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    Hi there,

    I am struggling to answer a few maths questions based on a variety of topics.

    I would appreciate any form of help!

    Q1 (Equations and inequalities)

    Football pitch area = 7140 m^2
    4x+5 m wide and 3x-7 m long
    What are the dimensions of the pitch?

    Q2 (Equations and inequalities)

    Jodie and Kate play netball for the same team
    In a month they score fewer than 15 goals
    Kate scored 4 more goals than Jodie
    What is the maximum number of goals Jodie could have scored?

    Q3 (Equations and inequalities)

    A pond is 8 m wide by 10 m long
    It has a path around it that is exactly the same width all round
    The area of the path is 80% of the area of the pond
    How wide is the path?

    Q4 (Similarity and congruence)

    Y and Z are similar cylinders
    Y has a volume of 6(pi) cm^3
    Z has a volume of 93.75(pi) cm^3
    The radius of cylinder Y is 0.6 cm
    Calculate the radius of cylinder Z

    Thanks in advance
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    (Original post by Pandora___)
    Hi there,

    I am struggling to answer a few maths questions based on a variety of topics.

    I would appreciate any form of help!

    Q1 (Equations and inequalities)

    Football pitch area = 7140 m^2
    4x+5 m wide and 3x-7 m long
    What are the dimensions of the pitch?

    Q2 (Equations and inequalities)

    Jodie and Kate play netball for the same team
    In a month they score fewer than 15 goals
    Kate scored 4 more goals than Jodie
    What is the maximum number of goals Jodie could have scored?

    Q3 (Equations and inequalities)

    A pond is 8 m wide by 10 m long
    It has a path around it that is exactly the same width all round
    The area of the path is 80% of the area of the pond
    How wide is the path?

    Q4 (Similarity and congruence)

    Y and Z are similar cylinders
    Y has a volume of 6(pi) cm^3
    Z has a volume of 93.75(pi) cm^3
    The radius of cylinder Y is 0.6 cm
    Calculate the radius of cylinder Z

    Thanks in advance
    Show your working and/or ideas, then we can help.
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    (Original post by RDKGames)
    Show your working and/or ideas, then we can help.
    For the first question, what I did was (4x+5)(3x-7) = 7140

    Then I expanded it (so 12x^2 +15x - 35 -28x = 7140)

    I then took away 7140 from both sides to have a quadratic equation to solve

    12x^2 -13x - 7175 = 0. I tried solving it using the quadratic formula, but the answer(s) I got was not correct.


    For the second question, I realised that I had to put together an inequality and then solve it, but I wasn't too sure with what the inequality should contain.

    I started off by trying to solve 15-x+4+x (K + J's goals in a month) < x (J's goals) < x+4 (K's goals), but I struggled with solving it.


    For the third question, I did 8 x 10 to give the area of the pond (80 cm^2) and found 80% of that which is 64 cm^2. The equation to find the width would have been something like a x b = 64, but I became discombobulated from then on.

    For the final question, I tried applying my knowledge of "the ratio of the volume is cubed the ratio of the radii", but I did not know how to answer the actual question with that in mind.
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    (Original post by Pandora___)
    For the first question, what I did was (4x+5)(3x-7) = 7140

    Then I expanded it (so 12x^2 +15x - 35 -28x = 7140)

    I then took away 7140 from both sides to have a quadratic equation to solve

    12x^2 -13x - 7175 = 0. I tried solving it using the quadratic formula, but the answer(s) I got was not correct.


    For the second question, I realised that I had to put together an inequality and then solve it, but I wasn't too sure with what the inequality should contain.

    I started off by trying to solve 15-x+4+x (K + J's goals in a month) < x (J's goals) < x+4 (K's goals), but I struggled with solving it.


    For the third question, I did 8 x 10 to give the area of the pond (80 cm^2) and found 80% of that which is 64 cm^2. The equation to find the width would have been something like a x b = 64, but I became discombobulated from then on.

    For the final question, I tried applying my knowledge of "the ratio of the volume is cubed the ratio of the radii", but I did not know how to answer the actual question with that in mind.
    Correct working for the first one, correct quadratic. You should indeed get x=25 since you can disregard the negative value. If you're not getting this then you're probably slipping up somewhere in your quadratic formula.

    Incorrect inequality. Let's denote Jodie's goals by J and Katie's goals by K. We are told they scored fewer than 15 in a month. So that means J+K&lt;15 We are also told that Kate scored 4 more than Jodie, meaning K=J+4 Since we know K in terms of J, we can use this to get our inequality ONLY in terms of J and get the required answer.

    Wrong. The area of the pond is 80, yes, but the path around the pond is different. Draw a diagram and label your pond and the path around it with the unknown variable for the width, you might need to dissect the path into 4 rectangles.

    Volume of a cylinder is determined by \pi r^2h. Since you know they are similar, the radius and height of Z is are the same as the radius and height of Y but multiplied by some constant k. So for Y: 6\pi = \pi r^2h and for Z: 93.75\pi=\pi (kr)^2 \cdot (kh). Try and figure out the radius of cylinder Z which is kr where r=0.6 as told in the question.
 
 
 
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