Problem: Express the following numbers in standard form: (i) 0.0000000000085                   (ii) 0.00000000000942                  (iii) 6020000000000000
(iv) 0.00000000837              
(v) 31860000000

(i) 8.5 × 10^-12

(ii)  9.42 × 10^-12

(iii) 602 × 10^15

(iv) 8.37 × 10^-9

(v) 3.186 × 10^10

Step-by-step explanation:

(i) 0.0000000000085

= 0.0000000000085 × 10^12/10^12 

= 8.5/10^12 

= 8.5 × 10^-12

(ii) 0.00000000000942

= 0.00000000000942 × 10^12/10^12 

= 9.42/10^12 

= 9.42 × 10^-12

(iii) 6020000000000000

= 602 × 10^15

(iv) 0.00000000837

= 0.00000000837 × 10^9/10^9 

= 8.37/10^9 

= 8.37 × 10^-9

(v) 31860000000

= 3.186 × 10^10

-TheUnknownScientist

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.

a 360 degree rotation

step-by-step explanation: