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Mathematics: Post your doubts here!

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2x^2 - 2x > 9
2x^2 - 2x - 9 > 0
Solve this. And suppose u got solme value a and b where b < a then ur final answer will be x > a and x < b
Anyone there to help me I’m kinda stuck in this ques that says
A curve has equation y=2x^2-2x
Find the set of values of x for which y >9
It’s from 9709/12/nov/dec/13
 
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Guys! Plz help me! Im stuck again on integration problem. I cant answer any of the question below.Picture2.png
 

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Can anyone please help me .
9709/12/O/N/17


Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the year. A collector bought the stamp for $10 000 at the beginning of 2005. Find its value at the beginning of 2015 correct to the nearest $100.
 
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Can anyone please help me .
9709/12/O/N/17


Each year, the value of a certain rare stamp increases by 5% of its value at the beginning of the year. A collector bought the stamp for $10 000 at the beginning of 2005. Find its value at the beginning of 2015 correct to the nearest $100.

Very similar to compound interest.
F = P(1 + r/100)^n
Where
F = Final amount
P = Initial amount
r = increment
n = number of years

F = 10,000(1 + 5/100)^10
F = 10,000(1.05)^10
F = 10,000(1.6289)
[ F = $16,289 ≈ $16,300 ]
 
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Very similar to compound interest.
F = P(1 + r/100)^n
Where
F = Final amount
P = Initial amount
r = increment
n = number of years

F = 10,000(1 + 5/100)^10
F = 10,000(1.05)^10
F = 10,000(1.6289)
[ F = $16,289 ≈ $16,300 ]
its a sequence question so i dont think they will give marks for this
btw there is no compound interest in the AS syllabus for maths
 
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Assalamu alaikum wa rahmatullah.
I picked up math again after a long time.

Pure Mathematics 1, by Hugh Neill and Douglas Quadling, Chapter 1, Miscellaneous exercise 1, questions 4, 20 and 22.
4. A(7,2) and C(1,4) are two vertices of a square ABCD.
a. Equation of the diagonal BD.
b. Coordinates of B and D.

For part a., I know the product of two diagonals is -1, but I can't get it
Q 20 is similar, but a rhombus.

22. Two lines have equations y=m1x+c1 and y=m2x+c2, and m1m2= -1. Prove that the lines are perpendicular.
(PS for 22, I couldn't type the 1s and 2s in subscript, sorry.)

Jazakumullahu khayr
 
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Assalamu alaikum wa rahmatullah.
I picked up math again after a long time.

Pure Mathematics 1, by Hugh Neill and Douglas Quadling, Chapter 1, Miscellaneous exercise 1, questions 4, 20 and 22.
4. A(7,2) and C(1,4) are two vertices of a square ABCD.
a. Equation of the diagonal BD.
b. Coordinates of B and D.

For part a., I know the product of two diagonals is -1, but I can't get it
Q 20 is similar, but a rhombus.

22. Two lines have equations y=m1x+c1 and y=m2x+c2, and m1m2= -1. Prove that the lines are perpendicular.
(PS for 22, I couldn't type the 1s and 2s in subscript, sorry.)

Jazakumullahu khayr

a)
m(AC) = (y₂ - y₁)/(x₂ - x₁)
m(AC) = (4 - 2)/(1 - 7)
m(AC) = 2/-6 = -1/3
Therefore m(BD) would be = - 1/(-1/3) = 3

The midpoints of both diagnols will be the same since they intersect.
Midpoint = (x₁ + x₂)/2 , (y₁ + y₂)/2
Midpoint = (7 + 1)/2 , (2 + 4)/2
Midpoint = (4 , 3)

Using point slope formula
y - y₁ = m(x - x₁)
y - 3 = 3(x - 4)
y - 3 = 3x - 12
[ y = 3x - 9 ]

b)
The distance from the midpoint to points B and D is the same as the distance from the midpoint to A and C.
d² = (x - 4)² + (y - 3)²
d² = (7 - 4)² + (2 - 3)²
d² = 9 + 1
d² = 10

10 = (x - 4)² + (y - 3)²
Substituting y = 3x - 9
10 = (x - 4)² +(3x - 9 - 3)²
10 = x² - 8x + 16 + 9x² - 72x + 144
10x² - 80x + 150 = 0
x² - 8x + 15 = 0
(x - 5)(x - 3) = 0
[ x = 5 , 3 ]

y = 3x - 9
y = 3(5) - 9 , 3(3) - 9
[ y = 6 , 0 ]

Hence B and D are (3 , 0) and (5 , 6)
 
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Hi, could someone help me with this question?
Use the inductive definition to find the Pascal sequences for (a)n=5 (b) n=6 (c) n=8
 
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