Original post by Mr plumby
t is a positive whole number.
The expression 2t(squared) + 5t + 2 can never have a value that is a prime number.
Explain why.
(any help, I have no idea? Thanks)
The expression 2t(squared) + 5t + 2 can never have a value that is a prime number.
Explain why.
(any help, I have no idea? Thanks)
Hint:
Spoiler
Original post by joostan
Hint:
Spoiler
Im lost.
Original post by Mr plumby
Im lost.
Can you factorise the given quadratic?
Just think of t as a number.
Prime numbers are only divisible by 1 and themselves.
Original post by joostan
Can you factorise the given quadratic?
Just think of t as a number.
Prime numbers are only divisible by 1 and themselves.
Just think of t as a number.
Prime numbers are only divisible by 1 and themselves.
Im still working on it but thanks anyway<
Original post by Mr plumby
Im still working on it but thanks anyway<
Im still working on it but thanks anyway<
Fill in the blanks
Prime numbers can not be factorised, but the quadratic you gave can be factorised.
Another tip for determining if the quadratic expression can be nicely factorized:
its discriminant b^2 - 4ac is a perfect square.
In the example quoted by TS, this is given by 5^2 -4(2)(2) = 9
So yes, it is indeed factorizable.
Hope it helps. Peace.
its discriminant b^2 - 4ac is a perfect square.
In the example quoted by TS, this is given by 5^2 -4(2)(2) = 9
So yes, it is indeed factorizable.
Hope it helps. Peace.
Showing that can be factorised is a start.
Based on the restrictions on t, you need to be able to say something further about these two factors.
E.g. can be factorised, but it can also be a prime for one positive whole number t.
Based on the restrictions on t, you need to be able to say something further about these two factors.
E.g. can be factorised, but it can also be a prime for one positive whole number t.
(edited 11 years ago)
1. The mass of a radioactive material decreases exponentially. It's half-life is the time required for the mass of the material to reduce to half it's initial value. The half life of pLutonium is 14.4 years.
(i) write down the percentage of the initial mass of plutonium remaining after 28.8 years.
(ii) The mass M grams of plutonium at time t years is given by the equation : M=Moe^-kt,
where Mo grams is the initial mass and k is a constant. Find k.
2. In an experiment, the mass of a substance is increasingly exponentially. At a time, the hours, after the start of the experiment, the mass, m grams, of the substance is given by : m=Ae^kt
where A and k are constants. It is given that, at the instant when t=15, the mass is 49g, and the rate at which the mass is increasing is 1.2 g per hour.
(i) Find the values of A and K.
(ii) Find the value of t for which the mass is 70g.
3. David puts a block of ice into a cool box. He wishes to model the mass m kg of the remaining block of ice at time t hours later. He finds that when t=5, m=2.1 and when t=50, m=0.21.
a. David at first guesses that the mass may be inversely proportional to time. Show that this model fits his measurements.
b. Explain why this model:
(i) is not suitable for small values of t.
(ii) cannot be used to find the time for the block to melt completely
David instead proposes a linear model -> m=at+b, where a and b are constants.
c. Find the values of the constants for whih the model fits the mass of the block when t=5 and t=50.
d. Interpret these values of a and b.
e. Find the time according to this model for the block of ice to melt completely.
(i) write down the percentage of the initial mass of plutonium remaining after 28.8 years.
(ii) The mass M grams of plutonium at time t years is given by the equation : M=Moe^-kt,
where Mo grams is the initial mass and k is a constant. Find k.
2. In an experiment, the mass of a substance is increasingly exponentially. At a time, the hours, after the start of the experiment, the mass, m grams, of the substance is given by : m=Ae^kt
where A and k are constants. It is given that, at the instant when t=15, the mass is 49g, and the rate at which the mass is increasing is 1.2 g per hour.
(i) Find the values of A and K.
(ii) Find the value of t for which the mass is 70g.
3. David puts a block of ice into a cool box. He wishes to model the mass m kg of the remaining block of ice at time t hours later. He finds that when t=5, m=2.1 and when t=50, m=0.21.
a. David at first guesses that the mass may be inversely proportional to time. Show that this model fits his measurements.
b. Explain why this model:
(i) is not suitable for small values of t.
(ii) cannot be used to find the time for the block to melt completely
David instead proposes a linear model -> m=at+b, where a and b are constants.
c. Find the values of the constants for whih the model fits the mass of the block when t=5 and t=50.
d. Interpret these values of a and b.
e. Find the time according to this model for the block of ice to melt completely.
Quick Reply
Related discussions
- My year 10 gyg :)
- maths department burning us out
- Jieay's Year 13 GYG - Actuarial Science applicant (2023/2024)
- Mathswatch
- I'm on the verge of a mental breakdown
- Sparx maths homework
- Binomial Expansion Help
- Grind to GYG
- New to this!
- Hopefully I will cry tears of joy
- FANB1984's GCSE (YR 11) GYG
- Is classroom AI good news for teachers and teaching assistants?
- Struggling with WJEC Further Maths A Level
- Should I continue doing tuition during my exam period?
- investing in my future - a y12 blog
- trying to get all As for AS
- Best timetable for studying 4 subjects?
- Sixth Form Help! (NCS vs LAET)
- tackling homework and revision
- live, laugh, love (and sometimes cry) - a blog <3
Latest
Trending
Last reply 2 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 2 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
