CPhill

Remember that  (1 / aⁿ )  = a^-n

Since 216 = 6³ , we have (1/216)  =(1 / 6³ )  = 6^-3

And 100,000 = 10⁵ , so, 1/100,000 = (1 / 10⁵ )  = 10 ^-5

And one millionth  = 1 / 1,000,000 = 1 / 10⁶ = 10^-6

The "formula" for the sum of an infinite sequence is given by

S = a₀ / (1 - r)....where S is the sum, a₀ is the initial value, and r is the common ratio...so we have...

6 = 2 / (1 - r)     mutiply both sides by 1-r

6(1 - r)  = 2        simplify

6 - 6r  = 2           rearrange

4 = 6r                solve for r

r = 2/3

12 in x 12 in  = 144 sq in

And, assuming 19,836 is in sq in, we have

19,836 / 144  = about 137.75 pieces....(and assuming that we have to have "whole" pieces, let's round this up to 138.....)

Well, 6 months ago, he must have owed 6 x 12.65 more than he does now = $75.90

So $75.90 + $132.50 = $208.40 ......just as "Anonymous" found.....!!!

Converting 6.71 x 10⁸ ,   we just move the decimal point 8 places to the left...so we have

671,000,000 mph

And if you wanted to find out how long it takes light from the Sun to reach Mars, we have

[ 1.42 x 10⁸]miles / [ 6.71 x 10⁸ ] mph =  about .2 hrs, or about 12 minutes

1 1/3 / 1/4  x  2/5 / 1/2

Remember that 1+1/3  = 4/3...so we have

4/3 / 1/4  x   2/5  / 1/2     and when we divide fractions like this, we just keep the munerator as it is, change to multiplication, and  "flip" the fraction in the denominator...so we have

[4/3 X 4/1 ]  x [ 2/5 x 2/1] = 

16/3  x  4/5 =

64/15

And that's ir...

sin = y / r      cosec = r / y  

cos = x / r      sec = r / x

tan = y / x       cot  = x / y

Here, we know y = 3 and r = 7  so...using the Pythagorean Theorem, x  = √(7^2 - 3^2)  = √(49 - 9) = √40 = 2√10

Knowing these values....can you finish this one ???

I'm assuming you have

√2 x √3  ???

This just = √6

Here's a couple of sites that can help you with this topic....

Use this....

rads x  180/ pi  =  degrees....

For instance

2pi/3  x  180/ pi  = (2/3) x 180  = 120 degrees   (notice that the "pi's" will cancel...)

Since the cosine function only has a range from -1 to 1, inclusive......this is undefined...to put it in another way.......there is no angle whose cosine is equal to 23/9.....