Alexia_17
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Hi,
I need help with just a few modelling type quadratics questions.


1) y = miles per gallon x= speed of car
y=-0.01x2 + 0.975x +16, x > 0

a) Use the model to find two speeds at which the car has a fuel consumption of 32.5 mpg.

b) Rewrite y in the form A-B(x-C)2
- I have B as 0.01 and C as 48.75. However I have 16 for A and the answer booklet says it is 39?? I don't know how to get to that answer.

2) A fertiliser company uses a model to determin how the amount of fertilser used, f kilograms per hectare, affects the grain yeild g, measures in tonnes per hectare.

g= 6 + 0.03f - 0.00006f2

a) One farm currently uses 20 kilograms of fertiliser per hectare. How much more feriliser would he need to use to increase his yeild grain by 1 tonne per hectare?

3) A football stadium has 25 000 seats. The football club knows that they will sell only 10,000 tickets if each ticket costs £30. They also expect to sell 1,000 more tickets every time the price goes down by £1.

a) The number of tickets sold, t, can be modelled by the linear equation
t=M-1000p
where £p is the price of each ticket and M is a constant. Find the value of M.

The total revenue, £r, can be calculated by multiplying the number of tickets sold by the price of ach ticket. This can be written as:

r=p(M-1000p)

b)Rearrange r into the form A-B(p-C)2 where A, B and C are constants to be found.

c) Using your answer to part b or otherwise, work out how much the football club should charge for each ticket if they wanted to make maximum amount of profit.
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M4cc4n4
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So for question one, you need to find the x values for which y=32.5
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Alexia_17
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(Original post by M4cc4n4)
So for question one, you need to find the x values for which y=32.5
Thank you, Ive spotted my mistake on that question now. ahah Any ideas about part 'b' or any other questions??
Thank you again.
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M4cc4n4
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You forgot to take away the 47.75^2 on b and as it is both - they add and when -0.01 it becomez 39.765625 or something
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xIshaa
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Did you manage to do 3a? Its 40,000 but idk how
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Sidraa131
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Yeah u eat the tickets and then times it by 34 and u get ur answer Hope that helps
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xIshaa
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mqb2766 can u help with question 3a pls
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mqb2766
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(Original post by xIshaa)
mqb2766 can u help with question 3a pls

A football stadium has 25 000 seats. The football club knows that they will sell only 10,000 tickets if each ticket costs £30. They also expect to sell 1,000 more tickets every time the price goes down by £1.

a) The number of tickets sold, t, can be modelled by the linear equation
t=M-1000p
where £p is the price of each ticket and M is a constant. Find the value of M.
You just need one point on the line to determine M. So use the "initial condition" when t=10,000 and p=£30
M = ....
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xIshaa
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(Original post by mqb2766)
you just need one point on the line to determine m. So use the "initial condition" when t=10,000 and p=£30
m = ....
ooooooooooohhhhhhhhhhhhhhhh ty
Last edited by xIshaa; 9 months ago
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xIshaa
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(Original post by mqb2766)
You just need one point on the line to determine M. So use the "initial condition" when t=10,000 and p=£30
M = ....
sry what about 3b
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mqb2766
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(Original post by xIshaa)
sry what about 3b
You write the expression as a "normal" quadratic then complete the square.
Do you know how to do this?
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xIshaa
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(Original post by mqb2766)
You write the expression as a "normal" quadratic then complete the square.
Do you know how to do this?
no
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mqb2766
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(Original post by xIshaa)
no
Is decent
https://www.mathsisfun.com/algebra/c...ng-square.html
Its not that hard and worth understanding. Its arguably the most useful form for a quadratic as it makes the location of the stationary point and its curvature very clear.

TBH, I could talk you through the question, but its better you try?
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xIshaa
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(Original post by mqb2766)
Is decent
https://www.mathsisfun.com/algebra/c...ng-square.html
Its not that hard and worth understanding. Its basically the normal form for a quadratic.

TBH, I could talk you through the question, but its better you try?
but its not a quadratic how am i suppose to complete the square
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mqb2766
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(Original post by xIshaa)
but its not a quadratic how am i suppose to complete the square
Why is it not a quadratic?
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xIshaa
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(Original post by mqb2766)
Why is it not a quadratic?
its not in that quadratic form like ax^2 + bx + c
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mqb2766
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(Original post by xIshaa)
its not in that quadratic form like ax^2 + bx + c
What is the "x" variable in this question?
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xIshaa
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(Original post by mqb2766)
What is the "x" variable in this question?
i mean how do u complete the square on p(M-1000p) because its not in that quadratic form
would you times everything in the bracket by p?
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mqb2766
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(Original post by xIshaa)
i mean how do u complete the square on p(M-1000p) because its not in that quadratic form
would you times everything in the bracket by p?
Yes.
Expand the brackets to get a "normal" quadratic, then complete the square.
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xIshaa
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(Original post by mqb2766)
Yes.
Expand the brackets to get a "normal" quadratic, then complete the square.
i got Mp - 1000p^2
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