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Thepotemich [5.8K]
3 years ago
14

A liquid vessel which is initially empty is in the form of an inverted regular hexagonal pyramid of altitude 25 feet and base ed

ge 10 feet. By how much will the surface rise when 6,779 liters of water is added?
Mathematics
2 answers:
mr_godi [17]3 years ago
8 0

Answer:

\text{Surface area } = 265.14\ ft^2

Step-by-step explanation:

A liquid vessel in the form of an inverted regular hexagonal pyramid.

Altitude of pyramid, h = 25 feet

Base edge of pyramid, a = 10 feet

\text{Volume of Pyramid}=\dfrac{\sqrt{3}}{2}a^2h

A liquid vessel contain maximum volume =\dfrac{\sqrt{3}}{2}\cdot 10^2\cdot 25=2165\ ft^3

Change cubic foot to liter

1\ ft^3 = 28.32\ liter

2165\ ft^3 = 61307.67\ liters

A vessel fill 6,779 liters of water.

6779 lt = 239.398 ft³

Therefore, 239.398=\dfrac{\sqrt{3}}{2}\cdot 10^2h

h=2.764\ ft

Surface area rise, a = 10 ft , h = 2.764 ft

\text{Surface area } = 3a\sqrt{h^2+\dfrac{3a^2}{4}}

\text{Surface area } = 3\cdot 10\sqrt{1.764^2+\dfrac{3\cdot 10^2}{4}}

\text{Surface area } = 265.14\ ft^2

Hence, The surface rise when 6,779 liters of water is added to vessel will be 265.14 ft^2

Misha Larkins [42]3 years ago
6 0
<span>Since: v =sqrt(3)/2 s^2h 

6779 liters x 0.0353cu ft/1 liter= 239.299 cu ft 
but by proportion s/h = 10/25 
s = 10/25 h 
and v = sqrt(3)/2 (10/25 h)^2 h 
239.299 = 0.139 h^3 

h = (239.299/0.139)^(1/3) = 11.985 ft</span>
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No it is not. If you had two fixed diagonals which are attached in the center, when they move it creates different parallelograms. The area would be close to zero if they were parallel.
8 0
3 years ago
At Friday's football game, 1,294 tickets were sold for a total amount of $8,816.00. If each student ticket costs $5.00, and each
NeTakaya

Answer:

512 student tickets.

Step-by-step explanation:

Let x be number of student tickets and y be number of adult tickets.

We have been given that at Friday's football game 1,294 tickets were sold. We can represent this information as:

x+y=1294...(1)

We are also told that each student ticket costs $5.00, and each adult ticket costs $8.00 and 1,294 tickets were sold for a total amount of $8,816. We can represent this information as:

5x+8y=8,816...(2)

From equation (1) we will get,

y=1294-x

Substituting this value in equation (2) we will get,

5x+8(1294-x)=8,816

5x+10352-8x=8,816

-3x+10352=8,816

-3x=8,816-10352

-3x=-1536

x=\frac{-1536}{-3}

x=512

Therefore, 512 student tickets were purchased at Fridays football game.

6 0
3 years ago
Factorization prima de 1024
Tamiku [17]
1024
/ \
32 32
/ \ / \
8 4 8 4
/\ /\ /\ /\
(2) 4 (2) (2)(2) 4 (2) (2)
/\ /\
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2x2x2x2x2x2x2x2x2x2 or 2^10

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3 0
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A survey of a group’s viewing habits over the last year revealed the following information: (i) 28% watched gymnastics (ii) 29%
almond37 [142]

Answer: D) 52%

Step-by-step explanation:

G = gymnastics

B = baseball

S = soccer

G = 28%

BA = 29%

S = 19%

G and BA = 14%

BA and S = 12%

G and S = 10%

GBS = 8%

So, as we can see at the Venn diagram attached (consider every number in %)

GBS = 8

A = G and S - GBS = 10 - 8 = 2

B = G and BA - GBS = 14 - 8 = 6

C = BA and S - GBS = 12 - 8 = 4

Only G = G - A - B - GBS = 28 - 2 - 6 - 8 = 12

Only BA = BA - B - C - GBS = 29 - 6 - 4 - 8 = 11

Only S = S - A - C - GBS = 19 - 2 - 4 - 8 = 5

So, 2+6+4+12+11+5+8 = 48

100 - 48 = 52%

3 0
3 years ago
Your charges will be $75.00 per month throughout the 2 years, so at the end of that time you will have paid?
alexgriva [62]

Answer:

$1800

Step-by-step explanation:

twelve months in a year 12*2=24

75*24=1800

7 0
2 years ago
Read 2 more answers
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