3 = 2x+9
Hence 3x-1 = 2x+9
collect like terms
3x-2x = 9+1
x = 10°
Since <1 = 3x-1
on substituting x = 10
<1 = 3(10)-1
<1 = 30-1
<1 = 29°
<1+<2 = 180 (angle on a straight line)
29+<2 = 180
<2 = 180-29
<2 = 151°
Similarly, on substituting x = 10 into <3
<3 = 2x+9
<3 = 2(10)+9
<3 = 20+9
<3 = 29°
<3+<4 = 180 (angle on a straight line)
29+<4 = 180
<4 = 180-29
<4 = 151°
The answer is 45 when you substitute all the variables in