Mathematics, 21.04.2020 18:04 neonbluefaith

Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)

Answers: 2

Show answers

Answers

Answer from: brookefrancett

ength (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3

Step-by-step explanation:

Let x is the side of identical squares

By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:

length (l) : (10-2x)width(w): (10-2x)height(h): x

The volume will be:

V = (10-2x) (10-2x) x

<=> V = (10x-2 $x^{2}$ ) (10-2x)

<=> V = 100x -20 $x^{2}$ - 20 $x^{2}$ + 4 $x^{3}$

<=> V = 4 $x^{3}$ - 40 $x^{2}$ + 100x

To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume

dV/dx = 12 $x^{2}$ -80x + 100

<=> 12 $x^{2}$ -80x + 100 =0

<=> x = 5 or x= 5/3

You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3

length (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3

Answer from: Quest

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

$\frac{1}{4}=\frac{x}{5}\\\\x=\frac{4}{5}\\\\x=0.8$

hence, first option 'a' is correct.

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$

here given table is,

price ($), x : 18 23 25 29 30 33

pairs sold, y : 16 13 10 8 6 2

so, $\sum x = 158$ , $\sum y = 55$ , $\sum xy = 1315$ ,

$\sum x^2 = 4308$ and $\sum y^2 = 629$ ,

thus, slop of the given line is,

$a = \frac{55\times 4308-158\times 1315}{6\times 4308-(158)^2}$

⇒ $a = \frac{29170}{884}$

⇒ $a =32.9977375566$ ≈ 33

Another question on Mathematics

Mathematics, 21.06.2019 15:30

What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters?

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

What situation is an example of an observational study

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

Agroup of three friends order a combo meal which includes two slices of pizza and a drink each drink is priced at $2.50 the combined total of $31.50 how much is the cost of a slice of pizza

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

Dots sells a total of 279 t-shirts ($2) and shorts ($4). in april total sales were $670. how many t-shirts and shorts did dots sell?

Answers: 1

Answer

You know the right answer?

Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squ...

Questions