Help?<br>what do I do? Thanks x

A lidless box is to be made with a volume of 256256 ft cubed 3. Find the dimensions of the box that requires the least amount of

sveta [45]

The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.

The dimensions of your box will be 8 ft square by 4 ft high.

_____

If the base dimension is x ft, the area (quantity of material) is

... a = x² + 4x(256/x²)

... a = x² + 1024x⁻¹

Then the derivative of area with respect to x is

... a' = 2x -1024x⁻²

Setting this derivative to zero and solving for x gives the value of x for minimum area.

... 0 = 2x -1024/x²

... 512 = x³

... x = 8 . . . . . . . . same as above.

7 0

3 years ago

1)

vaieri [72.5K]

Answer:

see explanation

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

8 - 6 = 10 - 8 = 2

This indicates that the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 2, thus

$a_{n}$ = 6 + 2(n - 1) = 6 + 2n - 2 = 2n + 4 ← explicit formula

Hence

$a_{130}$ = (2 × 130) + 4 = 260 + 4 = 264

8 0

3 years ago

Clare has a set of cubes with a volume of 1 cm³ each. She also has a box with a volume of 24 cm³. Exactly two layers of cubes ca

Damm [24]

Answer:

12 cubes

Step-by-step explanation:

If the total volume of the box is 24 cm³ and the volume of each cube is 1 cm³ then that means that 24 total cubes can fit perfectly inside the box. Since there can only be two layers of cubes then we simply need to divide the total amount of cubes that will fit in the box by 2 to find the number of cubes in each layer...

24 / 2 = 12 cubes

Finally, we can see that each layer within the box will contain 12 cubes

5 0

3 years ago

The perimeter of a rectangle is 140 feet. The length of the rectangle is 6 more than 2 times the width. What is the length of th

Alja [10]

The equations we get are
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)

The first equation can be written as
l - 2w = 6

So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146

Divide by 3 on both sides.
l = 48 $\frac{2}{3}$

Your answer is 48 $\frac{2}{3}$ .

5 0

3 years ago

PLEAE help with this

ratelena [41]

Answer:

x = 67°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180 for x , that is

x = 180° - (38 + 75)° = 180° - 113° = 67°

5 0

2 years ago

Help?what do I do? Thanks x