Answer:
the answer is D.
Step-by-step explanation:
distribute property requires you to multiply the number outside the parenthesis in everything in the parenthesis. hope this helps.
G2=g1*2
g3=g1*2²
196=x*4
/4 /4
49
Answer:
The answer is D: 2+2+b=12
Step-by-step explanation:
Hope this helps!
![f(x,y)=\dfrac{y^3}x](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D%5Cdfrac%7By%5E3%7Dx)
a. The gradient is
![\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath](https://tex.z-dn.net/?f=%5Cnabla%20f%28x%2Cy%29%3D%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%5C%2C%5Cvec%5Cimath%2B%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%5C%2C%5Cvec%5Cjmath)
![\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cnabla%20f%28x%2Cy%29%3D-%5Cdfrac%7By%5E3%7D%7Bx%5E2%7D%5C%2C%5Cvec%5Cimath%2B%5Cdfrac%7B3y%5E2%7Dx%5C%2C%5Cvec%5Cjmath%7D)
b. The gradient at point P(1, 2) is
![\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cnabla%20f%281%2C2%29%3D-8%5C%2C%5Cvec%5Cimath%2B12%5C%2C%5Cvec%5Cjmath%7D)
c. The derivative of
at P in the direction of
is
![D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}](https://tex.z-dn.net/?f=D_%7B%5Cvec%20u%7Df%281%2C2%29%3D%5Cnabla%20f%281%2C2%29%5Ccdot%5Cdfrac%7B%5Cvec%20u%7D%7B%5C%7C%5Cvec%20u%5C%7C%7D)
It looks like
![\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20u%3D%5Cdfrac%7B13%7D2%5C%2C%5Cvec%5Cimath%2B5%5C%2C%5Cvec%5Cjmath)
so that
![\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2](https://tex.z-dn.net/?f=%5C%7C%5Cvec%20u%5C%7C%3D%5Csqrt%7B%5Cleft%28%5Cdfrac%7B13%7D2%5Cright%29%5E2%2B5%5E2%7D%3D%5Cdfrac%7B%5Csqrt%7B269%7D%7D2)
Then
![D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}](https://tex.z-dn.net/?f=D_%7B%5Cvec%20u%7Df%281%2C2%29%3D%5Cdfrac%7B%5Cleft%28-8%5C%2C%5Cvec%5Cimath%2B12%5C%2C%5Cvec%5Cjmath%5Cright%29%5Ccdot%5Cleft%28%5Cfrac%7B13%7D2%5C%2C%5Cvec%5Cimath%2B5%5C%2C%5Cvec%5Cjmath%5Cright%29%7D%7B%5Cfrac%7B%5Csqrt%7B269%7D%7D2%7D)
![\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}](https://tex.z-dn.net/?f=%5Cboxed%7BD_%7B%5Cvec%20u%7Df%281%2C2%29%3D%5Cdfrac%7B16%7D%7B%5Csqrt%7B269%7D%7D%7D)