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nadya68 [22]
3 years ago
8

A stand is a frustum shape, formed by removing a small square-based pyramid from the top of

Mathematics
1 answer:
kupik [55]3 years ago
8 0

The frustum can be considered as consisting of a square pyramid, less the

cut volume.

  • The mass of the stand, is approximately 18.60905 kg

Reasons:

The given parameter of the frustum are;

The density of the frustum, ρ = 85 g/cm³

Height of pyramid, h = 9 cm

Side length of base = 10 cm

Height of frustum

By proportional shapes, the side length of the top of the frustum can be found as follows;

\dfrac{4 \, cm}{9 \, cm} = \dfrac{x}{10 \, cm}

x = \dfrac{4 \, cm}{9 \, cm} \times 10 \, cm = 4\frac{4}{9} \, cm

V = \dfrac{h}{3} \times \left(B_1 + B_2 + \sqrt{B_1 \times B_2} \right)

B₁ = 10², B₂ = \left(4\frac{4}{9} \right)^2

Therefore;

V = \dfrac{4}{3} \times \left(10^2 + \left(4\frac{4}{9}  \right)^2  + \sqrt{10^2 \times  \left(4\frac{4}{9}  \right)^2} \right) \approx 218.93

The volume of the stand, V ≈ 218.93 cm³

Mass = Volume × Density

∴ Mass of the stand, m = 218.93 cm³ × 85 g/cm³ = 18,609.05 grams = 18.60905 kg.

Learn more here:

brainly.com/question/24323975

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Evgesh-ka [11]

Answer:

AC = 7.12 units

Step-by-step explanation:

A right triangle has two legs and a hypotenuse. The hypotenuse is opposite the right angle. As Angle C is the right angle, then the triangle can be constructed as shown in the picture attached. The sides of the triangle have a relationship known as the Pythagorean Theorem a² + b² = c². In the theorem, the legs of the triangle are a and b while the hypotenuse is c. Substitute a = x, b = x+6, and c = √52. Simplify and solve.

a² + b² = c²

x² + (x+6)² = √52²

x² + x² + 12x + 36 = 52

2x² + 12x - 16 = 0

You can use the quadratic formula to solve by substituting a = 2, b = 12, and c = -16.

The quadratic formula is x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}.

Substitute and you'll have:

x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-12+/-\sqrt{12^2-4(2)(-16)} }{2(2)}=\frac{-12+/-\sqrt{144+128} }{4)}

\frac{-12+/-\sqrt{272} }{4}=\frac{-12+/-16.5 }{4} = 1.12, 7.13

Only 1.12 is a solution since 7.13 will not satisfy the Pythagorean theorem

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AC = 1.12 + 6 = 7.12

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3 years ago
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Step-by-step explanation:

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This is a rather famous probability problem.

The easiest way to solve this is to calculate the probability that you WON'T roll a "double 6" (or a twelve) each time you roll the dice.  There are 36 ways in which dice rols can appear and only one is a twelve.  So, for one roll, the probability that you will NOT get a twelve is (35/36)^n where 35/36 is about .97222222 and n would equal 1 for the first trial.  So for your first roll the odds that you WON'T get a 12 is .97222222.

For the second roll we calculate (35/36) to the second power or (35/36)^2 which equals about .945216.

When we get to the 24th roll we calculate (.97222222)^24 which equals 0.508596.  

For the 25th roll, we calculate (.97222222)^25 which equals  0.494468.  For the first time we have reached a probability which is lower than 50 per cent.  That is to say, after 25 rolls, we have reached a point in which the probability is less than 50 per cent that we will NOT roll a twelve.

To phrase this more clearly, after 25 rolls we reach a point where the probability is greater then 50 per cent that you will roll a 12 at least once.

Please go to this page 1728.com/puzzle3.htm and look at puzzle 48. (The last puzzle on the page).  An intersting story associated with this probability problem is that in 1952, a gambler named Fat the Butch bet someone $1,000 that he could roll a 12 after 21 throws.  (He miscalculated the odds [as we know you need 25 throws] and after several HOURS, he lost $49,000!!!)

Please go that page and it has a link to the Fat the Butch story.


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scZoUnD [109]
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Answer:

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