M>a + m>b = 90 (complementary angle)
2x + 4x +30 = 90
6x + 30 = 90
6x + 30 -30 = 90-30
6x = 60
6x/6 = 60
x=10
The m>a = 2x
m>a = 20
Supplemenary angles must add up to 180. So, 180- 20 = 160
So the measure of the angle supplementary to angle a is 160°
<span><span><span>A Brief History of </span>π</span><span>Pi 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.</span></span>
Answer:
The total time it takes her to swim the four laps is 3.65 minutes.
Step-by-step explanation:
Here, according to the given data:
The time taken to complete 1st lap = 54.73 seconds
The time taken to complete 2nd lap = 54.56 seconds
The time taken to complete 3rd lap = 54.32 seconds
The time taken to complete 4th lap = 54.54 seconds
Now, the TOTAL TIME taken to swim all 4 laps = SUM OF ALL 4 TIMES
= (54.73 + 54.56 + 54.32 + 54.54) seconds
= 219.35 Seconds
Now, 60 seconds = 1 minute
⇒ 1 seconds = 1/60 minute
⇒219.35 seconds = 219.27 x (1/60) minutes = 3.6558 minutes
Hence, the total time it takes her to swim the four laps is 3.65 minutes.
Answer:
3072
Step-by-step explanation:
double the number until the 11th time which would be -3072 so C
To find all the positive integers less than 2018 that are divisible by 3, 11, and 61, you will use what you know about factors.
3, 11, and 61 are all answers. So are 33, 183, 671, and 2013.
If you put these in factors, the product will be divisible by them!
3 x 11 = 33
3 x 61 = 183
11 x 61 = 671
3 x 11 x 61 = 2013
Take each number and square it, cube it, etc...
9, 27, 81, 243, 729
121, 1331
9 x 11 = 99
27 x 11 = 297
81 x 11 = 891
121 x 9 =1089
121 x 3 = 363
61 x 9 = 549
61 x 27 = 1647
Everything in bold is a correct answer.
