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Gnoma [55]
3 years ago
7

Peter owns a hotel. He has found that when he charges $119 for a night’s stay, the average occupancy is 372 people. In addition,

Peter has found that with every $15 increase in the nightly cost, the hotel occupancy decreases by an average of 25. Write an expression to represent the nightly cost with x $15 price increases.
Mathematics
1 answer:
ozzi3 years ago
7 0
Without price increase,
Cost/night = $119
Average occupancy = 372
The revenue will be 119*372 = $44,268

For every $15 price increase, the occupancy decreases by 25.
Therefore with x price increases,
Cost/night = $119 + 15x
Occupancy = 372 - 25x
The revenue will be $(119 + 15x)*(372 - 25x)

Answer:
The nightly cost with x $15 price increases is $119 + 15x.
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lara31 [8.8K]

f(x,y)=x^4+y^4-4xy+1

has critical points wherever the partial derivatives vanish:

f_x=4x^3-4y=0\implies x^3=y

f_y=4y^3-4x=0\implies y^3=x

Then

x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1

  • If x=0, then y=0; critical point at (0, 0)
  • If x=1, then y=1; critical point at (1, 1)
  • If x=-1, then y=-1; critical point at (-1, -1)

f(x,y) has Hessian matrix

H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}

with determinant

\det H(x,y)=144x^2y^2-16

  • At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
  • At (1, 1), the determinant is 128, and f_{xx}(1,1)=12, which indicates a local minimum.
  • At (-1, -1), the determinant is again 128, and f_{xx}(-1,-1)=12, which indicates another local minimum.
4 0
3 years ago
A movie rental store chain membership fee of $10 plus $1.50 per movie rented what is the password I mean it shows the cost of a
djyliett [7]
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4 0
3 years ago
If and , find .<br><br> A. <br> B. <br> C. <br> D.
trapecia [35]
Answer: option D. 2x^2 + (3/2)x  - 5

Explanation:

1) polynomials given:

 f(x) = x/2 - 2 and g(x) = 2x^2 + x - 3

2) question: find (f + g) (x)

That means that f(x) + g(x), so you have to add up the two polynomials given.

3) x/2  - 2 + 2x^2 + x - 3

4) Combine like terms:

a) terms with x^2: you only have 2x^2, so it is not combined with other term.

b) terms with x: x/2 + x

that is a sum of fractions: x/2 + x = [x + 2x] / 2 = 3x / 2 = (3/2)x

c) constant terms: - 2 + (-3) = - 2 - 3 = - 5

5) Result: 2x^2 + (3/2)x - 5

That is the option d.


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Step-by-step explanation:

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Answer:

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