CPhill

$\sqrt{7+\sqrt{5-\sqrt{3+x}}}=3$

Square both sides

7  +  sqrt [ 5 - sqrt (3+ x) ]  =  9

sqrt  [ 5 - sqrt (3 + x) ]  =  2         square both sides again

5 - sqrt (3 + x)  = 4

-sqrt (3 + x)  =  -1    square both sides one last time

3 + x =   1

x =  1  - 3  =    -2

a^2 = k / sqrt (b)   where k is the proportionality constant

So

2^2  = k / sqrt (81)

4  = k / 9

4 * 9  = k =  36

So

If  ab =  48  then  a =  48/ b

Then

(48/b)^2  =  36 / sqrt (b)

2304 / b^2 =  36 / sqrt (b)

2304 / 36  =  b^2 / sqrt (b)

2304/36 = b^2 / b^(1/2)

2304/36  = b^(3/2)      

(2304/36)^(2/3)  = (64)^(2/3)  = (64^(1/3))^2  = 4^2  =   b  =  16 

G =  k / S              where k is the proportionality constant

2  =  k /  9

9 * 2   =  k =   18

So

G =   18 / 6   =   3 gallons

9:33 AM to  11:18 AM =  1 hr 45 min =  1.75 hrs

12:07 PM to 6:45 PM =  6 hours + 38 min    =  6 + 38/60 hrs =  6 + 19/30 hrs

So

Hrs worked x pay per hr =  

( 1.75  + 6 + 19/30) ( $15)   = $125.75 =  $126  to the nearest dollar

OK....no prob.....this one is a little difficult to see,  at first

The graph of  h ( x - 3)  shifts this parabola to the RIGHT by 3 units

We need to find  the place on the parabola where its width =  3 units

Note that this appears to be along the line y = 3

The parabola  intersects this line  at  (-2, 3)  and  ( 1, 3)    (note that the width is 3 !!! )

So  point  (-2,3)  is shifted to  point (1,3)  by  h(x - 3)  and (1,3)  is the point of intersection of both graphs !!!

{Hope that makes sense !! }

If the graph of _____ is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is that point?

If the graph of   (what ) ???

It is incorrect anyway   !!!!!

2x - 5   ≤ -x + 12     rearrange as

2x + x  ≤  12 + 5

3x ≤  17

x ≤  17/3   

x  =  ( inf, 17/3 ] 

Note that  x (x^2 -1)  = (x)(x + 1) ( x - 1)

Multiply throght by ths  factorization and we have

2x^2  + 3x   - 5 =  A ( x - 1)(x + 1)  + B(x)(x + 1)  + C(x)(x - 1)         simplify

2x^2 + 3x  -5 =  A ( x^2 -1)  + B( x^2 + x)  + C(x^2 - x)

2x^2 +  3x - 5 =  (A + B + C)x^2  + (B - C)x  - A

Equating terms we have this syatem

A + B + C  =  2

B - C  = 3           (1)

A = 5

So

5 + B + C = 2 

B + C  =  -3     (2)

Adding (1) and (2)  we get  that  2B  = 0   so B =  0

So

5 + 0 + C  =2

C = 2 -5   =  -3

(A,B,C)  =  (5, 0 , -3)

In triangle ABC, angle  BCA  = 90° 

And the shaded area is composed of equilateral triangle BOC (BO = BC = CO  = 4)   plus sector COA

Area of triangle   BOC  = (1/2) 4^2  sin 60°  =  8sqrt (3) / 2  =    4sqrt (3)

Area of sector COA  = (1/3)area of circle =   (1/3) pi (4^2)  = (16/3) pi 

Total area =   4sqrt (3)  +  (16/3) pi

ab =     (4sqrt 3) ( 16/3)  =  64 / sqrt 3