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erastova [34]
3 years ago
10

The line graph shows the number of cars owned by some families how many families were there

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer:3

Step-by-step explanation:tw

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Jacob is tiling his square walk with square tiles. He is able to fit 5 tiles up and 5 tiles across. If each tile has a length of
frozen [14]

Answer:

The perimeter of the kitchen wall = 60 b

Step-by-step explanation:

The number if tiles used in the length side of the square walk = 5 tiles

The length of 1 tiles  = 3 b

So, the length of 5 tiles = 5 x ( Length of 1 tile)  

= 5 x (3 b)  =  15 b

So, the length of the square walk = 1 5 b

Perimeter of SQUARE  = 4 x SIDES

⇒ Perimeter of the wall  = 4 x (Side)

                                        = 4 x (15 b)  = 60 b

Hence, the perimeter of the kitchen wall = 60 b

8 0
3 years ago
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
URGENT HELP THIS IS FOR DWREAD ONLY
QveST [7]

Answer:

(-1,0) and (3,0)

Step-by-step explanation:

The x-intercepts are the points where the graph crosses the x-axis. (-1,0) and (3,0)

6 0
3 years ago
Find the value of x.<br> 31°<br> to<br> 35°
VMariaS [17]

Step-by-step explanation:

the sum of all angles in a triangle is always (ALWAYS !) 180°.

180 = 31 + 35 + x = 66 + x

x = 180 - 66 = 114°

3 0
1 year ago
Read 2 more answers
What is this method called?????​
Serga [27]

Answer:

The algebraic method is a collection of several methods used to solve a pair of linear equations with two variables.

Step-by-step explanation:

8 0
2 years ago
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