Answer:
x= 12
Step-by-step explanation:
Please see attached picture for full solution.
Answer:
![\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B%5Csqrt%7B9%7D%20%5Csqrt%7B25%7D%7D%29%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B15%7D%29%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B3%7D%29%20%3D%2048.190)
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately ![\theta \approx 48](https://tex.z-dn.net/?f=%20%5Ctheta%20%5Capprox%2048)
Step-by-step explanation:
For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.
a=[1,2,-2], b=[4,0,-3,]
The dot product on this case is:
![a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10](https://tex.z-dn.net/?f=%20a%20b%3D%20%281%29%2A%284%29%20%2B%20%282%29%2A%280%29%2B%20%28-2%29%2A%28-3%29%3D10)
Since the dot product is not equal to zero then the two vectors are not orthogonal.
Now we can calculate the magnitude of each vector like this:
![|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3](https://tex.z-dn.net/?f=%20%7Ca%7C%3D%20%5Csqrt%7B%281%29%5E2%20%2B%282%29%5E2%20%2B%28-2%29%5E2%7D%3D%5Csqrt%7B9%7D%20%3D3)
![|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5](https://tex.z-dn.net/?f=%20%7Cb%7C%20%3D%5Csqrt%7B%284%29%5E2%20%2B%280%29%5E2%20%2B%28-3%29%5E2%7D%3D%5Csqrt%7B25%7D%3D%205)
And finally we can calculate the angle between the vectors like this:
![cos \theta = \frac{ab}{|a| |b|}](https://tex.z-dn.net/?f=%20cos%20%5Ctheta%20%3D%20%5Cfrac%7Bab%7D%7B%7Ca%7C%20%7Cb%7C%7D)
And the angle is given by:
![\theta = cos^{-1} (\frac{ab}{|a| |b|})](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7Bab%7D%7B%7Ca%7C%20%7Cb%7C%7D%29)
If we replace we got:
![\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190](https://tex.z-dn.net/?f=%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B%5Csqrt%7B9%7D%20%5Csqrt%7B25%7D%7D%29%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B10%7D%7B15%7D%29%20%3D%20cos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B3%7D%29%20%3D%2048.190)
Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel
And the anfle is approximately ![\theta \approx 48](https://tex.z-dn.net/?f=%20%5Ctheta%20%5Capprox%2048)
It should be neither. There is no pattern
Answer:
9 blue marbles
Step-by-step explanation:
4 : 3 ratio
12 : x
12 / 4 = 3
4 × 3 : 3 × 3
12 : 9
She saw 1088 people go down the slide hope my answer helps