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hammer [34]
3 years ago
5

PLESE HELP GEOMETERY

Mathematics
1 answer:
nalin [4]3 years ago
4 0

In this problem, you must use SohCahToa which basically means:

Sin - opposite over hypotenuse

Cosine - adjacent over hypotenuse

Tangent - Opposite over hypotenuse


So in this picture we have 4 -which is on the opposite side of x - and a 5 -which is the hypotenuse of the triangle. This means we must use sin.

Using a calculator you put in:

sin^{-1} (\frac{4}{5} )

Your answer is 53.13 degrees

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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x
nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

f_x=8x

f_y=4y

g_x=3

g_y=3

Setting up the Lagrange multiplier equations:

f_x=\lambda g_x

⇒ 8x = 3λ                                        .....................(1)

f_y=\lambda g_y

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944                            ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0
2 years ago
Farouc Jaffer.
harkovskaia [24]

Answer:

1996.66.......

Step-by-step explanation:

6 0
3 years ago
POSTED THIS QUESTION TWICE NOW!!!!!!!!! SOMEBODY PLEASE HELP LIKE FR!!!! I JUST NEED THIS LAST QUESTION!!!
iVinArrow [24]
The answer is A(12-x) (10-x)=0
5 0
3 years ago
What us the surface area of the box ?​
Aleonysh [2.5K]

Answer:

243

Step-by-step explanation:

6x3x13.5=243

3 0
3 years ago
Marti’s photo album has a total of 45 pictures. Each page holds 4 pictures. She said she can only fill 10 pages completely.
amm1812

Answer:

She can only fill 10 pages completely.

Step-by-step explanation:

She can fill 10 pages, because 40/10=4.  She does not have enough pages left to fill another page fully.

8 0
2 years ago
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