Post by: dinosaur93 on November 11, 2011, 05:07:21 pm
A building is on fire. From the rooftop of the building, a citizen attach a rope to a adjacent building as a last alternative to flee the firey building. Let the path of rope be modelled by the following equation:
f(x) = 0.057x2 - 1.34x + 10, 0 ≤ 0 ≤ 20
x is the distance between the rooftop to an adjacent building and f(x) being the height of a rope connecting two 2 buildings...
A 3 meter high fence is found 7 metres from the rooftop.
Question 1
How do you show that the rope passes over the fence?
Distance of the rope and the ground of the fence:
f(3) = 0.057(3)2 - 1.34(3) + 10 = 6.493 metres
Fence is only 3 metres high, while the rope is 3.413 metres high
Question 2
Find the exact height of the rope from the ground as its lowest point.
Question 3
The building is on fire. Is it safe for a citizen to drop to the ground at the lowest point of the rope if he is 1.7m tall? (If he falls more than 1m to the ground, the citizen will be injured.)
???
Post by: brightsky on November 11, 2011, 05:18:21 pm
for q2, we know the shape of the parabola already, so all we need to do is find where the stationary point and that will automatically give us the minimum point. deriving f(x), we get: f'(x) = 0.114x - 1.34. let this = 0 to find the stationary point.
0.114x - 1.34 = 0 --> x = 11.754. to find the height, i.e. the corresponding 'y'-value, plug this back into the original equation to get f(x) =2.1247..m
for q3, since f(x) describes the height of the rope, presumably from ground level, then yes it is safe for him to drop to the ground given that he hangs from the rope first before dropping. this is because 1 + 1.7 = 2.7 > 2.124..
Post by: dinosaur93 on November 11, 2011, 05:21:07 pm
Post by: dinosaur93 on November 11, 2011, 05:31:12 pm
A cylinder is cast from 750cm3 of molten metal.
a. find the expression for the height of the cylinder in terms of r.
b. Given the surface area of the cylinder is
c. Hence, find the height of the cylinder with the minimum surface area giving your answer to 2 d.p.
Post by: brightsky on November 11, 2011, 05:38:20 pm
V = pi*r^2*h = 750
rearranging:
h = 750/(pi*r^2)
b.
let A be surface area.
A = 2pi*r^2 + 2pi*r* 750/(pi*r^2)
dA/dr = 4pi*r - 1500/r^2
to find stationary point, let dA/dr = 0.
4pi*r - 1500/r^2 = 0
r = 4.92
since the parabola is U-shaped (coefficient in front of r^2 is >0), hence this is the x-coordinate for the MINIMUM point.
c.
just plug r = 4.92 back into the equation h = 750/(pi*r^2).
Post by: dinosaur93 on November 12, 2011, 04:06:43 pm
Kindly pls elaborate to justify your answer, thank you! :D
Question 1
The equation of the normal to the curve
Question 2
The
Probability Qs
Question 3
Two letters are randomly selected from the words 'maths methods'. The probability that the two letter are both t is ___?___.
Cubic Functions
Question 4
A cubic function,
Question 5
The circle with equation
Post by: REBORN on November 12, 2011, 04:30:10 pm
Find dy/dx.
Sub x = 1 for dy/dx. You get 7/2. This is grad of tangent. Thus grad of normal is negative reciprocal of this.
Then use y = mx + c using pt (1,2)
Post by: azn_dj on November 12, 2011, 04:43:21 pm
(the only angle where sin(\theta) and cos(\theta) are equal is \pi /4
Question 3:
2/12*1/11 = 2/121
(sample decreases for second alternative)
Post by: azn_dj on November 12, 2011, 04:48:27 pm
x^2 - 6x + 3^2 + y^2 + 2y + 1^2 -3^2 -1^2 -39 = 0
(x-3)^2 + (y+1)^2 = 49
(x-3)^2 + (y+1)^2 = 7^2
Centre is (3,-1) and the radius is 7.
Post by: azn_dj on November 12, 2011, 04:49:47 pm
Post by: dinosaur93 on November 12, 2011, 05:50:16 pm
I'm not sure how it came about...
Shouldn't it be
Post by: Gaijin on November 16, 2011, 05:34:31 pm
Cubic Functions
Question 4
A cubic function,, has a remainder of -4 when divided by (x-2) and has a remainder of 11 when divided by (x + 1). The values of a and b are ____?____. .
let P=P(x)=2x^3 + ax^2 +bx +2 Using remainder theorem P(2)=-4 and P(-1)=11
P(2)=2(2)^3 + a(2)^2 +b(2) +2=-4
18+4a+2b=-4
2a+b=-11 ....A
P(-1)=2(-1)^3 + a(-1)^2 +b(-1) +2=11
-2+a+b+2=11
a-b=11 ....B
A+B Using simultaneous equations
a=0
b=-11
Post by: Gaijin on November 16, 2011, 05:41:34 pm
according to the solutions.... the answer for Q3 is
That is the correct answer
Question 3:
2/12*1/11 = 2/121
(sample decreases for second alternative)
azn_dj's method is correct but it should be:
2/12*1/11 = 2/132 =1/66
Post by: dc302 on November 16, 2011, 11:46:59 pm
Post by: b^3 on November 16, 2011, 11:49:27 pm
I actually pointed out everything that Gaijin said but somehow my posts got deleted... must have been the server problem or something.Yeh when the new server went down, AN went back to the database that was two days before that. I'm not sure if those two days of posts are going to be back when AN moves back to the new server (I remember someone saying they are saved somewhere), so they may reapper, don't know what order though.
Post by: paulsterio on November 17, 2011, 12:14:14 am
Post by: dc302 on November 17, 2011, 12:56:02 am
they should reappear in the right order, but it might mean that our posts now may get deleted :S
Gah really? That just makes things even more confusing..