All categories

3 years ago

NEED HELP HW PLZ I WILL GIVe BRAINLIEST

Mathematics

1 answer:

Alexus [3.1K]3 years ago

3 0

Answer:

circles are cool because lines

You might be interested in

3) Postcards: Marcie wants to make a box to hold her postcard collection from a piece of

klasskru [66]

The volume of the box is the amount of space in it.

The dimension of the postcard is:

$\mathbf{Length = 10}$

$\mathbf{Width = 18}$

Let x represents the length of the cut.

So, the dimension of the box is:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

(a) The function that represents the volume of the box

This is calculated as:

$\mathbf{V(x) = Length \times Width \times Height}$

So, we have:

$\mathbf{V(x) = (10 - 2x) \times (18 - 2x) \times x}$

Expand

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Hence, the volume function is: $\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

(b) The dimension that maximizes the volume

We have:

$\mathbf{V(x) = 180x - 56x^2 + 4x^3}$

Differentiate

$\mathbf{V'(x) = 180- 112x + 12x^2}$

Set to 0

$\mathbf{180- 112x + 12x^2 = 0}$

Using a calculator, we have:

$\mathbf{x = 7.3,2.1}$

The value x = 7.3 is greater than the dimension of the box.

So, we have:

$\mathbf{x = 2.1}$

Recall that:

$\mathbf{Length = 10 -2x}$

$\mathbf{Width = 18 -2x}$

$\mathbf{Height = x}$

So, we have:

$\mathbf{Length = 10 -2 \times 2.1 = 5.8}$

$\mathbf{Width = 18 -2 \times 2.1 = 13.8}$

$\mathbf{Height = 2.1}$

Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1

(c) The maximum volume

This is calculated as the product of the dimension of the box

So, we have:

$\mathbf{Volume = 5.8 \times 13.8 \times 2.1}$

$\mathbf{Volume = 168.1}$

Hence, the maximum volume of the box is 168.1 cubic inches

Read more about volumes at:

brainly.com/question/17056191

5 0

3 years ago

You plan on buying new flooring for your bedroom. Your bedroom is a rectangle that is 12.7 ft. by 14.25 ft. How many square feet

joja [24]

Answer:

180.975 square feet

Step-by-step explanation:

est: 181 square feet

4 0

3 years ago

The side length, s, of a cube is x - 2y. If V = s3, what is the volume of the cube?

Ira Lisetskai [31]

Answer:

Answer: A.

Step-by-step explanation:

7 0

3 years ago

Tom always keeps his 4 gardens clean. He takes 20 minutes to clean a single garden. How much time will it take to clean all four

Nataly [62]

If each garden takes 20 minutes to clean, it will take him (20 x 4) to clean the gardens.

20 x 4 = 100

80 minutes

or 1 hour and 10 minutes.

5 0

3 years ago

Read 2 more answers

A farmer harvests crops on 2/5 acre of land in 1/3 hour.

Lady bird [3.3K]

Find out how much per hour, multiply 2/5 by 3

2/5 * 3/1 = 6/5
The farm harvests 1 1/5 acres per hour

8 0

3 years ago