CPhill

(5x-3)^2+6(5x-3)  =

(5x - 3)(5x - 3  + 6) =

(5x-3)(5x + 3)  =

25x^2 - 9

None...they don't even allow fresh fruit in.........

If the sin is 5/12 in the second quadrant, then x = -√[12^2 - 5^2] = -√119

So, the cosine = -√119 / 12 ....  and the tangent =  - 5/ √119 

According to Wikipedia, the land area of Canada is about 3,500,000 sq mi   Sweden is about 158,000 sq mi

So   3,500,000 / 158,000 = about 22 Swedens could fit into Canada

We need to calculate the time for the stone to fall...we have

-9.5 = -4.9t^2      divide both sides by -4.9

1.94 = t^2            take the square root of each side

t = 1.39 secs.

Since sound travels at 343m/s...the time for the sound to travel back up the well =  9.5m / 343m/s  = about 0.028 sec.

So the splash is heard [1.39 + 0.028 ] = about 1.418 seconds after the stone is dropped

We can calculate this by first finding a side length, s ....we have

43.3 = (1/2) s^2 (sin 60)  =

43.3 = (1/2) s^2 (√3/2)      mutiply both sides by 4/√3

(43.3)(4/√3) = s^2        take the square root of both sides

s = about 10

So the altitude is (10/2)√3  = 5√3  = about 8.66 linear units

Check......  (1/2)bh = (1/2)(10)(5√3)  = about 43.3

Sometimes, this is difficult....for instance, let's suppose that someone told you the zeroes of a function were 0 and 2

The volume held by the hemisphere is

(2/3)pi*(2 in)^3  =  (16/3) pi  in^3

And the cylinder holds twice as much, so....

(32/3)*pi in^3  = pi * (1.25 in)^2 * h      where h is the height  ...   divide both sides by pi

(32/3) in^3 = 1.5625 in^2   * h       solve for h

Height of cylinder  = (32/3) in^3 / 1.5625 in^2   = about 6.826 in

 57, 909, 000

Put a decimal after the 5 and then write 7909

So we have

5.7909

Now....multiply this by 10 raised to the number of decimal places we moved the number to the left in the original number = 7

5.7909 x 10⁷

Oops...I mis-read this...... it was supposed to be    $b$/ $a$   ...!!!

Let  me revise my answer as

17, 576,000 / 260,000  = 67.6