CPhill

To see heureka's answer more clearly....note that he wrote 666 in terms of base 2, i.e., 2^x = 666

And "x" = ln666/ ln2  = 9.3793783670712621

So, we have

2^19112000 / 666 =

2^19112000/ 2^{9.3793783670712621}  =

2 ^{(19112000-9.3793783670712621)} =

2^{19111990.6206216329287379}

Still.....a pretty large number !!!

The cofunction identity of sinΘ = cos (90-Θ)

So sin (87°) = cos(90-87)° = cos(3°)

Here's another way to do this without simultaneous equations.....

Call the time on the bicycle "x".....then the time walking was (6-x)

And....rate times time = distance

So the amount of time on the bike times its rate plus the amount of time walking times that rate = total distance.

40x + 4(6-x)  = 186

40x + 24 - 4x = 186   simplify

36x = 162      divide both sides by 36

x = 4 + 1/2 hrs = 4 hrs 30 minutes

And that's the time on the bike

Anonymous's answer can be seen clearly by the following diagram......

Point "A" could only have a symmetric point  about a diagonal whose slope was 1. (In other words, the point (8, -2) would have to lie on the rectangle.....it doesn't). But diagonal BC has a slope of 1/4. And point "B" could only have a  symmetric point about a diagonal whose slope was -1. (Point (-2,-8) would have to lie on the rectangle...it doesn't either).  But diagonal AD has a slope of -1/4.

The axes of symmetry are the x axis and the y axis.

Both answers are the same thing

3.2 = 3  + 2 /10   =  32 / 10 =   16 / 5

y = (x -3√5)(x - √5)

y = x^2 - 4√5 x + 15

I'm assuming you're asking how many pages they each need to read to finish the book

Harold needs to read (100,000 - 4536 ) pages

And his friend needs to read (100,000 - 65684) pages

You can probably take it from there....

Let the first page = n    and let the second page = n + 1

So

n (n + 1) = 1056

n^2 + n = 1056    rearrange

n^2 + n - 1056 = 0     factor

( n -32) ( n+ 33) = 0

Setting both factors to 0, we have that n = 32  and n = -33

The first is obviously correct.

And n + 1 = 33

So....the two pages are 32 and 33

53 is a prime number.....no factors of 15 divide it...

Thus, this is in simplest form....