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
Cellus
Paladinen [302]

Answer:

9/4

Step-by-step explanation:

The quadratic function can be rearranged to look like this:

x^2-3x-1=0

Now we see that the constant b is equal to -3. Using the hint, we find:

(-3/2)^2=9/4

Hope that helps!

4 0
3 years ago
The systolic blood pressure (BP) of adults in the USA is nearly normally distributed with a mean of 121 and standard deviation o
Wittaler [7]

Answer:

Around 0.73% of adults in the USA have stage 2 high blood pressure

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 121 and standard deviation of 16.

This means that \mu = 121, \sigma = 16

Around what percentage of adults in the USA have stage 2 high blood pressure

The proportion is 1 subtracted by the p-value of Z when X = 160. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{160 - 121}{16}

Z = 2.44

Z = 2.44 has a p-value of 0.9927.

1 - 0.9927 = 0.0073

0.0073*100% = 0.73%

Around 0.73% of adults in the USA have stage 2 high blood pressure

5 0
3 years ago
hurry I'm going to give free brainly to all who answer in 1 minute Q: If a person was born in 1962 how old would they be Q:16549
vladimir1956 [14]

Answer:

they would be 58 rn. and simp means someone who is willing to do anything for someone they like. they try to get with that person everyday and they like them alot.

Step-by-step explanation:

hope this helped

8 0
3 years ago
Match the circle equations in general form with their corresponding equations in standard form. x2 y2 − 4x 12y − 20 = 0 (x − 6)2
frosja888 [35]

The equation given is matched with the respective vertex forms.

<h3>What is the standard Equation for a circle ?</h3>

The standard equation for a circle is given by

(x-h)² + (y-k)² = r²

The equation given in the question are

x² + y²  − 4x + 12y − 20 = 0

(x − 6)²  + (y − 4)²  = 56

x²  + y²  + 6x − 8y − 10 = 0

(x − 2)²  + (y + 6)²  = 60

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

5x²  + 5y²  − 10x + 20y − 30 = 0

(x+3)²  + (y-4)²  = 35

2x²  + 2y²  − 24x − 16y − 8 = 0

(x-1)²  + (y+2)²   = 11

The first equation is

x² + y²  − 4x + 12y − 20 = 0

It can be written ad

x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0

(x-2)² +(y+6)²= 60

The second equation is

x²  + y²  + 6x − 8y − 10 = 0

x² +6x +9-9 +y²  -8y +16-16 -10 = 0

(x+3)²  + (y-4)²  = 35

The third equation is

3x²  + 3y²  + 12x + 18y − 15 = 0

(x + 2)²  + (y + 3)²  = 18

The fourth equation is

5x²  + 5y²  − 10x + 20y − 30 = 0

(x-1)²  + (y+2)²   = 11

The fifth equation is

2x²  + 2y²  − 24x − 16y − 8 = 0

(x − 6)²  + (y − 4)²  = 56

To know more about standard equation of Circle

brainly.com/question/13658927

#SPJ1

7 0
2 years ago
Convert this franction into a percentage 9/12?
kolbaska11 [484]

<span>Hello, Yoloalanis. In order to solve this question that you have just posted, you only have to do a few simple steps. So, We can do this!</span>

<span />Let's start with your fraction. You will first have to change 9/12 into a decimal. In order to do this, you will have to divide the numerator by the denominator. A numerator is also known as the top part of the fraction. A denominator is the bottom part of the fraction. So, when you divide nine by twelve, you get 0.75 as a decimal. Now, you just have to multiply the decimal by 100 or to make it simpler, just move the decimal two places to the right. To sum it all up, you will get 75%.

Hope it helps :)

5 0
3 years ago
Read 2 more answers
Other questions:
  • Express ' in seconds.<br>30"<br>NEXT QUESTION<br>© ASK FOR HELP​
    15·1 answer
  • Please help thanks so much 20 points.
    10·1 answer
  • Find the y-intercept of the line on the graph.
    15·1 answer
  • Fruit salad can be made with any $3$ of these $5$ fruits: apples, bananas, grapes, strawberries, and pineapples. If strawberries
    11·1 answer
  • F(x) = x^2. What is g(x)?<br> g(x)
    12·1 answer
  • Nagoya read a book cover to cover in a single session at a rate of 55 pages per hour after 4 hours he had 350 pages left to read
    8·1 answer
  • Marco wants his total purchase for the month to be less than $450 write and solve an inequality to find how much more he can spe
    8·1 answer
  • Please help me with this question.
    8·1 answer
  • Find the sum of a polynomials -4xsquare 9x-3 and 7xsquare-5x 4
    14·1 answer
  • HELP WILL GIVE BRAINLIEST
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!