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Vesnalui [34]
3 years ago
9

13 Use the given angle to find the missing angles 109 pleaseee before Monday ​

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

here

Step-by-step explanation:

hope this helps:)

ITS ABOUT ALTERNATIVE ANGLES

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there are 3 method to show that 40 is the sum of two prime. among all the prime , find the difference between the two largest pr
Maurinko [17]

Answer:

the difference is 39? for the answer

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2 years ago
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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as
Olin [163]

Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

7 0
3 years ago
If the perimeter changes does the area increase
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Answer:


Yes

Step-by-step explanation:

Yes,the area is the space inside a shape. If we change the borders of the shape, in space in the interior will change.

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X=14
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Im assuming you want to find out what x and y are
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Can you please help me
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Here’s the answer and each step I took to solve it. With the example I made on the side just continue to repeat that for each one to get the answers. You just replace that one number for the X to take the place for the next X value as you go down the table solving them.

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