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4 years ago

Select all irrational numbers.

Mathematics

2 answers:

Lyrx [107]4 years ago

7 0

34 94. 916............

lakkis [162]4 years ago

4 0

<h2>Answer:</h2>

All are irrational numbers

<h2>Explanation:</h2>

In mathematics an Irrational number is defined as any number that cannot be written as a complete ratio of two integers. An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal point. All the given numbers have un-ended numbers after the decimal point so they are irrational numbers.

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Use Lagrange multipliers to find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Enter the dimens

Dima020 [189]

Answer:

(x,y,z) = (12,12,12) cm

Step-by-step explanation:

The box is assumed to be a closed box.

The surface area of a box of dimension x, y and z is given by

S = 2xy + 2xz + 2yz

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

xyz = 1728

The constraint can be rewritten as

xyz - 1728 = 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) = 2xy + 2xz + 2yz - λ(xyz - 1728)

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

(∂L/∂x) = 2y + 2z - λyz = 0

λ = (2y + 2z)/yz = (2/z) + (2/y)

(∂L/∂y) = 2x + 2z - λxz = 0

λ = (2x + 2z)/xz = (2/z) + (2/x)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x)

(∂L/∂λ) = xyz - 1728 = 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

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

(2/y) = (2/x)

y = x

Also,

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

(2/z) = (2/y)

z = y

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

x = y = z

Putting these into the constraint equation or the solution of the fourth partial derivative,

xyz - 1728 = 0

x³ = 1728

x = 12 cm

x = y = z = 12 cm.

7 0

3 years ago

Amelia and Joey decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Amelia went first a

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Answer:

outer ring worth 14 pts

bull's-eye worth 74.333333 pts

Step-by-step explanation:

let the worth point of landing an arrow on the outer ring be "x" and on bull's eye be "y"

For amelia

$3x + 3y = 267$

For joey

$4x + 3y = 281$

subtracting the first equation from the second

$x = 14$

$3x + 3y = 267$

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4 years ago

In circle B with the measure of minor arc AC= 84°, find m

ELEN [110]

Answer:

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Step-by-step explanation:

Based on the inscribed angle theorem, the inscribed angle, m<ADC is ½ the measure of minor arc AC.

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m<ADC = ½(84)

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Answer:

Step-by-step explanation:

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Midsegment of triangle Find X

Charra [1.4K]

Answer:

$10 = x$

Step-by-step explanation:

This is what is called the Midsegment Theorem, which states that the relation of a triangle's midpunkt is parallel to the triangle's third side, and the mid-segment length is half the third side length, so you would take half of $4x + 20$ and set that expression equal to the midsegment:

2x + 10 = 3x

-2x - 2x

____________

$10 = x$

You then plug this back into both expressions above to get the double-segment of 60 and the mid-segment of 30. We can tell this is correct because 30 and 60 are relatively proportional to each other.

I am joyous to assist you anytime.

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3 years ago