Archimedes was asked by his king to figure out a way of telling if people were giving him fake gold objects. That was when Archimedes discovered his famous principle: an object placed in water displaces the same volume of water as the object’s volume. Explain how Archimedes used this to solve his problem.

Answers

Answer 1

Answer:

The Archimedes Principle

Step-by-step explanation: He took the 5 kg crown and dipped it in a vessel full of water. He calculated the displaced water.

Then he took 5 kg pure gold bricks and dipped it in a vessel full of water. He then calculated the displaced water and he found that the vessel with pure gold bricks displaced more water than the vessel with the crown. This is the Archimedes principle which states that the body at rest in a fluid is acted upon by a force pushing upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.

Hope it helps you:))))

Have a good day

Answer 2

Answer:

Archimedes Principle

Step-by-step explanation:

Archimedes used the principle of buoyancy, which states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. By applying this principle, Archimedes was able to determine the density of an object and distinguish between real gold and fake gold objects.

To solve his problem, Archimedes first measured the weight of the suspect gold object on a scale. He then filled a container with water and recorded the amount of water displaced when the object was submerged. According to the principle of buoyancy, the weight of the water displaced by the object is equal to the weight of the object itself.

Next, Archimedes compared the weight of the object to the weight of an equivalent volume of pure gold. Since the density of gold is known, he could calculate the expected weight of a genuine gold object with the same volume as the suspect object. If the weight of the suspect object matched the expected weight, it was likely made of real gold. However, if the weight was significantly different, it indicated that the object was made of a less dense material, such as a gold alloy or another metal.

By using the principle of buoyancy and comparing the weight of objects to the weight of the water they displaced, Archimedes devised a method to identify fake gold objects and ensure the integrity of the king's treasure. This principle is known as Archimedes' principle and has since become a fundamental concept in physics.


Related Questions

DOES the given value make the inequalities true? x + 9 > 21, when x = 15?

Answers

Answer:

Yes.

Step-by-step explanation:

When [tex]x=15[/tex],

[tex]x+9=15+9=24 > 21[/tex].

Answer:

Yes this is true

Step-by-step explanation:

24 is greater than 21; which means this statement is always true.

Find the length of the third side. If necessary, write in simplest radical form.

Answers

[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}[/tex]

Which measure is of an angle that is coterminal with a 425° angle?
425° – (1,000n)°, for any integer n
425° – (840n)°, for any integer n
425° + (960n)°, for any integer n
425° + (1,440n)°, for any integer n

Answers

The measure of angle that is coterminal with 425° is 425° + (1440n)°

What are coterminal angles?

Coterminal angles are angles in multiples of the angles in standard positions examples(360°).

It is mostly gotten by adding  360° or multiples of 360 to the angle.

One of the unique behavior of coterminal angles is that their sine, cosine and tangent are equal.

Analysis:

From the options, the only one with an addition of 360 or multiples of 360 is 425 + 1440n

If we put n = 1, the coterminal angle gotten is 1865.

if we find the sine of 425°, we get 0.9063 which is same as the sine of 1865°.

In conclusion, the coterminal angle to 425° is 425° + (1440n)°.

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Answer:

B. 425° – (840n)°, for any integer n

Which is the most reasonable estimate of 132% of 48?
5.2
6.5
52
65

Answers

I believe it would be 65

Answer:

65

Step-by-step explanation

Just did it on egde

What is the area of the trapezoid shown? The figure is not drawn to scale.

284.31 in.²
303.75 in.²
568.62 in.²
607.5 in.2

Answers

Answer:

284.3

Step-by-step explanation:

Trapezoid Formula:

A=a+b/2*h

plug in the numbers

Protons have a small negative electrical charge.
True
False

Answers

Answer:

False

Step-by-step explanation:

Protons have positive charge.

Answer:

Protons have a positive charge.

Step-by-step explanation:

Toni participates in a 10-mile charity walk. For each mile she walks, a sponsor will donate $9 to the charity. The graph represents the function that models the amount of money the sponsor will donate given the number of miles, x, Toni walks. what is the domain of the fuction

Answers

The domain of the function when Toni participates in a 10-mile charity walk will be [0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90]

What is a function?

It should be noted that a function simply means a relation that's used to express a variable with another variable.

In this case, it should be noted that a domain simply means the set of possible values of the independent variable. The function here is 9x. The domain is all x-values or inputs of a function. Therefore, the domain is depicted above.

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pleaseeee help I really need help so baddd​

Answers

Answer:

Step-by-step explanation:

What do you need help with

A major river flowing out of the Himalayas

Answers

Answer:

The Ganges

Step-by-step explanation:

Answer:

Ganga

Step-by-step explanation:

Ganga is the holy river of IndiaIt has risen from Himalayas.It flows throughout the Ind and falls at Sundarban inside Bay of Bangal

A website advertises 85 video games for $1969. How much would 160 video games cost at the same unit
price?

Answers

Answer:

$3705.60

Step-by-step explanation:

1969/85=23.16

23.16x160=3705.6

Help please thank you ​

Answers

When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other. The supplementary angles are 153° and 27°. The Complementary angles are 34° and 56°.

What are Supplementary Angles?

When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.

for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.

What are Complementary Angles?

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

The supplementary angles are 153° and 27°.

The Complementary angles are 34° and 56°.

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: The proliferation of the Internet has given rise to a new method of advertising, called spamming, that essentially is a more cost-effective method of the telephone solicitation method known as cold calling. If a company buys three mailing lists with 2,500, 3,500, and 4,000 email addresses respectively and spams them with promotional material, how many potential customers has it reached?

Answers

The number of potential customers that the company has reached is 10,000  e--mail addresses.

What is a word problem in mathematics?

A word problem is a real-life problem and it can be approached with the use of a mathematical model, interpretation into variables, and arithmetic operations usage.

Given that:

A company buys three mailing lists with 2500, 3500, and 4000 addresses respectively.

The number of potential customers that the company has reached is:

= 2500  3500 + 4000 e--mail addresses.

= 10,000  e--mail addresses.

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Shane's age is 8 years more than three times Edward's age. Their combined age is 56 years.

How old is Shane?

Answers

24 the answr is 24 this was mad easy
Answer: Shane is 44 .

Explanation:
y=shane's age
x=edward's age
y=3x+8
56=sum of their combined ages

56=4x+8
48=4x
x=12

y=3(12)+8
y=44

Find the midpoint of the line segment
1) (-2,-4), (10,8)

Answers

Answer:

(4, 2)

Step-by-step explanation:

the midpoint of points (x1, y1) and (x2, y2) is ([tex]\frac{x_{1} + x_{2}}{2}[/tex],[tex]\frac{y_{1} + y_{2}}{2}[/tex])

plug in points (-2, -4) and (10, 8) to get ((10+(-2))/2), (8+(-4))/2) = (4, 2)

What does the remainder theorem conclude given that f(x)x+3 has a remainder of 11?

Answers

By the remainder theorem of polynomial division, the complete equation is f(-3) = 11

How to complete the blanks?

The equation is given as:

f(x)/x + 3

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Given that the quotient has a remainder of 11.

It means that:

f(-3) = 11

Hence, the complete equation is f(-3) = 11

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Ms. Stewart teaches three science classes. Her students are freshmen and
sophomores. Her student data are shown in the relative frequency table.

Which statement is false?

Answers

It’s D because it’s just obvios that there’s not 15% of the kids

The statement that is false is 15% of her students are in biology, the correct option is A.

How to form two-way table?

Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n

List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  X_i  and Y_j  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

We are given that;

The relative frequency table

Now,

This is because the relative frequency table shows that 0.15 of her students are freshmen in biology and 0.2 of her students are sophomores in biology. Therefore, the total percentage of her students in biology is 0.15 + 0.2 = 0.35, which is 35%, not 15%.

The other statements are true based on the relative frequency table.

Therefore, by the two-way table the answer will be 15% of her students are in biology.

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Help ?!!!!!!!!!!?!!!!!!

Answers

The answers of the given geometrical shapes are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

what is mensuration?

Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.

Analysis:

1. volume of cylinder =π [tex]r^{2}[/tex]h. where r = 6/2 = 3 yard, h = 8 yard

                                  =  [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 8 = 226.29 cubic yard

2. volume of cone = [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 2inches, h = 11

                              =  [tex]\frac{1}{3}[/tex] x [tex]2^{2}[/tex] x   [tex]\frac{22}{7}[/tex]  x 11 = 46.1 cubic inches

3. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 8, h = 12

                                   =   [tex]\frac{22}{7}[/tex] x [tex]8^{2}[/tex] x 12 = 2413.71 cubic inches

4. volume of cone =  [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 4, h = 14

                               =  [tex]\frac{1}{3}[/tex]  x  [tex]\frac{22}{7}[/tex] x [tex]4^{2}[/tex] x 14 = 234.67 cubic millimeter

5. volume of cone =  [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h. where r = 5, h = 13

                              =  [tex]\frac{1}{3}[/tex] x  [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 13 = 340.48 cubic yards

6. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 3, h = 4

                                   = [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 4 = 113.14 cubic feet

7. volume of cone = [tex]\frac{1}{3}[/tex] x π  [tex]r^{2}[/tex]h.  r = 6, h = 14

                               =  [tex]\frac{1}{3}[/tex] x  [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 14 = 528 cubic centimeter

8. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 6, h = 8

                                   =   [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 8 = 905.14 cubic centimeter

9. volume of cylinder =  π [tex]r^{2}[/tex]h. where r = 1.5, h = 4

                                    =   [tex]\frac{22}{7}[/tex]  x [tex]1.5^{2}[/tex] x 4 = 56.57 cubic feet

In conclusion, the volume of cylinders and cones for the given dimensions are:

1. 226.29 cubic yard

2. 46.1 cubic inches

3. 2413.71 cubic inches

4. 234.67 cubic millimeter

5. 340.48 cubic yards

6. 113.14 cubic feet

7. 528 cubic centimeter

8. 905.14 cubic centimeter

9. 56.57 cubic feet

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0 x + 12 + x = 18

Solve ?​

Answers

Answer:

x = 3

Step-by-step explanation:

2x + 12 = 18

2x = 18-12

2x = 6

x = 3

give brainliest please!

hope htis helps :)

Answer:6

Step-by-step explanation:

0x+12+x=18

0x+x=18-12

x=6

Please help will give 30 points.

Answers

Answer: I think that the answer would be B. This is what i got after doing the work

Hurry help

If p is true and ~ q is false, then p -> ~ q is ____ false.
-Sometimes
-Always
-Never

Answers

Answer:

Never

Step-by-step explanation:

If p is true and ~ q is false, then p -> ~ q is ____ false

This translates to:

true -> true

So it will never be false.

Which function is a quadratic function?
Op(x) = 2x(x2 +6) +1
O m(x) = 4(x + 3) - 2
1
O f(x) = -8x²(x² − 6) + 1
O h(x) = 3x(x - 2) - 4

Answers

Answer:

h(x) = 3x(x - 2) - 4

Step-by-step explanation:

A quadratic function is a polynomial having a degree of 2.

==============================================================

On expanding h(x) :

⇒ h(x) = 3x (x - 2) - 4

⇒ h(x) = 3x² - 6x - 4

=============================================================

Hence, h(x) is a quadratic function.

Answer:

h(x) = 3x(x - 2) - 4

Step by-step explanation

A quadratic function has a degree of 2.

Firstly, we expand h(x):

h(x) = 3x (x - 2) - 4

OR h(x) = 3x squared - 6x - 4
Therefore, it is h(x)

Consider the equation:
6x+55=x²
1) Rewrite the equation by completing the square.

Answers

Step-by-step explanation:

-x^2+6x+55=0

x^2-6x-55=0

x^2-6x+(3)^2-55-(3)^2=0

(x-3)^2-64=0

. The Flower Bouquet flower shop charges $1.50 for placing an order and $0.50 for each flower ordered. Which equation could be used to find n,the number of flowers purchased if the total bill was $9. (1 point)
A $9 = (0.50 + 1.50)n
B 0.50n + 1.50 = $9
C $9 = 50n + 1.50
D 0.50 n + 1.50n = $9

Answers

the answer is B because $1.50 is the initial charge and you dont know how many flowers are in a bouquet, so $0.50 would be your coefficient and $9 is your total, so the initial cost and cost for the amount of flowers is equal to 9

The equation that could be used to find the number of flowers purchased if the total bill was $9 is:0.50n + 1.50 = $9.

Since each flower costs $0.50, multiplying the cost per flower by the number of flowers (n) gives the total cost of the flowers then 0.50n represents the cost of the flowers.

and, 1.50 represents the fixed cost for placing the order.

and $9 represents the total bill, which includes the cost of the flowers and the fixed cost.

By adding the cost of the flowers (0.50n) to the fixed cost (1.50), the equation sets the total bill equal to $9 we get the Equation as

0.50n + 1.50 = $9

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A man stands on his balcony, 140 feet above the ground. He looks at the ground, with his sight line forming an angle of
75 with the building, and sees a bus stop. The function d=140 sec 0 models the distance from the man to any object given
his angle of sight 0. How far is the bus stop from the man? Round your answer to the nearest foot.

Answers

The bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet

How to determine the distance?

The distance function is given as:

d = 140 sec(x)

Where x represents the angle of sight.

In this case,

x = 75

So, we have:

d = 140 sec(75)

Evaluate the product

d = 541

Hence, the bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet

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Solve for h
h - 3h - 8 = 14
H=?

Answers

Answer:

-22

Step-by-step explanation:

h-3h-8=14

-2h=14+8

-2h=22

h=-11

The initial step that must be taken before solving almost any problem is to understand what the problem is asking for us to do and what is provided to us to complete that goal.  Looking at the problem statement, we can see that we are being requested to solve for h and we are provided an expression to do so.  Let's begin solving the expression by combining like terms.

Combine like terms

[tex]h - 3h - 8 = 14[/tex][tex](h - 3h) - 8 = 14[/tex][tex](- 2h) - 8 = 14[/tex]

Just a quick explanation on what combine like terms means, it basically just means to combine the coefficients of the numbers associated with the same variables.  Like in this example we can combine h and -3h because they have have the variable h associated with them.

Add 8 to both sides

[tex](- 2h) - 8 = 14[/tex][tex](- 2h) - 8+ 8 = 14 + 8[/tex][tex]- 2h= 22[/tex]

Divide both sides by -2

[tex]- 2h= 22[/tex][tex]\frac{- 2h}{-2}= \frac{22}{-2}[/tex][tex]h= \frac{22}{-2}[/tex]

Simplify the expression

[tex]h= - \frac{22/2}{2/2}[/tex][tex]h= - \frac{11}{1}[/tex][tex]h= - 11[/tex]

Therefore, after completing the steps above we were able to determine that the value of h is equal to -11.

Meril Starts driving at 14 00​

Answers

A.50km
C. Draw a straight line to 1530
D. Draw a diagonal ending at 200km and 1700

A certain medication is eliminated from the bloodstream at a rate of about 17% per
hour. the medication reaches a peak level in the bloodstream of 60 milligrams.
determine the multiplier used to predict the amount of medication remaining 2
hours after the peak level.

Answers

Using an exponential function, it is found that the multiplier used to predict the amount of medication remaining 2 hours after the peak level is of 0.6889.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

A(0) is the initial value.r is the decay rate, as a decimal.

In this problem, we have that the decay rate is of r = 0.17, hence:

[tex]A(t) = A(0)(0.83)^t[/tex]

After 2 hours, the multiplier is given by:

[tex]A(2) = A(0)(0.83)^2 = 0.6889A(0)[/tex]

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three consecutive integers such that the smallest and three times the largest is 330 . what is the smallest integer?

Answers

Interfere 330 because it’s 330

PLEASE HELP I WILL GIVE BRAINLIEST!!

Find an angle in the range between 0 and 2ㅠ radians that is coterminal with
-ㅠ/2
a) 7ㅠ/2
b) 3ㅠ/2
C) 5ㅠ/2
d) ㅠ/2

Answers

The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.

How to find a coterminal angle?

For any angle A, all the coterminal angles are of the form:

B = A + n*(2ㅠ).

Where n is an integer different than zero.

In this case, the angle is A = -ㅠ/2

So the coterminal angles are of the form:

B = -ㅠ/2 + n*(2ㅠ)

We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:

B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2

Then we can conclude that the correct option is b.

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What is the mode: 18,21,22,18,19

Answers

Answer:

18

Step-by-step explanation:

Mode =  modal class (Recurring)
The number/value that appears the most which in this case is 18 because it can be seen twice.

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