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questionable_i
BrownBelt
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Joined: Sat Oct 10,
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Can anyone help me with these questions?

Q1

Q2

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you

EconsPhDTutor
OrangeBelt
Posts: 39
Joined: Sat Jan 23,
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questionable_i wrote:Can anyone help me with these questions?

Q1

Q2

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you
Hello.

Q1. 5^(-x).
Q2. 15/(√2).

Please see this PDF for the full solutions.

For Q3, I think there might be a typo. Because if you try for example n = 1, we have 4^1 + 5 × (4^1 + 1) - 2^(2 × 1) + 1 = 4 + 5 × 5 - 4 + 1 = 26, which is not divisible by 19.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

questionable_i
BrownBelt
Posts: 535
Joined: Sat Oct 10,
Total Likes:1

EconsPhDTutor wrote:
questionable_i wrote:Can anyone help me with these questions?

Q1

Q2

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you
Hello.

Q1. 5^(-x).
Q2. 15/(√2).

Please see this PDF for the full solutions.

For Q3, I think there might be a typo. Because if you try for example n = 1, we have 4^1 + 5 × (4^1 + 1) - 2^(2 × 1) + 1 = 4 + 5 × 5 - 4 + 1 = 26, which is not divisible by 19.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

www.EconsPhDTutor.com

Maybe this might help as the question goes:
Show that if n is a positive integer, is divisible by 19.

questionable_i
BrownBelt
Posts: 535
Joined: Sat Oct 10,
Total Likes:1

kennethTutor wrote:
questionable_i wrote:Can anyone help me with these questions?

1. The straight line 3y=6-2x meets the curve (2x+1)^2+6(y-2)^2-49=0 at the points P and Q. Find the point P and Q and leave your answer in surd form.

2. α and β are roots of the equation x^2+2x=h. The quadratic equation 8x^2-6x+k=0 har roots of (1-α)/α and (1-β)/β. Find the values of h and k.

3.Find the range of values of k for which the expression 2(k-3)x-25-x^2 is always negative for all real values of x.

I need it ASAP.
For Q1, basically we solve simultaneous equations by using Substitution method. I did not get any surds for my answer, so you might want to check the question again.

Solution: http://imgur.com/OIhjQ0W

For Q2, we find the Sum of Roots (SOR) and Product of Roots (POR) for both equations. We use the SOR and POR to find the values of the unknowns h and k.

Solution P1: http://imgur.com/zkog0A5
Solution P2: http://imgur.com/L552BGx

For Q3, we use discriminant b^2 - 4ac < 0, as the curve is always negative. This means that the curve does not cut the x-axis, therefore there are no real roots.

Solution: http://imgur.com/sbKZD3A

kennethTutor
OrangeBelt
Posts: 39
Joined: Mon Jul 13,
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questionable_i wrote: Maybe this might help as the question goes:
Show that if n is a positive integer, is divisible by 19.
We simplify to get 4^n for every term. Two indices law are required here (stated in my solution).

Solution: http://imgur.com/Gxpte6T

Once we get 19.4^n, it is divisible by 19 as 19 is a factor of the expression.

KSP2013777
OrangeBelt
Posts: 92
Joined: Fri Dec 28,

I tried many times but my answer has an extra 1/2. Pls help.

Thank you.

kennethTutor
OrangeBelt
Posts: 39
Joined: Mon Jul 13,
Total Likes:2

I tried many times but my answer has an extra 1/2. Pls help.

Thank you.
Since c is an constant, we can absorb the 1/2 into the constant. Remember when we differentiate a constant, we get 0.

Solution: http://imgur.com/a/pBRcn

Look for the second solution.

KSP2013777
OrangeBelt
Posts: 92
Joined: Fri Dec 28,

Thank you very much for your help, kennethTutor.

KSP2013777
OrangeBelt
Posts: 92
Joined: Fri Dec 28,

Can somebody pls help me with this question?

Thank you.

KSP2013777
OrangeBelt
Posts: 92
Joined: Fri Dec 28,