1. Let f(x)=3x+2 and g(x)=x^2 -5x-1. Find f(g(x)).
We are putting g into f
3 ( x^2 - 5x - 1) + 2 =
3x^2 -15x - 3 + 2 =
3x^2 - 15x - 1
Let's suppose that the band has 100 members
(1/5) * 100 = 20 play percussion
(1/2) (20) =10 play snare
10 /100 = 1 /10 CORRECT, Alston !!!
f ( x) - g(x) =
(2x^2 + 3x -9 ) - ( 5x + 11) = 2x^2 - 2x -20
Add h(x)
(2x^2 - 2x - 20 ) + (3x^2 + 1) = 5x^2 -2x - 19
******
Let 18 = z
Let x = z + a and y = z + b
So we have
1/ (z + a) + 1/ (z + b) = 1 / z
(2z + a + b) / [ (z + a) (z + b) ] = 1 / z cross-multiply
(2z + a + b) z = (z + a) ( z + b)
2z^2 + az + bz = z^2 + az + bz + ab
z^2 = ab
Which means that 18^2 = ab = 324
a b x = z + a y = z + b
1 324 19 342
2 162 20 180
3 108 21 126
4 81 22 99
6 54 24 72
9 36 27 54
12 27 30 45
Smallest value of x + y = 30 + 45 = 75
The two numbers are 12 and 18
Product = 12 x 18 = 216
Find the distance between A and B
sqrt [ ( 3 - - 1)^2 + ( 2 - - 2)^2 ] = sqrt [ 4^2 + 4^2 ] = sqrt (32)
Take 1/2 of this = sqrt (32) / 2 = the radius of the circle
Area = pi (sqrt (32) / 2 ) ^2 = pi (32 / 4) = 8 pi units^2
Midpoint of first segment =
[ ( 2 + 0)/2 , (3 + 0) /2 ] = ( 1 , 3/2 )
Midpoint of second segment
[ (-5 + 6) /2 , ( 3 + 0) / 2 ] = ( 1/2 , 3/2)
Since the y values of these midpoints are the same, the slope of the lie containing them = 0
Excellent, 4M !!!!!
Very nice, 4M !!!!
