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natta225 [31]
2 years ago
7

ANTHONY SURVEYED 320 STUDENTS AND FOUND OUT THAT 120 OF THEM HAVE A PET BASED ON THIS INFORMATION HOW MANY

Mathematics
1 answer:
lbvjy [14]2 years ago
6 0
I believe it would be 360 students.
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PLEASE HELP ASAP A glass stand to display a doll is in the shape of a right triangular pyramid. The area of the base is 40.5 squ
Effectus [21]

Answer: 202.5\ in.^3

Step-by-step explanation:

Given

The area of the base is A=40.5\ in.^2

height of the triangular prism is h=15\ in.

The volume of a triangular prism is  V=\dfrac{1}{3}Ah

The volume of given Prism is

V=\dfrac{1}{3}\times 40.5\times 15=202.5\ in.^3

The volume of the triangular prism is 202.5\ in.^3

8 0
2 years ago
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
2 years ago
Which number has the greatest value
irina1246 [14]
9.31 is the answer, in the decimal 31 has the greatest value
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3 years ago
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Are the following figures similar?
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C Yes; the corresponding angles are congruent
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94 times 39 = what?????
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The answer is 3,666

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