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
Pepsi [2]
3 years ago
6

An open rectangular box is 4 feet long and has a surface area of 20 square feet. Find the dimensions of the box for which the vo

lume is as large as possible.
Can someone please explain the steps to the answer if you can?
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
3 0
SA=2H(L+W)+LW for open box
20=2H(4+W)+4(W)
distribute
20=8H+2WH+4W
divide both sides by 2
10=4H+WH+2W
solve for 1 variable, pick W
10-4H=WH+2W
10-4H=W(H+2)
(10-4H)/(H+2)=W

V=LWH
subsitute 4 for V, subsitute H for H and (10-4H)/(H+2) for W
V=(4)(H)(10-4H)/(H+2)
V=(40H-16H²)/(H+2)
find max value
take deritivitive of this thing
V'=-16(H²+4H-5)/((H+2)²)
using sign chart
sign changes from positive to negative at H=1

so at H=1
find W

W=(10-4H)/(H+2)
W=2

the dimeionts are

length=4ft
width=2ft
height=1ft
(the volume is 8 cubic feet)
You might be interested in
Tom throws a Frisbee into the air from a height of 4 feet with
siniylev [52]

Answer:

68 feet

Step-by-step explanation:

Vertical motion model:

h = -16t² + vt + s

Given v = 64 and s = 4:

h = -16t² + 64t + 4

This is a parabola.  The maximum of a parabola is at the vertex.

For y = ax² + bx + c, the vertex is at x = -b/(2a).

Therefore, the time to reach the maximum height is:

t = -64 / (2 × -16)

t = 2

And the maximum height is:

h = -16(2)² + 64(2) + 4

h = 68

So the Frisbee reaches a maximum height of 68 feet.

5 0
3 years ago
Find two integers whose sum is 3 and product is -108.
AleksandrR [38]

Answer:

12 and -9

Step-by-step explanation:

12 x -9 = -108

12 + -9 = 3

7 0
3 years ago
HELP ME PLEASE ASAP!!
timama [110]

Answer:

8

Step-by-step explanation:


8 0
3 years ago
Solve the absolute value inequality: 1x + 12 + 5 < 27​
san4es73 [151]

Answer:10

Step-by-step explanation:

Dont know how to explain on here but I know for sure its 10 :)

5 0
3 years ago
Plot the points - 5.5 and 3.5 on the number line. Then use the number line to show and find the distance between the two points.
Mkey [24]
0.5+1+1+1+1+1+1+1+1+0.5=9
5 0
3 years ago
Other questions:
  • the big wheel could have a 52 inch diameter and the small wheel could have an 18 inch diameter.What is the circumference of the
    12·1 answer
  • 1=5 2=25 3=325 4=4325 6=?
    11·1 answer
  • Find the value of x that will make A||B<br><br> Thanks for helping. :)
    7·2 answers
  • What’s the area of a regular pentagon with a side length of 4 meters ?
    15·1 answer
  • Need help please help the middle one
    10·2 answers
  • Solve for the variable in 7 ∕28 = 25∕ x A. 20 B. 100 C. 4 D. 5
    15·1 answer
  • Calculate the number of degrees of one exterior and one interior angle of a regular 34-gon
    12·1 answer
  • Given that the quadrilateral shown is a rhombus, which statements are correct? A) mz1 = 32° D) m26 = 58° B) m 2 = 58° E) m27 = 3
    7·1 answer
  • A quadrilateral has two angles that measure 10° and 70°. The other two angles are in a ratio of 3:11. What are the measures of t
    11·1 answer
  • FACTORING POLYNOMIALS
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!