8.1 I think but there's an app called, tiger something and it tells,you the answers
Answer:
7/10
Step-by-step explanation:
Have a nice day
Basically all you need to do is estimate what 32.7 x 2.8 is. If what you get is close to 91.56, then Tom's answer is reasonable. If what you get is not close to 91.56, then his answer is not reasonable. Do you know how to estimate by rounding?
Answer:
(green) y= 7/6x -1
(Black) y= -2x+4
(Blue) x= -4
(Red) x= +4
Step-by-step explanation:
you can enter 2 sets of coordinates per line into a calculator to help you find the equation for each one.
The vector pointing from (2, 1) to (1, 3) points in the same direction as the vector
. The derivative of
at (2, 1) in the direction of
is
![D_{\vec u}f(2,1)=\nabla f(2,1)\cdot\dfrac{\vec u}{\|\vec u\|}](https://tex.z-dn.net/?f=D_%7B%5Cvec%20u%7Df%282%2C1%29%3D%5Cnabla%20f%282%2C1%29%5Ccdot%5Cdfrac%7B%5Cvec%20u%7D%7B%5C%7C%5Cvec%20u%5C%7C%7D)
We have
![\|\vec u\|=\sqrt{(-1)^2+2^2}=\sqrt5](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20u%5C%7C%3D%5Csqrt%7B%28-1%29%5E2%2B2%5E2%7D%3D%5Csqrt5)
Then
![D_{\vec u}f(2,1)=(f_x(2,1),f_y(2,1))\cdot\dfrac{(-1,2)}{\sqrt5}=\dfrac{-f_x(2,1)+2f_y(2,1)}{\sqrt5}=-\dfrac2{\sqrt5}](https://tex.z-dn.net/?f=D_%7B%5Cvec%20u%7Df%282%2C1%29%3D%28f_x%282%2C1%29%2Cf_y%282%2C1%29%29%5Ccdot%5Cdfrac%7B%28-1%2C2%29%7D%7B%5Csqrt5%7D%3D%5Cdfrac%7B-f_x%282%2C1%29%2B2f_y%282%2C1%29%7D%7B%5Csqrt5%7D%3D-%5Cdfrac2%7B%5Csqrt5%7D)
![\implies f_x(2,1)-2f_y(2,1)=2](https://tex.z-dn.net/?f=%5Cimplies%20f_x%282%2C1%29-2f_y%282%2C1%29%3D2)
The vector pointing from (2, 1) to (5, 5) has the same direction as the vector
. The derivative of
at (2, 1) in the direction of
is
![D_{\vec v}f(2,1)=\nabla f(2,1)\cdot\dfrac{\vec v}{\|\vec v\|}](https://tex.z-dn.net/?f=D_%7B%5Cvec%20v%7Df%282%2C1%29%3D%5Cnabla%20f%282%2C1%29%5Ccdot%5Cdfrac%7B%5Cvec%20v%7D%7B%5C%7C%5Cvec%20v%5C%7C%7D)
![\|\vec v\|=\sqrt{3^2+4^2}=5](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20v%5C%7C%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%3D5)
so that
![(f_x(2,1),f_y(2,1))\cdot\dfrac{(3,4)}5=1](https://tex.z-dn.net/?f=%28f_x%282%2C1%29%2Cf_y%282%2C1%29%29%5Ccdot%5Cdfrac%7B%283%2C4%29%7D5%3D1)
![\implies3f_x(2,1)+4f_y(2,1)=5](https://tex.z-dn.net/?f=%5Cimplies3f_x%282%2C1%29%2B4f_y%282%2C1%29%3D5)
Solving the remaining system gives
and
.