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
Artyom0805 [142]
3 years ago
12

Suppose an airline policy states that all baggage must be box shaped with a sum of length, width, and height not exceeding 174 i

n. What are the dimensions and volume of a square-based box with the greatest volume under these conditions? Write a function for the volume V of the box in terms of w, one of the edges of the square bottom. (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The length of the square-end edge isn. The box height is in. The greatest volume of the box is in.3
Mathematics
1 answer:
Leya [2.2K]3 years ago
8 0

Answer:

The square-based box with the greatest volume under the condition that the sum of length, width, and heigth does not exceed 174 in is a cube with each edge of 58 in and a volume of 195112 in^{3}

Step-by-step explanation:

For this problem we have two constraints, that are as follows:

1) Sum of length, width, and heigth not exceeding 174 in

2) Lenght and width have the same measure (square-based box)

We know that volume is equal to the product of all three edges, and with the two conditions into account we have the next function:

V=(w^{2})(174-2w)\\V=174w^{2}-2w^{3}

The interval of interest of the objective function is [0, 87]

This problem requieres that we maximize the function that defines the volume. We start calculating the derivative of the function, wich is:

V'=348w-6w^{2} \\V'=(348-6w)(w)

We need to remember that the derivative of a function represents the slope of said function at a given point. The maximum value of the function will have a slope equal to zero.

So we find the value in wich the derivative equals zero:

0=(348-6w)(w)\\w_1=0\\w_2=348/6=58

The first value (w=0) will leave us with a 'height-only box', so the answer must be w=58 in

The value is between the interval of interest.

And, once we solve for the constraints, we have that:

Lenght = Width = Heigth = 58 in

Volume = 195112 in^{2}

You might be interested in
Help identify measure of arc UV
weqwewe [10]
M<UWV =180- 99 -36= 45
45 = 1/2(94+20- arcUV)
45=57 - arcUV/2
arcUV / 2 = 57-45
arcUV / 2 =12
arcUV = 12(2)
arcUV = 24

answer is B. 24

6 0
3 years ago
HELP.
wolverine [178]

Answer:

x=8

Step-by-step explanation:

5 0
3 years ago
Help me with this question please
mojhsa [17]

Step-by-step explanation:

so, he will not wear any pants ? socks ? not to mention underwear ?

anyway, we have to deduct the $35 for the shoes, as he is seemingly buying them in any case.

so, we are left with 100 - 35 = $65 for shirts.

as one shirt costs $15, we need to see how often 15 fits into 65, as that is the answer how many shirts he can buy for this money.

65 / 15 = 4.333333333...

since he cannot buy a part shirt, we can only rely on the integer part of the calculation.

so, he can buy 4 shirts and will have $5 left.

8 0
2 years ago
What is m∠VWX? 75° 69° 119° 25°
Bogdan [553]

Answer:

Step-by-step explanation:

Sum of interior angles of a triangle = Exterior angle

m∠VWX + m∠WVX = Exterior angle = 155°

m∠VWX + 86° = 155°

m∠VWX = 69°

6 0
3 years ago
Read 2 more answers
a coin is flipped and a six-sided die, numbered 1 to 6, is rolled. find the probability of flipping tails and rolling a number l
pantera1 [17]

Answer:

5/6

Step-by-step explanation:

There is a 1 out of 2 chance that you will roll tails, so the probability is 1/2.

A number less than three is a 2 and 1, so the probability is 2/6.

Add 1/2 + 2/6. (Change 1/2 to 3/6 so you can add.)

3/6 + 2/6 = 5/6

<em>I hope this is correct and helps you! </em>

6 0
3 years ago
Other questions:
  • The base of a pyramid has n sides. Write and expression for the number of faces of the pyramid
    6·1 answer
  • LAN mailed a package that weighed 5.63 pounds . what is the first step in rounding this number to the nearest tenth? what is the
    6·1 answer
  • One day, Donnie observes that the wind is blowing at 6 miles per hour. A unladen swallow nesting near Donnie’s house flies three
    11·1 answer
  • Please help! 10 points
    14·2 answers
  • Write the equation of a line in standard form that has x-intercept (P,0) and y-intercept (0,R).
    8·1 answer
  • What is 3.7 plus 2.774
    13·2 answers
  • WILL MARK BRAINLIEST PLSS HELPPP.Triangle RST has vertices R(–1, 1), S(3, 1), and T(3, –4). What
    14·1 answer
  • The sum of two numbers is 90. Their difference is 18. Find<br> the numbers.
    6·2 answers
  • Rewrite the equations
    11·1 answer
  • ANSWER THE QUESTION FOR BRAINLIST !!
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!