Find the order pairs for the x- and y- intercepts of the equation 2x-6y=24

the math magician Archimedes believed that pi was between 3 1/7 and 3 10/71. Was Archimedes correct? explain

Rufina [12.5K]

A Brief History of πPi has been known for almost 4000 years—but even if we calculated the number of seconds in those 4000 years and calculated pi to that number of places, we would still only be approximating its actual value. Here’s a brief history of finding pi:The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for pi, which is a closer approximation.The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for pi.The first calculation of pi was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. Archimedes knew that he had not found the value of pi but only an approximation within those limits. In this way, Archimedes showed that pi is between 3 1/7 and 3 10/71.A similar approach was used by Zu Chongzhi (429–501), a brilliant Chinese mathematician and astronomer. Zu Chongzhi would not have been familiar with Archimedes’ method—but because his book has been lost, little is known of his work. He calculated the value of the ratio of the circumference of a circle to its diameter to be 355/113. To compute this accuracy for pi, he must have started with an inscribed regular 24,576-gon and performed lengthy calculations involving hundreds of square roots carried out to 9 decimal places.

Mathematicians began using the Greek letter π in the 1700s. Introduced by William Jones in 1706, use of the symbol was popularized by Leonhard Euler, who adopted it in 1737.

An Eighteenth century French mathematician named Georges Buffon devised a way to calculate pi based on probability. You can try it yourself at the Exploratorium's Pi Toss exhibit.

4 0

3 years ago

WILL GIVE BRAINLEIST : A party hat is in the shape of a cone. What is the volume of the hat in cubic centimeters?

Brut [27]

36xpi or 113.1 cm^3
hope that helped!! :)

7 0

3 years ago

sammy's bucket holds 2,530 milliliters of water. Marie's bucket holds 2 liters 30 milliliters of water. Katie's bucket holds 2 l

Zanzabum

Answer:

Marie's bucket holds the least amount of water.

Step-by-step explanation:

Sammy's bucket holds 2.53 liters of water. (2530 / 1000 = 2.530)

Marie's bucket holds 2.03 liters of water. (2 + 0.030 = 2.030)

Katie's bucket holds 2.35 liters of water. (2 + 0.350 = 2.350)

If you compare all these values, 2.03 is the least out of all of them.

8 0

3 years ago

Seven more than twice his age is 51 in algaebric expression

kozerog [31]

7 + 2x = 51

hope this helps

8 0

3 years ago

Read 2 more answers

The Earth rotates every 24 hr and as diameter of 7, 926 mi. If you're standing on the equator, how fast are you traveling in mil

Vlada [557]

<h3>Answer: Approximately 1038 mph</h3>

The more accurate value is 1037.51097384802

Round that however you need to.

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Explanation:

We need the circumference of the equator. Think of the equator as the largest possible circle (or belt) to fit around the earth.

C = pi*d

C = pi*7926

C = 7926pi

C = 24,900.2633723527

In 24 hours, a person at the equator travels roughly 24,900.2633723527 miles since the earth does a full rotation in this timespan.

Divide the two quantities distance over time to get the speed

rate = distance/time

rate = (24,900.2633723527 miles)/(24 hours)

rate = ( (24,900.2633723527)/(24) ) miles per hour

rate = 1,037.51097384802

rate = 1038 mph

I'm rounding to 4 sig figs since the diameter is given to be in four sig figs.

This speed of roughly 1038 mph is a linear speed and not an angular speed.

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Extra info (optional section)

Upon further research, I found an article from NASA JPL (jet propulsion laboratory) which states quote:

"To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr)"

Their figure of 1000 mph seems to be a rough estimate, more or less. It's fairly close to the 1038 figure we got earlier.

8 0

3 years ago