Answer:
I do not see anything
Step-by-step explanation:
?????????
1,132 people came to watch the balloon festival.
The Lagrangian,
![L(x,y,z,\lambda,\mu)=x+2y+9z-\lambda(x-y+z-1)-\mu(x^2+y^2-1)](https://tex.z-dn.net/?f=L%28x%2Cy%2Cz%2C%5Clambda%2C%5Cmu%29%3Dx%2B2y%2B9z-%5Clambda%28x-y%2Bz-1%29-%5Cmu%28x%5E2%2By%5E2-1%29)
has critical points where its partial derivatives vanish:
![L_x=1-\lambda-2\mu x=0](https://tex.z-dn.net/?f=L_x%3D1-%5Clambda-2%5Cmu%20x%3D0)
![L_y=2+\lambda-2\mu y=0](https://tex.z-dn.net/?f=L_y%3D2%2B%5Clambda-2%5Cmu%20y%3D0)
![L_z=9-\lambda=0](https://tex.z-dn.net/?f=L_z%3D9-%5Clambda%3D0)
![L_\lambda=x-y+z-1=0](https://tex.z-dn.net/?f=L_%5Clambda%3Dx-y%2Bz-1%3D0)
![L_\mu=x^2+y^2-1=0](https://tex.z-dn.net/?f=L_%5Cmu%3Dx%5E2%2By%5E2-1%3D0)
tells us
, so that
![L_x=0\implies-8-2\mu x=0\implies x=-\dfrac4\mu](https://tex.z-dn.net/?f=L_x%3D0%5Cimplies-8-2%5Cmu%20x%3D0%5Cimplies%20x%3D-%5Cdfrac4%5Cmu)
![L_y=0\implies11-2\mu y=0\implies y=\dfrac{11}{2\mu}](https://tex.z-dn.net/?f=L_y%3D0%5Cimplies11-2%5Cmu%20y%3D0%5Cimplies%20y%3D%5Cdfrac%7B11%7D%7B2%5Cmu%7D)
Then with
, we get
![x^2+y^2=\dfrac{16}{\mu^2}+\dfrac{121}{4\mu^2}=1\implies\mu=\pm\dfrac{\sqrt{185}}2](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D%5Cdfrac%7B16%7D%7B%5Cmu%5E2%7D%2B%5Cdfrac%7B121%7D%7B4%5Cmu%5E2%7D%3D1%5Cimplies%5Cmu%3D%5Cpm%5Cdfrac%7B%5Csqrt%7B185%7D%7D2)
and
tells us
![x-y+z=-\dfrac4\mu-\dfrac{11}{2\mu}+z=1\implies z=1+\dfrac{19}{2\mu}](https://tex.z-dn.net/?f=x-y%2Bz%3D-%5Cdfrac4%5Cmu-%5Cdfrac%7B11%7D%7B2%5Cmu%7D%2Bz%3D1%5Cimplies%20z%3D1%2B%5Cdfrac%7B19%7D%7B2%5Cmu%7D)
Then there are two critical points,
. The critical point with the negative
-coordinates gives the maximum value,
.
Answer:
9:15 or 3:5
Step-by-step explanation:
A ratio can compare a part of a whole to a whole.
In this case, our whole is the total number of shots attempted: 15.
The basketball player successfully made 9 of the attempts. 9 is our other number in this ratio.
Put these values in a ration.
part:whole
9:15
Notice that 9 and 15 can be simplified by dividing both numbers by 3.
3:5
This is your simplified ratio.
Hope this helps!