The answer is B. 120
nCr = n! / ((r! * (n - r)!)
n = 10
r = 3
10C3 = 10! / ((3! * (10 - 3)!)
= 10! / ((3! * 7!)
= (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 3628800 / 30240
= 120
Answer:
OPTION B: ![$ \frac{-2\sqrt{5}}{5} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B-2%5Csqrt%7B5%7D%7D%7B5%7D%20%24)
Step-by-step explanation:
Given ![$ cot \theta = -\frac{\sqrt{5}}{2} $](https://tex.z-dn.net/?f=%24%20cot%20%5Ctheta%20%3D%20-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%20%24)
We know that, ![$ \frac{1}{cot \theta} = tan \theta $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B1%7D%7Bcot%20%5Ctheta%7D%20%3D%20tan%20%5Ctheta%20%24)
![$ \implies tan \theta = \frac{1}{-\frac{\sqrt{5}}{2}} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20tan%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%7D%20%24)
![$ = -\frac{2}{\sqrt{5}} $](https://tex.z-dn.net/?f=%24%20%3D%20-%5Cfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%20%24)
Multiplying and dividing by
, we get:
![$ tan \theta = - \frac{2 \sqrt{5}}{\sqrt{5}\times \sqrt{5}}} $](https://tex.z-dn.net/?f=%24%20tan%20%5Ctheta%20%3D%20-%20%5Cfrac%7B2%20%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B5%7D%5Ctimes%20%5Csqrt%7B5%7D%7D%7D%20%24)
![$ \implies tan \theta = -\frac{2\sqrt{5}}{5} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20tan%20%5Ctheta%20%3D%20-%5Cfrac%7B2%5Csqrt%7B5%7D%7D%7B5%7D%20%24)
Hence, OPTION B is the answer.
Okay, you now a triangle has 180º degrees and to add to 180º, you have to add all the numbers you have like this:
2x+x+90 (the box is 90º)=180º; add like terms like 2x+x
3x+90=180; cancel 90 by subtracting it and also subtract 90 from 180
3x=90;divide 3 to isolate x and also divide 90/3
x=30 :)
The right answer for the question that is being asked and shown above is that: "1. t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground." the axis of symmetry, and what does it represent is <span>1. t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground</span>