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
loris [4]
3 years ago
10

A rectangular box has a base that is 4 times as long as it is wide. The sum of the height and the girth of the box is 200 feet.

(a) Express the volume V of the box as a function of its width w. Determine the domain of V (w).
Mathematics
1 answer:
enyata [817]3 years ago
6 0

Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.

Step-by-step explanation:

The dimensions of the box are:

L = length

W = width

H = heigth.

We know that:

L = 4*W

And the girth of a box is equal to: G = 2*W + 2*H

then we have:

2*W + 2*H + H = 200ft

2W + 3*H = 200ft

Then we have two equations:

L = 4*W

2W + 3*H = 200ft

We want to find the volume of the box, which is V = W*L*H

and we want in on terms of W.

Then, first we can replace L by 4*W (for the first equation)

and:

2*W + 3*H = 200ft

3*H = 200ft - 2*W

H = (200ft - 2*W)/3.

then the volume is:

V(W) = W*(4*W)*(200ft - 2*W)/3

V(W) = (1/3)*(*W^2*800ft - 8W^3)

The domain of this is the set of W such that the volume is positive, then we must have that:

W^2*800ft > 8W^3

To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)

W^2*800ft = 8W^3

800ft = 8*W

100ft = W.

This means that if W is equal or larger than 100ft, the equation gives a negative volume.

Then the domain is 0 < W < 100ft.

You might be interested in
What does it mean for two fractions to be equivalent? For two ratios to be equivalent?
nadya68 [22]
When two fractions are equivalent that means that different fractions have the same number
6 0
3 years ago
Quick is this right??? Answer and question in pic
Olin [163]

Answer:

-199

Step-by-step explanation:

  • put -6 in place of x in equation
3 0
2 years ago
-2 = 6/7*p <br> How do you solve the equation.
Sophie [7]
Solve for p by simplifying both sides of the equation, then isolating the variable.
p= - 7/3
3 0
3 years ago
Read 2 more answers
Di ketahui f(x)=ax+b tentukan fungsi f(1)=3danf(2)=5
Komok [63]
F(x) = ax + b
maka..
f(1) = 3
a(1) + b = 3 --> a+b = 3

f(2) = 5
a(2) + b = 5 --> 2a+b = 5

untuk mencari nilai a dan b nya, di eliminasi, maka dapat
a=2 dan b=1
5 0
3 years ago
Write in exponential notation 6 times 6 times 6 times 6 times 6
Darina [25.2K]
Exponent form : 6^5

explanation :
we are given five 6's , so we simply start out with the number that is being multiplied over and over again .
which in this case , is 6.

6 • 6 • 6 • 6 • 6 = 7776

To make things easier though, we write repetitive numerals in exponent form. You will still get the same answer either way .

6^5 = 7776

answer : 6^5
7 0
3 years ago
Read 2 more answers
Other questions:
  • A sprinkler that sprays water in a circular area can spray up to a radius of 22 ft.
    15·2 answers
  • What is the length of AB
    9·2 answers
  • Which equation can be used to find the unknown length, a, in this triangle?
    8·1 answer
  • Find all real zeros of the function f(x)=-5x(x^2-49)(x-2)
    6·1 answer
  • What do each of these measure?
    13·2 answers
  • I need help on this Algebra question
    5·1 answer
  • ASAP!! Which graphs have same domain?
    14·1 answer
  • Duane Coldren has a check for $343 and a check for $88.91.
    10·1 answer
  • PLEASE HELP IK THIS IS KIND OF A SIMPLE QUESTION I JUST DONT WANNA SOLVE IT
    7·1 answer
  • Goodmorning everyone I need help in math please, I need solution also​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!