Answer: D
Step-by-step explanation:
Using the equation plot in the coordinates of the points to see if they fit the equation.
5x-3y < 30
A) 5(-3) -3(5) < 30
-15 -15 < 30
-30 < 30 This is true
B) 5(0) -3(0) < 30
0 - 0 < 30
0< 30 This is true
C) 5(-5) - 3(3) < 30
-25 - 9 < 30
-34 < 30 This is also true
D) 5(3) - 3(-5) < 30
15 + 15 < 30
30 < 30 This is not true because 30 is not greater that 30
Answer:
A. 64/125
B. 124/125.
Step-by-step explanation:
A). As the events ( germinate or not germinate) are independent we multiply the probabilities.
Prob(All seeds germinate) = 4/5*4/5*4/5 = 64/125.
B). Probability of at least one germinating = 1 - probability that none germinate
Probability of 1 seed not germinating = 1 -45 = 1/5.
So Prob(at least one germinating)
= 1 - (1/5 * 1/5 * 1/5)
= 1 - 1/125
= 124/125.
![\\ \rm\Rrightarrow f(x)=-5cos\dfrac{x}{2}+5](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20f%28x%29%3D-5cos%5Cdfrac%7Bx%7D%7B2%7D%2B5)
Compare to standard equation of SHM
![\\ \rm\Rrightarrow y=Acos(\omega x+\phi)](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20y%3DAcos%28%5Comega%20x%2B%5Cphi%29)
Here
![\\ \rm\Rrightarrow \omega x=\dfrac{x}{2}](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20%5Comega%20x%3D%5Cdfrac%7Bx%7D%7B2%7D)
![\\ \rm\Rrightarrow \omega=1/2](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20%5Comega%3D1%2F2)
Well the above one are for extra knowledge .
Solution:-
![\\ \rm\Rrightarrow 10=-5cos\dfrac{x}{2}+5](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%2010%3D-5cos%5Cdfrac%7Bx%7D%7B2%7D%2B5)
![\\ \rm\Rrightarrow 10-5=-5cos\dfrac{x}{2}](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%2010-5%3D-5cos%5Cdfrac%7Bx%7D%7B2%7D)
![\\ \rm\Rrightarrow 5=-5cos\dfrac{x}{2}](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%205%3D-5cos%5Cdfrac%7Bx%7D%7B2%7D)
![\\ \rm\Rrightarrow cos\dfrac{x}{2}=-1](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20cos%5Cdfrac%7Bx%7D%7B2%7D%3D-1)
![\\ \rm\Rrightarrow \dfrac{x}{2}=cos^{-1}(-1)](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20%5Cdfrac%7Bx%7D%7B2%7D%3Dcos%5E%7B-1%7D%28-1%29)
![\\ \rm\Rrightarrow \dfrac{x}{2}=\pi](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20%5Cdfrac%7Bx%7D%7B2%7D%3D%5Cpi)
![\\ \rm\Rrightarrow x=2\pi](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20x%3D2%5Cpi)
So.
![\\ \rm\Rrightarrow x=2\pi+2\pi n](https://tex.z-dn.net/?f=%5C%5C%20%5Crm%5CRrightarrow%20x%3D2%5Cpi%2B2%5Cpi%20n)
Answer: B is the answer yup B