Post by: dinosaur93 on December 09, 2011, 05:12:50 pm
2. Express the area of a equilateral triangle as a function of:
a. the length s of each side.
b. the altitude h.
3. A van travels half the distance of a journey at an average speed of 80km/h and half an average speed of x km/h. Define a function, S, which gives the average speed for the total journey as a function of x.
4. A cylinder is inscribed in a sphere with a radius of length 6 cm.
(http://i.imgur.com/7oOo3.jpg)
a. Define a function, V1, which gives the volume of the cylinder as a function of the height (h) (State the rule and domain.)
b. Define a function, V2, which gives the volume of the cylinder as a function of the radius (r) (State the rule and domain.)
5. The shape has area of A cm2. Find A in terms of x. State the maximal domain and range which is defined if x + x + x < 9.
(http://i.imgur.com/iW0MY.jpg)
Post by: pi on December 09, 2011, 05:18:52 pm
Post by: monkeywantsabanana on December 09, 2011, 05:23:48 pm
This isn't a SAC right (kinda looks like one)? You really should have a go first yourself.
Are you allowed to bring SACs home ?? :O
Post by: pi on December 09, 2011, 05:25:17 pm
This isn't a SAC right (kinda looks like one)? You really should have a go first yourself.
Are you allowed to bring SACs home ?? :O
Depends what school you are, we had one spesh SAC we could bring home.
Post by: TrueTears on December 09, 2011, 05:25:26 pm
Post by: b^3 on December 09, 2011, 05:27:47 pm
Post by: dinosaur93 on December 09, 2011, 05:45:24 pm
Post by: pi on December 09, 2011, 06:53:05 pm
haha, nah, these are just from some other book where I try and answer im my leisure time..
Haha, that's good then :)
Start with 1) then
1. Express the total surface area S of a cube as a function of the volume V of the cube?
Just some hints:
Try rearranging one of the above into
Post by: dinosaur93 on December 10, 2011, 08:19:44 pm
How do you do numbers 3, 4 and 5 then?
Post by: brightsky on December 10, 2011, 08:34:30 pm
4) draw the 2-d version of the diagram (that is, a square inscribed in a circle). mark in the centre of the circle. the radius is hence 'half' the diagonal of the square, so 2(r/2)^2 = 6^2, r^2 = 72, r = 6sqrt(2). also recognise that h = 2*r = 12 sqrt(2). should be able to complete the problem from here.
5) find the area of the shape by subtracting the x*x*x 'chunk' from the bigger 9*5x 'rectangle'.
Post by: dinosaur93 on December 11, 2011, 05:33:10 pm
7. If f(x) = 3x2, 0
8. f is the function of defined by f(x) =
a. f* : [-1, 1]
b. f* : R
c. f* : [-2, 2]
d. f* : [-1,
e. f* : [0,
9. Let h : [a, 2]
a. -1
b. 0
c. 1
d. -2
e.
10. If the angle between the lines 2y = 8x + 10 and 3x - 6y = 22 is
a. 1.17
b. 1.40
c. 2
d. 0.86
e. 1
Post by: REBORN on December 11, 2011, 06:58:30 pm
Dom of f is [0,6]
Dom of g is (-inf,2]
Intersection gives [0,2]
Post by: dinosaur93 on December 15, 2011, 10:09:20 am
6. If f : [0, 2]
R, where f(x) = sin 2x and g : [0, 2
is _______?________
7. If f(x) = 3x2, 0x
, x
8. f is the function of defined by f(x) =, x
R. A suitable restriction for f, f* such that f*-1 exists would be
a. f* : [-1, 1]
b. f* : R
c. f* : [-2, 2]
d. f* : [-1,)
e. f* : [0,
9. Let h : [a, 2]
a. -1
b. 0
c. 1
d. -2
e.
10. If the angle between the lines 2y = 8x + 10 and 3x - 6y = 22 is, then
is approximately by: ??? Interesting Qs...
a. 1.17
b. 1.40
c. 2
d. 0.86
e. 1
anyone?
Post by: samad on December 15, 2011, 02:57:48 pm
The domain of an addition (f+g) or product (f*g) function is the intersection of the domains of the two functions f and g. for q7 this means intersection of dom f and dom g, i.e dom (f+g) = [0,2]
For q 8, this is a reciprocal function that must be restricted so that it is one to one. Consider the function x2 + 2, it is a parabola with one axial intercept at (0,2). The receprocal of this function has an axial intercept at (0, 1/2) and one asymptote, y=0. The turning point of the function is (0, 1/2). Therefore, to get a one to one function, we must have either (-infiinity, 0] or [0, infinity). Therefore, answer is E.