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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

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Alexandra [31]

Answer:

a) 0.75

b) 0.0625

c) 0.1875

d) 0.375

Step-by-step explanation:

Let's start by first finding the probability a teacher orders 6 boxes. Since it is a four sided dice, the probability of getting a 1 is going to be 0.25.

Similarly, for any other number on the dice, the teacher orders 2 boxes. We can think of this as NOT rolling a 1. Using our previous answer, this comes out to be: 1 - 0.25 = 0.75

It should be remembered in the following answers that teachers ordering 6 or 2 boxes are not influenced by the results of other teachers. These are statistically independent events.

a) As given above, this probability is 0.75

b) The probability that both teachers order 6 boxes will be their individual probabilities multiplied. This comes out to be: 0.25 x 0.25 = 0.0625

c) Like in part (b), this is both of their probabilities multiplied:

   0.25 x 0.75 = 0.1875

d) This is nearly the same as part (c), but with a little twist. The order matters. There are two scenarios:

  1.   First teacher gets 6 boxes, and the second gets 2.
  2.   First teacher gets 2 boxes, and the second gets 2.

Both of these events have a probability of 0.1875, as shown in (c). To get the total probability of this event happening, we must add these together:

0.1875 + 0.1875 = 0.375

4 0
3 years ago
Tell whether the angles are adjacent or vertical. Then find the value of x.
maxonik [38]

Answer:

  x = 63°

Step-by-step explanation:

~ They are adjacent angles because they have a common (one) vertex.

~ To find the value of x we must make an equation.

Angles on a straight line add up to 180°.

  117 + x = 180

  x = 180 - 117

  x = <u>63°</u>

8 0
3 years ago
Jerry bought 4.2 lbs of jelly beans for $3.98 per lb. Sales tax is 6%. What was the total amount Jerry paid for the jelly beans?
Illusion [34]

Answer:

4.2 x 3.98 = 16.716

6% Sales tax = 1.06

16.716 x 1.06

About 17.72

4 0
3 years ago
Please awnser this correctly! I will make you Brainliest!
Andrews [41]
Volume of cone: pi * r^2 * h/3
Given volume, height

942in^3 = 3.14 * r^2 * 9/3
942in^2 = r^2 * 9.42
Divide by 9.42
r^2 = 100, r = -10, 10
Cannot be negative so...

Solution: radius is 10 in.
8 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=5%202%2F3%20-10" id="TexFormula1" title="5 2/3 -10" alt="5 2/3 -10" align="absmiddle" class="l
polet [3.4K]
52/3 - 10
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52/3 - 10/1
Make sure they both have the same denominator
52/3 - 30/3
Now you can take the numerator and subtract it.
22/3
Now you simply simplify
7 1/3
So the answer is 7 1/3
6 0
3 years ago
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