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
Nutka1998 [239]
3 years ago
7

An open top rectangular box is to be made from a rectangular piece of metal that is 3cm wide and 8cm long by cutting a square fr

om each corner and then folding up the sides. Find the size of the corner squares that will give the box having the largest volume.
Mathematics
1 answer:
Tanzania [10]3 years ago
5 0

Answer:

x  = 0.67 cm

Step-by-step explanation:

Let call  " x " the length of the side of the square to cut from each corner

then the sides of the future box would be

L = 8 - 2x       and   D = 3 - 2x

The volume of the box is:

V = L*D*x

And such volume as function of x is

V(x)  = ( 8 - 2x ) * ( 3 - 2x ) * x     ⇒  V(x)  = ( 24 - 16x - 6x + 4x²) * x

V(x)  =  4x³ - 22x² + 24x

Taking derivatives on both sides of the equation we get:

V´(x) = 12x² - 44x + 24

Then    V´(x) = 0       ⇒   12x² - 44x + 24 = 0    ⇒  3x² -  11x + 6 = 0

We got a second degree equation solving for x

x₁,₂  = [11 ± √ 121 - 72 ] / 6

x₁  = ( 11 + 7 ) / 6         x₁  =  3   we dismiss this solution since according to problem statement  one side would become negative

Then

x₂  =  (  11 - 7 ) / 6    ⇒    x₂  =  4/6      ⇒   x₂  =  0.67 cm

As the second drivative is smaller than 0 then there is a maximun in that point

V´´(x)  = 12x - 44  < 0

Sides of the box

L = 8 - 2x    ⇒  L = 8 - 2*(0.67)   ⇒  L  = 8  - 1.34    ⇒  L = 6.66 cm

D = 3 - 2x   ⇒   D = 3 - 2* (0.67) ⇒  D = 3 - 1.34    ⇒   D = 1.66 cm

Heigh  =  x  = 0.67 cm

V(max) = 6.66*1.66*0.67

V(max) = 7.41 cm³

You might be interested in
What is between 0.1 and 0.2
aliya0001 [1]
Theres an infinite amount of numbers because you could have 0.10123 to 0.19998298 its never ending 
8 0
3 years ago
graph the line that passes through the point (0, -3) and is perpendicular to another line whose slope is 2
Nadya [2.5K]

Answer:

 y = -1/2x -3

Step-by-step explanation:

The line perpendicular to one with a slope of 2 will have a slope that is the negative reciprocal of 2, that is, -1/2. The given point is the y-intercept of the required line, so we can write its equation directly in slope-intercept form:

y = mx + b

where m is the slope (-1/2), and b is the y-intercept (-3). Your line is ...

 y = -1/2x -3

4 0
3 years ago
Find cos 18, sin 18. cos 3x=sin2x then x=18.
Rzqust [24]
X = 18°
cos 54° = sin 36°
cos 3 x = sin 2 x
cos ( 2 x + x ) = sin 2 x
cos 2 x cos x - sin 2 x sin x = 2 sin x cos x
( cos² x - sin² x ) cos x - 2 sin² x cos x = 2 sin x cos x   / : cos x
                                                                         ( divide both sides by cos x )
cos² x - sin² x - 2 sin² x = 2 sin x
1 - sin² x - 3 sin² x - 2 sin x = 0
- 4 sin² x - 2 sin x + 1 = 0               substitution:  u = sin x
- 4 u² - 2 u + 1 = 0
u = 2 -√20 / - 4        sin 18° =  (√ 5 - 1 )/4 
sin 18 =  \frac{ \sqrt{5} -1 }{4}
cos 18° = √( 1² - ((√5 - 1)/4)²
cos 18° = (10+2√5)^(1/2) / 4

6 0
2 years ago
Learning
Pie

Answer:

gsjdudvegdiddbdb

Step-by-step explanation:

njshsuebsbhssnshssje

3 0
2 years ago
A car sells for $25,000. If the rate of depreciation is 15%, what is the value of the car after 7 years?
TEA [102]
I believe the value of the car after 7 years will be 3,750. Do you agree?  
3 0
3 years ago
Read 2 more answers
Other questions:
  • Rhonda was organizing photos in a photo album. She took 60 photos and divided them evenly between p pages. Which algebraic expre
    6·1 answer
  • In the diagram below, DE is parallel to XY. What is the value of y?
    8·2 answers
  • MATH<br><br>Answer and I will give you brainiliest <br>Answer and I will give you brainiliest <br>​
    5·1 answer
  • When shooting free throws, David is successful 7 out of every 10 shots.if he attempts 100 free throws ,about how many times will
    11·1 answer
  • If f(x)= 4x+3 and g(x)= 3x evalute f(x). g(x) for x=-1 over 2
    10·1 answer
  • Nina has 3 feet ribbon that she wants to cut into 8 equal sized pieces. What is true about the length of each ribbon? A) each pi
    6·2 answers
  • 0.0025 cm &lt;&lt; in scientific notation
    11·1 answer
  • Bridget and Caroline win some money and share it in the ratio 5:3. Bridget gets £65. How
    15·1 answer
  • in a parking lot 60% of the cars are four-door cars.If there are 75 four-door cars in the parking lot how many cars are in the p
    9·1 answer
  • -1.424-(-2.9)-0.576<br>plz show work​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!