Answer:
y = 8x
Step-by-step explanation:
When the number of people increased by 10, the caterer charged an additional $80. Therefore, we estimate that the cost per person is $8. In order to verify:
$8/person * 15 people = $120. True. $8/person * 25 people = $200. True.
Therefore, if we let x represent the number of people being cater for and y represent the cost, the equation to model the situation is simply y = 8x.
hope it helps!
Since it varies directly, divide the number of shots by the number of goals:
48 shots / 4 goals = 12
This tells you they score a goal every 12 shots.
Multiply shots needed by number of goals:
12 x 3 = 36
They need 36 more shots to score 3 more goals.
Answer:
4
Step-by-step explanation:
set
![f(x,y)=x+y\\](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dx%2By%5C%5C)
constrain:
![g(x,y)=x^2+y^2 = 7\\h(x,y)=x^3+y^3=10](https://tex.z-dn.net/?f=g%28x%2Cy%29%3Dx%5E2%2By%5E2%20%3D%207%5C%5Ch%28x%2Cy%29%3Dx%5E3%2By%5E3%3D10)
Partial derivatives:
![f_{x}=1\\f_{y} =1 \\g_{x}=2x \\g_{y}=2y\\h_{x}=3x^2 \\h_{y}=3y^2](https://tex.z-dn.net/?f=f_%7Bx%7D%3D1%5C%5Cf_%7By%7D%20%3D1%20%5C%5Cg_%7Bx%7D%3D2x%20%5C%5Cg_%7By%7D%3D2y%5C%5Ch_%7Bx%7D%3D3x%5E2%20%5C%5Ch_%7By%7D%3D3y%5E2)
Lagrange multiplier:
![grad(f)=a*grad(g)+b*grad(h)\\](https://tex.z-dn.net/?f=grad%28f%29%3Da%2Agrad%28g%29%2Bb%2Agrad%28h%29%5C%5C)
![\left[\begin{array}{ccc}1\\1\end{array}\right]=a\left[\begin{array}{ccc}2x\\2y\end{array}\right]+b\left[\begin{array}{ccc}3x^2\\3y^2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C1%5Cend%7Barray%7D%5Cright%5D%3Da%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2x%5C%5C2y%5Cend%7Barray%7D%5Cright%5D%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3x%5E2%5C%5C3y%5E2%5Cend%7Barray%7D%5Cright%5D)
4 equations:
![1=2ax+3bx^2\\1=2ay+3by^2\\x^2+y^2=7\\x^3+y^3=10](https://tex.z-dn.net/?f=1%3D2ax%2B3bx%5E2%5C%5C1%3D2ay%2B3by%5E2%5C%5Cx%5E2%2By%5E2%3D7%5C%5Cx%5E3%2By%5E3%3D10)
By solving:
![a=4/9\\b=-2/27\\x+y=4](https://tex.z-dn.net/?f=a%3D4%2F9%5C%5Cb%3D-2%2F27%5C%5Cx%2By%3D4)
Second mathod:
Solve for x^2+y^2 = 7, x^3+y^3=10 first:
![x=\frac{1}{2} -\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} +\frac{\sqrt{13}}{2} \\x=\frac{1}{2} +\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} -\frac{\sqrt{13}}{2} \\x+y=-5\ or\ 1 \or\ 4](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%20-%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D%20%5C%20or%20%5C%20y%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D%20%5C%5Cx%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D%20%5C%20or%20%5C%20y%3D%5Cfrac%7B1%7D%7B2%7D%20-%5Cfrac%7B%5Csqrt%7B13%7D%7D%7B2%7D%20%5C%5Cx%2By%3D-5%5C%20or%5C%201%20%5Cor%5C%204)
The maximum is 4
Answer:
9
Step-by-step explanation: