VCE Maths questions help (2 Viewers)

[boredsatan]

The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is:
I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please explain which one is correct and why
y = sin(2x - pi/4) or y = sin2(x-pi/4)

 

[boredsatan]

let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out

 

[fan96]

The equation of the image of the graph of y = sin x under a transformation of a dilation of factor 1/2 from the y-axis followed by a translation of pi/4 units in the positive direction of the x axis is:
I'm narrowed it down two 2 options, but don't know which one is correct. Can someone please explain which one is correct and why
y = sin(2x - pi/4) or y = sin2(x-pi/4)

I'm not familiar with that specific terminology, but if "dilation of factor 1/2 from the y-axis" means compressing the function horizontally, then you replace with and to shift it right you would replace with , in that order.



Dilate:



Shift graph:

let f: [0, pi/2] → R, where f(x) = cos(3x) -2. The graph of f is transformed by a reflection in the x-axis followed by a dilation of factor 3 from the y-axis. How would you work out the resulting graph, super confusing so wold greatly appreciate if someone helped out

Reflect across x axis:



Dilate:

 

[boredsatan]

An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners.
I've found the volume to be = (84-2x)(40-2x)(x)

State the maximal domain for V when it is considered as a function of x. Confused how to do this part
Any help would be appreciated

 

[boredsatan]

An open tank is to be made from a sheet of metal 84 cm by 40 cm by cutting congruent squares of side length x cm from each of the corners.
I've found the volume to be = (84-2x)(40-2x)(x)

State the maximal domain for V when it is considered as a function of x. Confused how to do this part
Any help would be appreciated

bump

 

[boredsatan]

A rectangle is defined by vertices N and P(x,y) on the curve with equation y = 16-x^2 and vertices M and Q on the x axis
a.i. Find the area, A of the rectangle in terms of x
ii. state the implied domain for the function defined by the rule given in part i

Can someone please help me with this?

 

[boredsatan]

A metal worker is required to cut a circular cylinder from a solid sphere of radius 5 cm. Express r in terms of h, where r cm is the radius of the cylinder and h cm is the height of the cylinder. Hence show that the volume, V cm^3, of the cylinder is given by V = (1/4)(pi)(h)(100-h^2)

 

[boredsatan]

n a tidal river, the time between high tides and low tides is 12 hours. The average depth of water at a point in the river is 5m. At high tide the depth is 8 m. Assume that the depth of the water, h(t) m, at this point is given by
h(t) = A sin(nt+e)+b, where t is the number of hours after noon. At noon there is a high tide.

a. find the values of A, n,b, and e

b. at what times is the depth of the water 6 m?

 

[boredsatan]

Bump
Can somebody PLEASE ANSWER all my questions above?

 

[boredsatan]

A new TV lottery game consists of the random selection, with replacement, of 3 marbles from a barrel. The 3 marbles are drawn from a group of 8 identical marbles except for colour. 3 of the marbles are blue and 5 are yellow. If X represents the number of blue marbles in the sample of 3, complete the probability distribution for X. The above is a binomial distribution, would n be 3 or 8? (please give reasong as well) Thanks
I'm really confused as to weather the sample size is 3 or 8, i checked the answer they said the sample size was 3, but I don't understand why

 

[boredsatan]

A new TV lottery game consists of the random selection, with replacement, of 3 marbles from a barrel. The 3 marbles are drawn from a group of 8 identical marbles except for colour. 3 of the marbles are blue and 5 are yellow. If X represents the number of blue marbles in the sample of 3, complete the probability distribution for X. The above is a binomial distribution, would n be 3 or 8? (please give reasong as well) Thanks
I'm really confused as to weather the sample size is 3 or 8, i checked the answer they said the sample size was 3, but I don't understand why

bump

 

[BLIT2014]

bump

marblesin the sample of 3

It gives you the answer in the question, how many marbles are being chosen is the sample size.

 

[boredsatan]

marblesin the sample of 3

It gives you the answer in the question, how many marbles are being chosen is the sample size.

Thanks
Also, how do you tell if something is conditional?

The length of music pieces (in minutes) played daily on Classical FM from 12 noon is a continuous random
variable X with pdf given by
f(x) = 0.025e^(-0.025x), x>=0
0, elsewhere
a. Find the probability, correct to 4 decimal places, that the first piece played on Monday is shorter than 12
minutes.
b. Find the average length of a piece of music on Classical FM.
c. Rachel turns on her radio at a quarter past twelve and hears a familiar tune being played. What is the
probability, correct to 4 decimal places, that she is listening to the first piece played on Monday?

I know how to do part a and b, but how do we know if part c is conditionl or not?
Thanks again

 

[boredsatan]

Thanks
Also, how do you tell if something is conditional?

The length of music pieces (in minutes) played daily on Classical FM from 12 noon is a continuous random
variable X with pdf given by
f(x) = 0.025e^(-0.025x), x>=0
0, elsewhere
a. Find the probability, correct to 4 decimal places, that the first piece played on Monday is shorter than 12
minutes.
b. Find the average length of a piece of music on Classical FM.
c. Rachel turns on her radio at a quarter past twelve and hears a familiar tune being played. What is the
probability, correct to 4 decimal places, that she is listening to the first piece played on Monday?

I know how to do part a and b, but how do we know if part c is conditionl or not?
Thanks again

Bump

 

[boredsatan]

Bump

Bump!

 

[boredsatan]

Bump!

Bump!

 

[boredsatan]

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?

 

[boredsatan]

f(x) = sqrt(x+1), and has a restricted domain of [0, infinity)
g(x) = x^2+4x+3, and has a restricted domain of (-infinity, -3]
How would i find the range of f(g(x)) without a calculator?

bump

 

[InteGrand]

bump

Have you found and simplified f(g(x))? Once you do this, you should be able to do the question.

 

[boredsatan]

Have you found and simplified f(g(x))? Once you do this, you should be able to do the question.

f(g(x)) = sqrt(x^2+4x+4), so would I use the domain of g(x) as the domain of f(g(x))?