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valentinak56 [21]
3 years ago
6

A motel charges Mr. Kim X dollars for his day, Mr. Kim stayed at the motel for 12 nights, if the rate per night for a room is Wh

ite dollars express why in the terms of X
Mathematics
1 answer:
Blababa [14]3 years ago
6 0

Answer:

$X = $12y

Step-by-step explanation:

In this question, we are asked to give an expression to represent the amount of money charged to a man who stayed in a motel for a particular number of days.

Firstly, we need to know the amount of money charged per day. This is visible from

the question and it is equal to $y.

Secondly, the number of days/night stayed is 12 days. This means that the amount of money he was charged is 12 * y = $12y

Since the amount of money charged is equal to $x, the amount to pay can be expressed in terms of y and x to be

$X = $12y

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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
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Answer:

A(-1,0) is a local maximum point.

B(-1,0)  is a saddle point

C(3,0)  is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is  

f(x,y)=x^3+y^3-3x^2-3y^2-9x

The first partial derivative with respect to x is  

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We now set each equation to zero to obtain the system of equations;

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Solving the two equations simultaneously, gives;

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The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2

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f_{xx}=6x-6

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At A(-1,0),

D=(6(-1)-6)(6(0)-6)=72\:>\:0 and f_{xx}=6(-1)-6=-18\:

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

D=(6(-1)-6)(6(2)-6)=-72\:

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

D=(6(3)-6)(6(0)-6)=-72\:

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

D=(6(3)-6)(6(2)-6)=72\:>\:0 and f_{xx}=6(3)-6=12\:>\:0

Hence D(3,2) is a local minimum point.

See graph in attachment.

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