Answer:
(2 x 5 x 5) / (2 x 3 x 4 x 5)
=40/120
= 4/12
= 1/3
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)
Answer:
Step-by-step explanation:
Look what happens if you do the multiplication of P(x):
P(x) = x^3 - 9x
This is a variation of the basic cubing function y = x^3.
The graph begins in QIII and ends in QI; in other words, if you go left the graph drops; if you go right, the graph rises (without limit, in both cases).
When you have two unit prices for two comparable items, you have to convert one of the prices to the other one.
Answer:
8
Step-by-step explanation:
The intersecting chord theorem is expressed as;
7 * x = 4 * 14
7x = 56
Divide both sides by 7
7x/7 = 56/7
x = 8
Hence the value of x is 8