O-Level Additional Math
-
Hi GuanHui
how to find the lowest postive integer of x and X+1 . both divisible by 7 -
![](\"http://img.photobucket.com/albums/v257/tbctbc/DSC00960.jpg\")
http://img.photobucket.com/albums/v257/tbctbc/DSC00960.jpg\">
The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, VO is 18cm and the base radius, OA is 9cm.
The radius, BC, of the base of the upper part is 6cm.
Taking pi to be 3.142, calculate
(a) the length of OC
(b) the total surface ara of the frustum -
blitz:
(a) Since VCB and VOA are similar, we have
The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, VO is 18cm and the base radius, OA is 9cm.
The radius, BC, of the base of the upper part is 6cm.
Taking pi to be 3.142, calculate
(a) the length of OC
(b) the total surface ara of the frustum
VC/VO=CB/OA
VC/18=6/9
solve, we get VC=12.
OC=VO-VC=6cm
(b) Curved surface area of a cone = pi x r x L
VB = square root of (VC square + BC square) = 13.416
VA = square root of (VO square + OA square) = 20.125
Curved surface area of the frustum
=curved surface area of larger cone - curved surface area of larger cone
= 3.142 x 9 x 20.125 - 3.142 x 6 x 13.416
= 316.18
Upper base of the frustum
= 3.142 x 6 x 6
= 113.11
Lower base of the frustum
= 3.142 x 9 x 9
= 254.50
Total = 316.18+113.11+254.50 = 684cm^2 (correct to 3s.f.) -
leeven:
It is not possible to have x and x+1 both divisible by 7, please check.Hi GuanHui
how to find the lowest postive integer of x and X+1 . both divisible by 7 -
FrekiWang:
Thanks so much! But I dont understand how to prove that the triangles are similiar
(a) Since VCB and VOA are similar, we haveblitz:
The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, VO is 18cm and the base radius, OA is 9cm.
The radius, BC, of the base of the upper part is 6cm.
Taking pi to be 3.142, calculate
(a) the length of OC
(b) the total surface ara of the frustum
VC/VO=CB/OA
VC/18=6/9
solve, we get VC=12.
OC=VO-VC=6cm
(b) Curved surface area of a cone = pi x r x L
VB = square root of (VC square + BC square) = 13.416
VA = square root of (VO square + OA square) = 20.125
Curved surface area of the frustum
=curved surface area of larger cone - curved surface area of larger cone
= 3.142 x 9 x 20.125 - 3.142 x 6 x 13.416
= 316.18
Upper base of the frustum
= 3.142 x 6 x 6
= 113.11
Lower base of the frustum
= 3.142 x 9 x 9
= 254.50
Total = 316.18+113.11+254.50 = 684cm^2 (correct to 3s.f.) -
Hi
Please help.
Thank you
Secondary Two Maths.
Factorise
1) -6x^2 + x + 1
2) -5x^2 + 63x - 36 -
suiyuan:
Hi
Please help.
Thank you
Secondary Two Maths.
Factorise
1) -6x^2 + x + 1
2) -5x^2 + 63x - 36
1) -6x^2 + x + 1 = (3x+1)(-2x+1)
2) -5x^2 + 63x - 36 = (5x-3)(-x+12) -
Hi Guan Hui,
Could you help solve this?
Solve the pair of simultaneous equation for the values of x and y.
xy=1/3
xy+x-y=1/2
Ans: x=-1/2, y= -2/3 or x=2/3, y=1/2
Thanks a million! -
blitz:
Thanks so much! But I dont understand how to prove that the triangles are similiar[/quote]One of the 3 ways to prove that trianges are similar is to show the two triangles have 2 pairs of equal angles. Since those BC and OA are parallel, it is easy to identify two equal pairs (in fact three pairs)
(a) Since VCB and VOA are similar, we haveFrekiWang:
[quote=\"blitz\"]
The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, VO is 18cm and the base radius, OA is 9cm.
The radius, BC, of the base of the upper part is 6cm.
Taking pi to be 3.142, calculate
(a) the length of OC
(b) the total surface ara of the frustum
VC/VO=CB/OA
VC/18=6/9
solve, we get VC=12.
OC=VO-VC=6cm
(b) Curved surface area of a cone = pi x r x L
VB = square root of (VC square + BC square) = 13.416
VA = square root of (VO square + OA square) = 20.125
Curved surface area of the frustum
=curved surface area of larger cone - curved surface area of larger cone
= 3.142 x 9 x 20.125 - 3.142 x 6 x 13.416
= 316.18
Upper base of the frustum
= 3.142 x 6 x 6
= 113.11
Lower base of the frustum
= 3.142 x 9 x 9
= 254.50
Total = 316.18+113.11+254.50 = 684cm^2 (correct to 3s.f.) -
wormy:
Since xy=1/3,Hi Guan Hui,
Could you help solve this?
Solve the pair of simultaneous equation for the values of x and y.
xy=1/3
xy+x-y=1/2
Ans: x=-1/2, y= -2/3 or x=2/3, y=1/2
Thanks a million!
1/3+x-y=1/2
x-y=1/6
x=1/6+y
subst x=1/6+y into xy=1/3
(1/6+y)y=1/3
y^2+1/6 y-1/3=0
6y^2+y-2=0
(3y+2)(2y-1)=0
y=-2/3 or y=1/2
when y=-2/3, x=1/6+y=1/6+(-2/3)=-1/2
when y=1/2, x=1/6+y=1/6+1/2=2/3
Alternatively, you can also start from x=(1/3)/y=1/3y and subst it into the 2nd expression, you should be able to obtain the same results.
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