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Thread: VCE Maths questions help

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    Re: VCE Maths questions help

    Quote Originally Posted by InteGrand View Post
    Answer to your last question: yes.

    Thanks. Also, do you know how to find the general solutions to the equations I posted above?
    Thanks
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Thanks. Also, do you know how to find the general solutions to the equations I posted above?
    Thanks
    Yes, I do.

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    Re: VCE Maths questions help

    Quote Originally Posted by InteGrand View Post
    Yes, I do.
    Could you please explain how to do it as read my textbook but got confused with it's explanation
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Also, can someone please explain how to find the general solution to the following equations.
    Cos 2(x+pi/3) = 1/2

    2 tan 2(x+pi/4) = 2√(3)

    2 sin(x+pi/3) = -1

    Thanks

    Silly question, but is
    sin 2(x+pi/3) the same as sin(2x+2pi/3)
    Quote Originally Posted by boredsatan View Post
    Could you please explain how to do it as read my textbook but got confused with it's explanation





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    Re: VCE Maths questions help

    If (x-1)^3 = 8
    then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

    Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
    And how would you work out the value of the base?

    How would you find the basic angle for a negative value?
    For instance cos(x) = -1/2

    How would you work out (x+1)^3 = -2 without a calculator?
    Thanks
    Last edited by boredsatan; 19 Jan 2018 at 9:30 AM.
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    If (x-1)^3 = 8
    then would x-1 = +- cube root of 8, or just + cube root of 8 and why?

    Also, does anyone know how you would work out sin(11pi/4), which is sin(2.75pi), and is in quadrant 2, and the rule for quadrant 2 is pi - base, but since it's 2.75, would you do (2pi) + (pi-base)?
    And how would you work out the value of the base?

    How would you find the basic angle for a negative value?
    For instance cos(x) = -1/2

    How would you work out (x+1)^3 = -2 without a calculator?
    Thanks
    Anyone?
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    Re: VCE Maths questions help

    Bump!
    Any one know how to do the above questions?

    Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
    I'm confused with the negative domain
    Thanks
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    Re: VCE Maths questions help

    Bump
    Can somebody PLEASE ANSWER all my questions above?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Also, does anyone know how to solve the equation sin x = 1/2 for [-pi, to 2pi]
    I'm confused with the negative domain
    Thanks
    The sine wave has symmetry across the origin, so it's an odd function, which means that .

    Basically that implies that the sine of a negative angle is the same as reversing the sign of the sine of the positive angle, i.e.

    .

    When we go in the positive direction, the first angle for which is .

    So that means that when we go in the negative direction, the first angle for which is .

    But is outside the range of , so it's not a solution to the equation.
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Also, does anyone know how you would work out sin(11pi/4)
    The period of is . So,



    Also, . So,



    Quote Originally Posted by boredsatan View Post
    How would you work out (x+1)^3 = -2 without a calculator?
    Thanks
    If you want the answer in exact form, then





    Last edited by fan96; 21 Jan 2018 at 8:01 PM.
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    Re: VCE Maths questions help

    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)
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    Re: VCE Maths questions help

    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
    Last edited by boredsatan; 23 Jan 2018 at 8:57 PM.
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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:



    Quote Originally Posted by boredsatan View Post
    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:



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    Re: VCE Maths questions help

    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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
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    Re: VCE Maths questions help

    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?
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    Re: VCE Maths questions help

    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)
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    Re: VCE Maths questions help

    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?
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    Re: VCE Maths questions help

    Bump
    Can somebody PLEASE ANSWER all my questions above?
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    Re: VCE Maths questions help

    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    bump
    marblesin the sample of 3

    It gives you the answer in the question, how many marbles are being chosen is the sample size.
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    Re: VCE Maths questions help

    Quote Originally Posted by BLIT2014 View Post
    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    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
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Bump
    Bump!
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