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Dima020 [189]
2 years ago
11

a flower garden is in the shape of an equilateral triangle. each side measures 15 3/8 ft. what is the gardens perimeter

Mathematics
1 answer:
lisov135 [29]2 years ago
7 0

Answer:

16.125 is the perimeter

Step-by-step explanation:

Multiply 15.375 × 3 because a triangle has three sides and is equilateral.

15.375 × 3 = 16.125

Have a great day!

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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
A scoop of ice cream is the shape of a whole perfect sphere sits in a right cone.
Andrei [34K]

Answer:

  10 cm

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = 4/3πr³

The volume of a cone is given by the formula ...

  V = 1/3πr²h

The ratio of the volume of the cone to that of the sphere is ...

  Vcone/Vsphere = (1/3πr²h)/(4/3πr³) = h/(4r)

In order for the ratio to have a value of 1, we must have ...

  h = 4r

The height of the cone must be 4×2.5 cm = 10 cm to fit all of the ice cream.

7 0
3 years ago
Read 2 more answers
A certain process for removing copper from copper bearing ore had been in use for a period of time, and it is known that this pr
Anika [276]

Answer:

d. Ore treated with the new process.

Step-by-step explanation:

This is a common practice in statistics, in which we use a sample of a population to infer something about the entire population. We should use a sample of 100.

For example, if we want to know the proportion of residents of Buffalo, New York, who are Bills fans, we are going to take a sample of like, 100 residents, and then use this to estimate for the entire city.

In this problem, we have that:

A new process that is supposed to increase the recovered amount is being tested. In a simple random sample of 100 batches of ore, an average of 42 pounds per ton were recovered using the new process.

So the population of interest is the ore treated with new process. We use a sample of 100 to gather information about the entire population.

So the correct answer is:

d. Ore treated with the new process.

5 0
3 years ago
Sin^22x - 2cos2x + 2=0
zhuklara [117]

Answer:

x=πn, n∈Z

Step-by-step explanation:

if sin²2x=1-cos²2x, then

1-cos²2x-2cos2x+2=0; ⇒ cos²2x+2cos2x-3=0; ⇔ (cos2x+3)(cos2x-1)=0;

\left[\begin{array}{cc}cos2x+3=0\\cos2x-1=0\\\end{array} \  \ \left[\begin{array}{cc}x \ 'does-not-exist'\\cos2x=1\\\end{array} \  \ 2x=2\pi n, n=Z \  x=\pi n, n=Z

5 0
2 years ago
the sum of three consecutive odd numbers equals an even integer is this sometimes, always, or never true
mel-nik [20]
Never true.

the sum of 3 odd numbers is always odd

5 0
3 years ago
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