<h3><u>Answer</u> :- </h3>
c) 0.01
<h3><u>Solution</u> :-</h3>
To Write percentage in decimal or fraction we divide it by 100
therefore,
![\begin{gathered}\\\implies\quad \sf 2\% = \frac{2}{100} \\\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5C%5C%5Cimplies%5Cquad%20%5Csf%202%5C%25%20%3D%20%5Cfrac%7B2%7D%7B100%7D%20%5C%5C%5Cend%7Bgathered%7D%20)
![\begin{gathered}\\\implies\quad \sf 2\% = 0.02 \\\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5C%5C%5Cimplies%5Cquad%20%5Csf%202%5C%25%20%3D%200.02%20%5C%5C%5Cend%7Bgathered%7D%20)
Half of 0.02 = ![\sf\frac{1}{\cancel2} \times\cancel{0.02}](https://tex.z-dn.net/?f=%5Csf%5Cfrac%7B1%7D%7B%5Ccancel2%7D%20%5Ctimes%5Ccancel%7B0.02%7D)
![\implies\boxed {0.01}](https://tex.z-dn.net/?f=%5Cimplies%5Cboxed%20%7B0.01%7D)
![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)
The numbers from least to greatest are 3.19, 3.195, 3 1/3, and 67/20. This is because 67/20 is equivalent to 3.35 in decimal form, which is greater than all of the other numbers, including 3 1/3, which is 3.3333.
Answer:
52:3
Step-by-step explanation:
divide 260 by 5 and 15 by 5
260 divided by 5 = 53
15 divided by 5 = 3
260:15 = 52:3
Answer:
Step-by-step explanation:
OK you should really have these by now.
Translation, reflection and rotations do not change segment lengths or angular relationships. They only change line slopes and/or y-intercepts.