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Lesechka [4]
3 years ago
9

ppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 108 in.

What are the dimensions and volume of a square based box with the greatest volume under theses conditions
Mathematics
1 answer:
zaharov [31]3 years ago
3 0

Answer:

dimensions are 36 x 36 x 36

Volume= 46656 inch³

Step-by-step explanation:

Supposing the dimensions x , x and y as the base is a square base.

So, their sum is : x + x +  y= 108

2x + y= 108

y= 108 - 2x --> eq(1)

Also, they are lengths, x,y >0

Next is to determine the maximum volume, the function is

V(x,y)= x.x.y => x²y

By subsitituing value of y from eq(1) in above equation

V(x)=x²(108-2x)

V(x)= 108x² - 2x³

In order to find critical point, take the derivative and set it to zero

V'(x)=  216 x - 6x² = 0

36 - x =0

<u>x = 36 in</u>

Plugging the value of 'x' in eq(1)

(1)=> y = 108 - 2(36)

<u>y= 36 in</u>

Therefore, the  volume of a square based box will be

V= x²y = 36² . 36

<u>V=46656 in³</u>

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Help me solve this image please!!!
tresset_1 [31]

Based on the information, Christian would have $5525.5 of an annuity.

<h3>How to calculate the annuity?</h3>

According to the given information, the number of coffees per week is 3 then, per month is 3x4 = 12

Each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54

Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133

n = number of payments = 8 x 12 = 96

We can use the formula for finding the future value as below

FV = C x [ ( 1 + r )n-1 ] / ( r )

FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)

= 54 x [ (1.13609 - 1)] / (0.00133)

= 54 x 0.13609 / (0.00133)

= 54 x 102.3233

= 5525.5

Therefore Christian would have $5525.5 of the annuity.

Learn more about annuity on:

brainly.com/question/5303391

#SPJ1

5 0
2 years ago
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d
aksik [14]

Answer:

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

<h3 /><h3>Step 1</h3>

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

f(t)=\left \{ {{0 ,\-t

Consider the second function:

f(t)=\frac{e^{-t/\mu}}{\mu}\\

Where Average waiting time = μ = 2.5

The function f(t) becomes

f(t)=0.4e^{-0.4t}

<h3>Step 2</h3>

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt

which is equal to 0.01

<h3>Step 3</h3>

Solve the equation for x

\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01

Take natural log on both sides

ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53

<h3>Results</h3>

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

3 0
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Sketch the graph of the inequality.
Bingel [31]

Answer: D. Check Desmos for confirmation. Its your best friend for Graphing.

Step-by-step explanation:

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What does Sokka drink when stranded in the desert in the show Avatar: The Last Airbender?
EleoNora [17]

Answer:

Cactus Juice

Step-by-step explanation:

After drinking cactus juice, Sokka begins to hallucinate. Katara, Sokka, Toph, and Momo stagger tiredly through the desert.

3 0
3 years ago
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Select the action you would use to solve 3x = 12. Then select the property
podryga [215]

Answer:

C: Divide both sides by 3

F: Division property of equality

Step-by-step explanation:

3x=12\\x=\frac{12}{3}\\x=4

3 0
2 years ago
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