Answer:
x= 62
y= 54
Step-by-step explanation:
Step one:
given data
let the numbers be x and y and the larger be x the smaller be y
The difference between two numbers is 8
x-y= 8-----------1
If the larger is subtracted from three times the smaller, the difference is 100
3y-x=100------------2
from eqn 1, x= 8+y
put this in eqn 2
3y-(8+y)=100
3y-8-y=100
collect liker terms
3y-y-8=100
2y=108
y= 54
put y= 54 in eqn 1
x-y=8
x-54= 8
x= 8+54
x=62
Answer:Put y over x or you can divide both numbers by x
Step-by-step explanation:
Answer: The value of cos theta is -0.352.
Step-by-step explanation:
Since we have given that
![\vec{u}=1\hat{i}+2\hat{j}-2\hat{k}\and\\\\\vec{w}=\hat{j}+4\hat{k}](https://tex.z-dn.net/?f=%5Cvec%7Bu%7D%3D1%5Chat%7Bi%7D%2B2%5Chat%7Bj%7D-2%5Chat%7Bk%7D%5Cand%5C%5C%5C%5C%5Cvec%7Bw%7D%3D%5Chat%7Bj%7D%2B4%5Chat%7Bk%7D)
We need to find the cos theta between u and w.
As we know the formula for angle between two vectors.
![\cos\ \theta=\dfrac{\vec{u}.\vec{w}}{\mid u\mid \mid w\mid}](https://tex.z-dn.net/?f=%5Ccos%5C%20%5Ctheta%3D%5Cdfrac%7B%5Cvec%7Bu%7D.%5Cvec%7Bw%7D%7D%7B%5Cmid%20u%5Cmid%20%5Cmid%20w%5Cmid%7D)
So, it becomes,
![\cos \theta=\dfrac{2-8}{\sqrt{1^2+2^2+(-2)^2}\sqrt{1^2+4^2}}\\\\\cos \theta=\dfrac{-6}{\sqrt{17}\sqrt{17}}=\dfrac{-6}{17}=-0.352\\\\\theta=\cos^{-1}(\dfrac{-6}{17})=110.66^\circ](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%3D%5Cdfrac%7B2-8%7D%7B%5Csqrt%7B1%5E2%2B2%5E2%2B%28-2%29%5E2%7D%5Csqrt%7B1%5E2%2B4%5E2%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%3D%5Cdfrac%7B-6%7D%7B%5Csqrt%7B17%7D%5Csqrt%7B17%7D%7D%3D%5Cdfrac%7B-6%7D%7B17%7D%3D-0.352%5C%5C%5C%5C%5Ctheta%3D%5Ccos%5E%7B-1%7D%28%5Cdfrac%7B-6%7D%7B17%7D%29%3D110.66%5E%5Ccirc)
Hence, the value of cos theta is -0.352.