Race Game

MATHS OBJ
1EAACBAECBE
11CDABECBCCA
21AEDCBACEDE
31ADADCCDABD
41BCEBDCEABE
51DBAECBECBE
1a
(6y²)³ / 2+y^6
= 6³y^6 / 24y^6
=6³*y^6/24*y^6
= 216/24
=9
1b
Log10(2m²+5m-2)=1
2m²+5m-2=10
2m²+5m-2-10=0
2m²+5m-12=0
Using m=-b+-?b²-4ac/2a
a=2
b=5
c=-12
m=-5+-?5²-4*2*(-12)/2*2
m=-5+-?2+96/4
m=-5+-?98/4
m=-5+-9.9/4
m=-5+9.9/4 or m=-5-9.9/4
M=1.225 or -3.725
2a)
W~ 3?D
Let our constant be K
W= K×3?D
10= K × 3?27
10/3= 3k/3
K= 10 /3
W when D= 64
W= 10/3 × 3?64
W= 10/3 × 4
W= 40/3
W= 13.3
==========
2a)
w*3?D
W=k 3?D
10=k*3?27
10/3 =k*3/3 k=10/3
W=10/3*3?64 = 10/3*4*40/3=13 1/3
2b)
X/2 + y/6 = 2/3
L.C.M = 6
Rx + y = 4 ---(1)
X/3 - y/2 = 5/3
L.C.M = 6
2x - 3y = 10 -----(2)
From eq (1)
3x + y = 4
Y= 4 - 3x ---- (3)
Sub for y in eq (2)
2x - 3(4-3x) = 10
2x - 12 + 9x = 10
11x = 22
X=2
Sub for x in eq (3)
Y = 4-3(1)
Y = 4-3-
Y = 1
===========
3a)
Sn = a(r^n - 1)
a = 5
r = 3
n= 8
5(3^8 - 1)/ (3-1) = 5(6561-1)/2
= 32800/2 = 164000
4a)
V=2/3?r
1527.4=2/3*22/7*r
1527.4=44r/21
32075.4=44r
r=32075.4/44
r=728.98
=729cm
4b
3^3y+1 = 81^-y
3^3y= 3^-4y
3y+1=-4y
1=-4y-3y
1=-7y
Y= - 1/7
===============
5a)
Red=4
Green = 6
Black= 10
Total=20
1)p(Red) = 4/20 = 1/5
2)p(green)= 6/20 = 3/10
3) p (black)= 10/20= 1/2
5b)
( X-1)(X-8)+12=0
X²-8x-X+8+12=0
X²-9x+20=0
X= -b +?b²-4ai
X= 9+/-?-9²-4×1×20÷ 2×1
X=9+/-?81-80÷2
X=9+/-?1÷2
X= 9+1/2 or 9-1/2
X= 10/2 or 8/2
X= 5 or 4
============
8b)
Let the pocket money be x
2x/5 =stations
X/4=school levies
X/6= food
X-(24x/5+x/4+x/6)=55
X-(24x+15x+10x)/60 =55
X-49x/60 =55
60*x-60-49x/60 = 55*60
60x-49x=#3,300
11x/11=3300/11
X=#300
The pocket money =#300
10a.
1/27^(x-2)=9^(2-x)
3^3(x-2)-1=3^2(2-x)
3-1(x-2)=4-2x
2x-4=4-2x
2x+2x=4+4
4x=8
X=8/4
X=2
10b
5x+y/x+5y= 3/1
5x+y= 3(x+5y)
5x+y=3x+15y
5x-3x=15y-y
2x=14y
X/y= 14/2 =7, y/x= 1/7
X2-y2/4xy
Divide all through by my
(X²- y²/) ÷(4xy/xy)
Xy- xy
(X/y- y/x) ÷4
(7- 1/7)÷4 ~~~49-1/7×1/4
48/7× 1/4= 24/7
= 4
11a)
A=(1 7,3 2) and B=(2 5,4 6)
i)A^-1=1/det(2 -7,-3 1)
Det= 2 -21=-19
A^-1=1/-19(2 -7,-3 1)
-1/19(2 -7,-3 1)
ii)B^T =(2 -4,5 6)
iii)AB =(1 7,3 2) (2 5,4 6)
(2 -28,6-8, 5+46,15+12)
(-26,-2, 51,27,)
11b)
7x^2 + 12x + 5 = 0
7x^2/7 + 12x/7 = -5/7
X^2 + 12x/7 = -5/7
X^2 12x/7 + (6/7)^2 - -5/7 + (6/7)2
(X+6/7)^2= -5/7 + 36/49
(X+6/7)^2 = -35+36/49
(X +6/7)^2 = 1/49
(X +6/7) = + and - ?1/19
X+ 6/7 = + and - 1/7
X = -6/7 + and - 1/7
X = -6+1/7 or -6-1/7
X= -5/7 or -7/7
X = -5/7 or -1