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frozen [14]
3 years ago
11

How do you know to use GCF or LCM to solve a word problem?

Mathematics
1 answer:
agasfer [191]3 years ago
6 0
By The wording and vocabulary
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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,
vichka [17]

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  

f_x=3x^2-6x-9

The first partial derivative with respect to y is  

f_y=3y^2-6y

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

3x^2-6x-9=0

3y^2-6y=0

Solving the two equations simultaneously, gives;

x=-1,x=3  and y=0,y=2

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

But, we would have to calculate the second partial derivatives first.

f_{xx}=6x-6

f_{yy}=6y-6

f_{xy}=0

\Rightarrow D=(6x-6)(6y-6)-0^2

\Rightarrow D=(6x-6)(6y-6)

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.

3 0
3 years ago
A person whose eye level is 20 feet above the ground is looking at a building. The angle of elevation to the top of the building
Inessa [10]
Distance of the person from the building (x)

tan 24 = 20/x => x = 20/tan 24 = 44.92 ft

The height of the building above the height of the person and the distance of the person from the building forms two legs of right angled triangle.

Therefore, if h is the height of the building, then;
tan 31 = (h-20)/44.92
h-20 = 44.92 tan 31
h = (44.92 tan 31) + 20 = 26.99 + 20 = 46.99 ft
8 0
2 years ago
X = 5y/(z-4y) <br><br> make y subject
Margarita [4]

Answer:

y=2x/5-4x

Step-by-step explanation:

multiply z-4y on both sides,match the Ys together and then make y common

3 0
2 years ago
ILL GIVE BRAINLIEST<br> 1 x/3 - 3/4= 5/12<br> solve for x
mel-nik [20]
X/3 - 3/4 = 5/2
x/3 = 3.25
x= 9.75 Or 9 3/4
4 0
1 year ago
Carrie works due south of her apartment. Her friend Sarah works due east of the
Zarrin [17]

Answer:

3 miles

Step-by-step explanation:

5-1+2=3

4 0
2 years ago
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