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IRISSAK [1]
2 years ago
9

Which integer is the smallest -6, 0, 3,6 -3,4 -4

Mathematics
1 answer:
Lina20 [59]2 years ago
3 0

Answer:

-6

I hope this helps!

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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 a seed is planted, it has a 75% chance of growing into a healthy plant.
Arlecino [84]

Answer:

It is binomial:

p= 0.75 = 75%

1-p = 0.25 = 25%

N = 10

k=7

"seven successes in 10 trials"

(10 choose 7) (0.75)^7 ( 0.25)^3 =

(10*9*8 / 3*2) * (0.75)^7 ( 0.25)^3 =

(5*3*8) (0.75)^7 ( 0.25)^3

120 (0.75)^7 ( 0.25)^3  

= 0.25028228759765625

or just over 25%

Step-by-step explanation:

5 0
2 years ago
Please Help. ASAP!!
Ratling [72]

Answer:

Equation:   x + (x+ 1) = 67

Step-by-step explanation:

We want to find two consecutive integers.

Let them be labeled as  x and x + 1

We want  x + (x + 1) = 67

x is the smaller number

x + 1 is the largest

We can solve for x.

x + (x + 1) = 2x + 1 = 67

2x = 66

x = 33

The largest integer is 34

3 0
2 years ago
Is 62.90 bigger or 62.09?
zhuklara [117]

Answer:

62.90

Step-by-step explanation:

62 and 90 hundredths is more than 62 and 9 hundredths.

To compare decimal, try to say the decimal with its place value, and its way easier to compare.

3 0
2 years ago
Read 2 more answers
How do you graph the equation Y = 4x + 2 and 4x - 3y = 12?
Pachacha [2.7K]

Answer:look below

Step-by-step explanation:

To graph y= 4x +2 plot the point (0,2) on the graph because the y-intercept is 2 then use the slope: 4 to find another point. Another point would be (1,6).

6 0
2 years ago
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