2x+5x+5=180 so x has to be 25
Answer:
yes it is a 75% decrease
Step-by-step explanation:
since 80-20=60
60/80=6/8=3/4
3/4=75%
The derivative of
at a point
in the direction of a vector
is
![\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}](https://tex.z-dn.net/?f=%5Cnabla%20f%28x_0%2Cy_0%2Cz_0%29%5Ccdot%5Cdfrac%7B%5Cvec%20a%7D%7B%5C%7C%5Cvec%20a%5C%7C%7D)
We have
![f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3D3e%5Ex%5Ccos%28yz%29%5Cimplies%5Cnabla%20f%28x%2Cy%2Cz%29%3D3e%5Ex%5Ccos%28yz%29%5C%2C%5Cvec%5Cimath-3ze%5Ex%5Csin%28yz%29%5C%2C%5Cvec%5Cjmath-3ye%5Ex%5Csin%28yz%29%5C%2C%5Cvec%20k)
and
![\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}](https://tex.z-dn.net/?f=%5Cvec%20a%3D-%5Cvec%5Cimath%2B2%5C%2C%5Cvec%5Cjmath%2B3%5C%2C%5Cvec%20k%5Cimplies%5C%7C%5Cvec%20a%5C%7C%3D%5Csqrt%7B%28-1%29%5E2%2B2%5E2%2B3%5E2%7D%3D%5Csqrt%7B14%7D)
Then the derivative at
in the direction of
is
![3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}](https://tex.z-dn.net/?f=3%5C%2C%5Cvec%5Cimath%5Ccdot%5Cdfrac%7B-%5Cvec%5Cimath%2B2%5C%2C%5Cvec%5Cjmath%2B3%5C%2C%5Cvec%20k%7D%7B%5Csqrt%7B14%7D%7D%3D-%5Cdfrac3%7B%5Csqrt%7B14%7D%7D)
Answer:
You would have 147 books
Step-by-step explanation:
Doge is smart, he has big brain.
Doge used a calculator