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
a_sh-v [17]
3 years ago
7

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

s. Find the dimensions of the tank with minimum weight.
Mathematics
1 answer:
marishachu [46]3 years ago
4 0

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

V = s^2h = 5324

h = 5324 / s^2

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top s^2

Side area 4sh

Total surface area A = s^2 + 4sh

We can substitute h = 5324 / s^2

A = s^2 + 4s\frac{5324}{s^2}

A = s^2 + 21296/s

To find the minimum of this function, we can take the first derivative, and set it to 0

A' = 2s - 21296/s^2 = 0

2s = 21296/s^2

s^3 = 10648

s = \sqrt[3]{10648} = 22

h = 5324 / s^2 = 5324 / 22^2 = 11

You might be interested in
What calculation is modeled on the number line?
vova2212 [387]

Answer:

top right

Step-by-step explanation:count how mnay it goes back each time

8 0
2 years ago
Read 2 more answers
Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours is a
Ivan

Answer:

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48

At most 3 hours?

P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X

What is the probability that it is less than the mean value by more than one standard deviation?

P(X

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

P(X=x)=\lambda e^{-\lambda x}

The cumulative distribution for this function is given by:

F(X) = 1- e^{-\lambda x}, x\ geq 0

We know the value for the mean on this case we have that :

mean = \frac{1}{\lambda}

\lambda = \frac{1}{Mean}= \frac{1}{2.725}=0.367

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48

At most 3 hours?

P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by: Var(X) =\frac{1}{\lambda^2}

And the deviation would be:

Sd(X) = \frac{1}{\lambda}= \frac{1}{0.367}= 2.725

And the mean is given by Mean = 2.725

Two deviations correspond to 5.540, so we want this probability:

P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity:

P(X

8 0
3 years ago
Principal = $8100; rate = 17%; time = 7 years What is the amount of interest earned?
miskamm [114]
<span>it must be nnnnnnnnnnnnnnnnnnnnnnnnn
4.37%

</span>
4 0
2 years ago
Pls someone help me or i’ll faint
never [62]
Answer:
a) DF = 20

b) DF =
Radical Form = sqrt(53)
Decimal Form = 7.28
5 0
2 years ago
Read 2 more answers
Part A<br> How can you determine whether JKL = PQR?<br><br> Part B<br> Is JKL = PQR
kotegsom [21]

Answer:

JKL = PQR and JKL = PQR

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Please explain 10-15. Thank you
    14·2 answers
  • The following dot plots shows the number of hours of sleep employees got before a major sale at three stores. Each dot represent
    7·2 answers
  • (7x-6y) and (x+y) <br> What is the sum?
    7·1 answer
  • While baking, Hannah discovered a recipe for cookies that required 3/4 cups of sugar for every 2+1/4 cups of flour. How many cup
    15·1 answer
  • The two angles shown are complementary angles.What is the value of x?
    7·2 answers
  • Liz wants to buy her favorite musical group’s new cd. the cd costs $15.24, including tax. liz gives the store clerk a twenty-dol
    12·1 answer
  • Regular hexagon ABCDEF is shown below. Find the measure of angle x.
    5·1 answer
  • Write the equation in standard form then factor the left side of the equation. 2x^2=28-x
    7·1 answer
  • What is the remainder of 715 divided by 9
    14·2 answers
  • alex has 3 bags with the same amount of marbles in them, totaling 12 marbles. kirian has 3 bags with the same amount in them tot
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!