幾題maths (中3to中4) 15點!!

1.
Slope of AB = (-6-3)/(-4-2) = 3/2
Slope of AO = 3/2 = slope of AB ∴A,O,B are collinear
∴ The straight line passing through A and B passes through the origin.2.For the family of straight lines with slope 1, the equation can be written asy = x + C, where C is an arbitrary constantFor real value of C, C can be any value.∴There are infinitely many straight lines with slope 13. AB = √[(a-2)² + (a-1-1)²]
= √[2(a-2)²]
= (a-2)√24.Let x be the surface area of the smaller ice cream.
Let y be the volume of the larger ice cream.Surface area of larger ice cream: 2x
Hence, area ratio: 2x/x = 2
Volume ratio: y/70 Since (A1/A2)^3=(V1/V2)²
2^3=(y/70)²
y²=8×70²
y²=39200
y=197.9..
The volume of the large ice-cream is 198 ml. 5.Original surface area = 4pir²
New surface area= 4pi(r×1.1)²=1.21×4pi r²
Percentage increase =(1.21×4pi r²-4pi r²)/(4pi r²) × 100% = 21%Original volume = 4/3pir^3
New volume=4/3pi(r×1.1)^3 = 1.331×4/3pir^3
percentage increase in volume = (1.331×4/3pi r^3-4/3pi r^3)/(4/3pi r^3)×100%
= 33.1%6.
Let √y be one of the required number, where y is a non-negative no.
so, y < √y
√y-y > 0
√y(1-√y) >0
{√y>0 and (1-√y)>0 or {√y<0 and (1-√y)<0 (rej. √y≧0)
∴1 > √y > 0 (so, 0<y<1)7.
Let $y be the pocket money he has for a monthLast month he spent
=(1-40%) y
=0.6ytherefore,this month he spent
=0.6y × (1+30%)
=0.6y × 1.3
=0.78ythe percentage of pockey moneyhe saves this month
= (y - 0.78y)/y × 100%
= 22%