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ryzh [129]
2 years ago
12

50 apples cost $25. How much would 75 apples cost?​

Mathematics
1 answer:
iren [92.7K]2 years ago
8 0

Answer:

$37.50

Step-by-step explanation:

If 50 apples cost $25 to find the cost of 1 apple, we divide the total cost by the total number of items. In this case, we do 25/50.

One apple costs 0.50. If we need 75 apples then we simply multiply 0.50 by 75 which gets us 37.50.

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Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.
Alika [10]
The Lagrangian for this function and the given constraints is

L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)

which has partial derivatives (set equal to 0) satisfying

\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}

This is a fairly standard linear system. Solving yields Lagrange multipliers of \lambda_1=-\dfrac{32}{11} and \lambda_2=-\dfrac{104}{11}, and at the same time we find only one critical point at (x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right).

Check the Hessian for f(x,y,z), given by

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

\mathbf H is positive definite, since \mathbf v^\top\mathbf{Hv}>0 for any vector \mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top, which means f(x,y,z)=x^2+y^2+z^2 attains a minimum value of \dfrac{480}{11} at \left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right). There is no maximum over the given constraints.
7 0
3 years ago
35 61 63 69 49 46 52 32 34 50<br> what is the mode
egoroff_w [7]

Answer:

no mode

Step-by-step explanation:

Mode is the most common number shown therefore....

since there are no numbers repeated, the answer is no mode

3 0
3 years ago
HELPPPPPPP PLSSSSSSSSSS
vichka [17]

Answer:

B

Step-by-step explanation:

I checked it and it’s right hope this helps!!

6 0
2 years ago
Please help! question : “ Give 3 possible solutions to x&gt;2.”
professor190 [17]

Answer:

26 , 10 , 3

Step-by-step explanation:

Any number larger than 2 will work.

8 0
3 years ago
Write an inequality to describe the possible values of x.
Papessa [141]

Answer:

d

Step-by-step explanation:

x<9+7, and x+7>9

solve

x<16

x>2

2<x<16

6 0
3 years ago
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