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Thread: VCE Maths questions help

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    Member boredsatan's Avatar
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    Re: VCE Maths questions help

    f(x) = (x-3)^2 (x+2)
    find x: f(x) >6
    what does the question mean?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    f(x) = (x-3)^2 (x+2)
    find x: f(x) >6
    what does the question mean?
    Find all values of x such that f(x) > 6.

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    Re: VCE Maths questions help

    (x-3)^2(x+2) >6
    so, (x-3)^2(x+2) =6
    so, (x-3)^2(x+2) - 6 = 0
    is this correct so far?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    (x-3)^2(x+2) >6
    so, (x-3)^2(x+2) =6
    so, (x-3)^2(x+2) - 6 = 0
    is this correct so far?
    anyone?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    (x-3)^2(x+2) >6
    so, (x-3)^2(x+2) >6
    so, (x-3)^2(x+2) - 6 > 0
    is this correct so far?
    yeah it's correct but keep the inequality signs, i have fixed it above

    once you solve that inequality you will see that the roots are +sqrt(3), -sqrt(3) and 4

    and if u draw the graph the inequality satisfies when -sqrt(3) < x < +sqrt(3) and x > 4
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    Re: VCE Maths questions help

    Consider the curve with equation y = 2x^2 - x
    a. express the gradient of the secant through the points on the curve where x = -1 and x = -1+ h in terms of h
    b. Use h = 0.01 to obtain an estimate of the gradient of the tangent to the curve at x = -1
    c. deduce the gradient of the tangent to the curve at the point where x = -1
    no idea how to do part b and c
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    Consider the curve with equation y = 2x^2 - x
    a. express the gradient of the secant through the points on the curve where x = -1 and x = -1+ h in terms of h
    b. Use h = 0.01 to obtain an estimate of the gradient of the tangent to the curve at x = -1
    c. deduce the gradient of the tangent to the curve at the point where x = -1
    no idea how to do part b and c
    Once you've done a), b) is easy (just put h = 0.01 in your formula from a)). To get the answer to c), take the limit as h -> 0 in your answer for part a).
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    Re: VCE Maths questions help

    (1√6 - 2√9+3√4)/(9√4-4√9)
    How would this be simplified?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    (1√6 - 2√9+3√4)/(9√4-4√9)
    How would this be simplified?
    Anyone?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    (1√6 - 2√9+3√4)/(9√4-4√9)
    How would this be simplified?
    sqrt(9) = 3,
    sqrt(4) = 2.
    The fraction will simplify to (sqrt(6))/(6).
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    Re: VCE Maths questions help

    is 3/(x-1)+2 a polynomial ? If no, why isn't it a polynomial?
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    is 3/(x-1)+2 a polynomial ? If no, why isn't it a polynomial?
    no

    polynomials have integer powers
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    Re: VCE Maths questions help

    Quote Originally Posted by Squar3root View Post
    no

    polynomials have integer powers
    what are integer powers?
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    Re: VCE Maths questions help

    thanks
    for the help
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    what are integer powers?
    Powers that are integers (whole numbers)

    Also polynomials must have POSITIVE integer powers not just integers, so y = x^-3 isn't a polynomial
    Last edited by pikachu975; 1 Jun 2017 at 5:50 PM.
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    what are integer powers?
    Last edited by 1729; 1 Jun 2017 at 5:54 PM.

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    is 3/(x-1)+2 a polynomial ? If no, why isn't it a polynomial?
    Quote Originally Posted by Squar3root View Post
    no

    polynomials have integer powers
    Quote Originally Posted by boredsatan View Post
    what are integer powers?
    Quote Originally Posted by pikachu975 View Post
    Powers that are integers (whole numbers)

    Also polynomials must have POSITIVE integer powers not just integers, so y = x^-3 isn't a polynomial
    Quote Originally Posted by 1729 View Post
    my bad

    yes this


    polynominals have integer powers > 0

    1729 mentioned toe subset above
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    Re: VCE Maths questions help

    How would you show that the points (5,2). (-2,1) and (1,5) form the vertices of an isosceles triangle?
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    Re: VCE Maths questions help

    all of the points (-1,-6), (0,-6), (1,-2) and (2,2) lie on the cubic with equation ax^3 + bx^2 + cx + d.
    Find the value of d
    determine 3 simultaneous equations that will enable solutions to a, b, and c to be found
    find the values of a, b, and c, and determine the equation of the cubic
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    Re: VCE Maths questions help

    a graph has the rule
    y = a/(x-b)^2 + c
    the y intercept is located ta (0,-1) and an asymptote exists at y = 2, determine the values of a, b, and c
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    Re: VCE Maths questions help

    Would appreciate any help. Have a maths exam in 4 days
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    Re: VCE Maths questions help

    If f(x) = 3x and g(x) = x+2, then what is the value of g(f(-1))
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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    all of the points (-1,-6), (0,-6), (1,-2) and (2,2) lie on the cubic with equation ax^3 + bx^2 + cx + d.
    Find the value of d
    determine 3 simultaneous equations that will enable solutions to a, b, and c to be found
    find the values of a, b, and c, and determine the equation of the cubic

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    If f(x) = 3x and g(x) = x+2, then what is the value of g(f(-1))
    First find f(-1).

    Then plug this into the equation for g(x) to get the value of g(f(-1)).

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    Re: VCE Maths questions help

    Quote Originally Posted by boredsatan View Post
    If f(x) = 3x and g(x) = x+2, then what is the value of g(f(-1))

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