1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Step2247 [10]
2 years ago
11

A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin

g squares the same size from each corner of a sheet, bending up the sides, and sealing the corners. Create an equation relating the volume V of the box to the length of the corner cut out x. Identify the dimensions of the box that will have the maximum volume.
Mathematics
1 answer:
Natalija [7]2 years ago
3 0

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2}   or  \frac{30-21.21 }{2}\\ = \frac{51.21 }{2}   or  \frac{8.79}{2}\\ = 25.605 or 4.395

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

You might be interested in
F(x) = 2/5x + 24 what is the value of x when f(x) =25
dybincka [34]

Answer:

exact form: 5/2

decimal form: 2.5

mixed number form: 2    2/1

Step-by-step explanation:

8 0
2 years ago
Help me please please help
Vilka [71]

Answer:

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
I need help with #13 and #14 please
goldenfox [79]
U have to multiply and then divide it and find that scale
5 0
3 years ago
Is 1/4 a rational or irrational number
ycow [4]
Hi there!

1/4 is a rational number.
Any number that can be written as a fraction is a rational number.

~ Hope this helps you ~
6 0
3 years ago
The American Water Works Association reports that the per capita water use in a single-family home is 74 gallons per day. Legacy
Lunna [17]

Answer:

Reject H0 since test statistic <-2.492

Step-by-step explanation:

Given that the American Water Works Association reports that the per capita water use in a single-family home is 74 gallons per day.

n = 25

x bar = 69

s= 8.3

std error = s/sqrt n = \frac{8.3}{5} \\=1.66

H0:\bar x = 74

Ha: \bar x

(Left tailed test at 5% significance level)

a) Reject H0 if t\leq-2.492

b) Test statistic = mean difference/std error

= \frac{69-74}{1.66} \\=-3.012\\

=-3.01

df =24

c) Reject H0

6 0
3 years ago
Other questions:
  • <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B16%7D%7B24%7D%20" id="TexFormula1" title=" \frac{2}
    12·2 answers
  • in a party,there is 40 percent more males than females.there are 475 males and females altogether.how many males were at the par
    7·1 answer
  • What is the quotient of the rational expressions shown below?
    8·2 answers
  • Please help with math homework show work<br><br>All of the questions
    9·1 answer
  • <img src="https://tex.z-dn.net/?f=%20-%202x%20%2B%205y%20%3D%2017%20%20%5C%5C%20x%20%2B%20y%20%3D%209" id="TexFormula1" title="
    11·1 answer
  • Plz answer 100 points!!!!!
    7·1 answer
  • Can I get help with this please ????
    10·1 answer
  • Please help me on this!
    5·1 answer
  • A savings account with $1,000 has no other
    9·1 answer
  • A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for ever
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!