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garri49 [273]
2 years ago
15

Describe how the graph is related to the graph of y = lxl.

Mathematics
1 answer:
loris [4]2 years ago
8 0

Answer:

The graph is 1 unit shift to right of y = lxl

Step-by-step explanation:

horizontal shift to right 1 unit of y = lxl

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A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 1584 cubic feet
liq [111]

Answer:

The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.

Step-by-step explanation:

We can find first the volume equation using the formula of the volume of a box.

V= xyz

Thus we get the constraint function

1584 = xyz

Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.

C=0.11 xy+ 2(0.06)xz+2(0.06yz \\ C =0.11 xy+0.12xz+0.12yz

Lagrange Multipliers to find minimum cost.

We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.

C_x=\lambda V_x \\ C_y = \lambda V_y \\ C_z = \lambda V_z

And the constraint function

xyz=1584

So we get

0.11y+0.12z=\lambda yz \\ 0.11x+0.12z=\lambda xz \\ 0.12x+0.12y=\lambda xy\\ xyz=1584

We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.

0.11xy+0.12xz=\lambda xyz \\ 0.11xy+0.12yz=\lambda xyz \\ 0.12xz+0.12yz=\lambda xyz

Then we can set each the equations equal to each other, so from the first one and the second equation we get

0.11xy+0.12xz= 0.11xy+0.12yz

We can subtract 0.11xy from both sides.

0.12xz=0.12yz

And we can divide both sides by 0.12z to get

x=y

We can repeat the process by setting the first and third equation equal to each other.

0.11xy+0.12xz= 0.12xz+0.12yz

We can subtract 0.12 xz from both sides

0.11xy=0.12yz

And we can solve by z

z= \cfrac{0.11x}{0.12}\\ z = \cfrac{11x}{12}

So if we replace that as well y = x on the constraint for the volume euqation we get

1584=x(x)\left(\cfrac{11}{12}x\right) \\ 1584=\cfrac{11}{12}x^3

We can then solve for x

x^3 = \cfrac{1584(12)}{11}

And taking the cube root

x = \sqrt[3]{\cfrac{1584(12)}{11}}

x = \sqrt[3]{1728}

x=12 ft

So then we can use the equations we have found for y and z in terms of x

y = x \\ y = 12 ft

And

z= \cfrac{11x}{12}\\z= \cfrac{11(12)}{12} \\ z=11ft

Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.

5 0
3 years ago
How many two-person committees can be formed from a group of six people,
finlep [7]

Answer:

3 two-person committee's can be formed from a group of six people

8 0
3 years ago
What is the slope of a line that contains points (3, 10) and (3, -2)?
marishachu [46]

Slope is y2-y1/x2-x1

Let’s make the point (3,10) our x1 and y1 and let’s make (3,-2) our x2 and y2

-2-10/3-3

-12/0 = undefined

The slope is undefined. If it were to be 0/-12, the answer would be 0. If any number were to be divided by 0, it would be undefined.

Hope I helped!

7 0
3 years ago
Read 2 more answers
A type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each
Inessa [10]

Answer:

B- 1/8 inch

Step-by-step explanation:

8 0
3 years ago
Can someone help me out
Likurg_2 [28]
False i think, i did it in my head so it might be wrong, but im pretty sure its false. hope it helped
8 0
3 years ago
Read 2 more answers
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