Find the L. C.M of the given pair of numbers using the prime factors method. 70 and 84

2| 70,84

2|35,42

3|35,21

5|35,7

.|5,7

LCM=2×2×3×5×5×7=2100

420

Step-by-step explanation:

Prime Number: a whole number greater than 1 that cannot be made by multiplying other whole numbers

First prime numbers: 2, 3, 5, 7, 11, 13, 17, ...

Prime Factorization: prime numbers that multiply together to make the original number.

LCM = least common multiple: smallest positive number that is a multiple of two or more numbers

Start by finding the prime factorization of each number.

Start with the smallest prime number: 2

70 ÷ 2 = 35

35 is not divisible by 2 or 3, but is divisible by 5:

35 ÷ 5 = 7

7 is a prime number, so cannot be divided any further

So  70 = 2 × 5 × 7

Start with the smallest prime number: 2

84 ÷ 2 = 42

Again divide by 2:

42 ÷ 2 = 21

Now divide by 3:

21 ÷ 3 = 7

So  84 = 2 × 2 × 3 × 7

Write each number as a product of primes, matching primes vertically when possible

84 = 2 × 2 × 3       × 7

70 = 2             × 5 × 7

Now bring down the primes in each column. The LCM is the product of these factors.

LCM = 2 × 2 × 3 × 5 × 7 = 420

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb