CPhill

(4 + √3)*(5 - 3√6) =

20 + 5√3 - 12√6 - 3√18  =

20 + 5√3 - 12√6 - 3√(9*2)  =

20 + 5√3 - 12√6 - 9√2 

32) y= -sqrt16x+32  (on number 32: just rewrite to make easy to graph using transformation of its parent function)

-√(16x + 32) =

-√16(x + 2) =

-4√(x + 2)

This is just the square root graph "flipped over" - the "-" out front indicates this - and shifted to the left two units. The "4" out front 'stretches" the graph vertically.

26) y=cubedrtx -4 (the sqrt sign is only overx)

This is the basic cubed root graph shifted down bt 4 units......

14) y=sqrtx-4 (the sqrt sign is over x-4)

This is the basic square root graph shifted to the right by 4 units. Here's the graph:

8)y=√x-2 (the sqrt sign is only over the x)

This is just the basic square root graph shifted down two units....here's the graph:

Since this is function is periodic, there will be many maximums and minimums. We can find a couple and maybe make a general statement of where they will occur. Taking the derivative, we have:

1.5cos(pi*t/12)(pi/12) = 0

cos(pi*t/12) = 0

The first place that the cosine  = 0 is at pi/2. So, setting pi*t/12 = pi/2, we have that

t = 6

And the next place that the cosine = 0 is at 3pi/2...so

pi*t/12 = 3/2*pi

t = 18

Taking the second derivative, we have

-1.5(pi/12)sin(pi*t/12)(pi/12) =

[-1.5(pi/12)^2]sin(pi*t/12)

And when t = 6 , this is negative, so a maximum occurs at (6,6)

And when t = 18, the second derivative is positive, so this indicates a minimum at... (18, 3).

In general, a maximum depth of 6 m will occur every (6 ± 24t) (hrs??)  and a minimum depth of 3 m will occur every (18 ± 24t)(hrs??) where t is some integer.

Here's a graph of the function:

2*(10 x10) + (8 x 12) + (12 x 10) =

200 + 96 + 120 =

416 sq ft.

We can use similar triangles here:

(ht. of pole) / (ht. of pole shadow) = (ht. of building) / (ht. of building shadow)

(2.5 m) / (1.57 m) = (ht. of building) / (42.25 m)

Therefore...multiplyinh both sides by 42.25 m. we have

(42.25 m)*(2.5 m) / (1.57 m) = (ht. of building) ≈ 67.28 m = 67 m. (rounded)

 sin3x =sin(x)*( 3cos^2 x - sin^2 x )

sin3x =

sin (2x + x) =

sin2xcosx + cos2xsinx =

(2sinxcosx)cosx + (cos^2x - sin^2x)sinx =

2sinxcos^2x + sinxcos^2x - sin^3x =

3sinxcos^2x - sin^3x =

sinx*(3cos^2x - sin^2x) ......and this equals the right hand side......

We can choose any 5 of the 7 seats for them to sit in. And for each of these choices, there are 5! ways to arrange the children.

So we have...

C(7,5) * 5!  = 2520 ways......