Answer:
a the first one
Step-by-step explanation:
1/11 means 1 divided by 11
Answer:
Boys: 21.22 Girls: 16.89
Answer: A
Step-by-step explanation:
Add all the data points and divide it by the number of the data points.
Implicit differentiation
chain rule is important here
I'll show the steps partially
![e^y+xe^yy'-4y'=2](https://tex.z-dn.net/?f=e%5Ey%2Bxe%5Eyy%27-4y%27%3D2)
![xe^yy'-4y'=2-e^y](https://tex.z-dn.net/?f=xe%5Eyy%27-4y%27%3D2-e%5Ey)
![y'(xe^y-4)=2-e^y](https://tex.z-dn.net/?f=y%27%28xe%5Ey-4%29%3D2-e%5Ey)
![y'=\dfrac{2-e^y}{xe^y-4}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7B2-e%5Ey%7D%7Bxe%5Ey-4%7D)
now evaluate for (-2,2)
x=-2 and y=2
![y'=\dfrac{2-e^2}{-2e^2-4}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7B2-e%5E2%7D%7B-2e%5E2-4%7D)
![y'=\dfrac{2-e^2}{-2e^2-4}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7B2-e%5E2%7D%7B-2e%5E2-4%7D)
![y'=\dfrac{e^2-2}{2e^2+4}](https://tex.z-dn.net/?f=y%27%3D%5Cdfrac%7Be%5E2-2%7D%7B2e%5E2%2B4%7D)
that's it, simplest form
The solution is
and ![x=-0.5](https://tex.z-dn.net/?f=x%3D-0.5)
Step-by-step explanation:
The expression is ![2x(x+1.5)=-1](https://tex.z-dn.net/?f=2x%28x%2B1.5%29%3D-1)
Multiplying the term
by
, we get,
![2x^{2} +3x=-1](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B3x%3D-1)
Adding both sides by 1,
![2x^{2} +3x+1=0](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B3x%2B1%3D0)
Taking factor, we get,
![\begin{array}{r}{x^{2}+2 x+x+1=0} \\{2 x(x+1)+1(x+1)=0} \\{(2 x+1)(x+1)=0}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Br%7D%7Bx%5E%7B2%7D%2B2%20x%2Bx%2B1%3D0%7D%20%5C%5C%7B2%20x%28x%2B1%29%2B1%28x%2B1%29%3D0%7D%20%5C%5C%7B%282%20x%2B1%29%28x%2B1%29%3D0%7D%5Cend%7Barray%7D)
Equating the factors to 0,
and ![\begin{aligned}x+1 &=0 \\x &=-1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx%2B1%20%26%3D0%20%5C%5Cx%20%26%3D-1%5Cend%7Baligned%7D)
Thus, the smaller value is ![x=-1](https://tex.z-dn.net/?f=x%3D-1)
The solution is
and ![x=-0.5](https://tex.z-dn.net/?f=x%3D-0.5)