# As-level -> Maths Pure HELP!!

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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=-0.01x

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)

- 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 - 0.00006f

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)

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.

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

1) y = miles per gallon x= speed of car

y=-0.01x

^{2}+ 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 - 0.00006f

^{2}

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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(Original post by

So for question one, you need to find the x values for which y=32.5

**M4cc4n4**)So for question one, you need to find the x values for which y=32.5

Thank you again.

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#4

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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#6

Yeah u eat the tickets and then times it by 34 and u get ur answer Hope that helps

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#8

(Original post by

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.

**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.

M = ....

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#9

(Original post by

you just need one point on the line to determine m. So use the "initial condition" when t=10,000 and p=£30

m = ....

**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 = ....

Last edited by xIshaa; 1 year ago

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#10

(Original post by

You just need one point on the line to determine M. So use the "initial condition" when t=10,000 and p=£30

M = ....

**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 = ....

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#11

(Original post by

sry what about 3b

**xIshaa**)sry what about 3b

Do you know how to do this?

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#12

(Original post by

You write the expression as a "normal" quadratic then complete the square.

Do you know how to do this?

**mqb2766**)You write the expression as a "normal" quadratic then complete the square.

Do you know how to do this?

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#13

(Original post by

no

**xIshaa**)no

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?

Last edited by mqb2766; 1 year ago

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#14

(Original post by

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?

**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?

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#15

(Original post by

but its not a quadratic how am i suppose to complete the square

**xIshaa**)but its not a quadratic how am i suppose to complete the square

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#16

(Original post by

Why is it not a quadratic?

**mqb2766**)Why is it not a quadratic?

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#17

(Original post by

its not in that quadratic form like ax^2 + bx + c

**xIshaa**)its not in that quadratic form like ax^2 + bx + c

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#18

(Original post by

What is the "x" variable in this question?

**mqb2766**)What is the "x" variable in this question?

would you times everything in the bracket by p?

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#19

(Original post by

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?

**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?

Expand the brackets to get a "normal" quadratic, then complete the square.

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#20

(Original post by

Yes.

Expand the brackets to get a "normal" quadratic, then complete the square.

**mqb2766**)Yes.

Expand the brackets to get a "normal" quadratic, then complete the square.

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