O-Level Additional Math

[LOL123]

hello, i would appreciate if someone can help me with these questions thanks in advance


1. Express the equation 100^x-10^(x+1)=11 as a quadratic equation in 10^x. Hence, find the value of x,correct to 2 decimal places.

2. (lgx)^2-lgx=0

3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0

Thank You!

[archie2]

can someone help with this question

John went to a stationery shop to buy some pens. A fountain pen cost $6, a roller ball pen cost $3 while a ballpoint pen costs $0.10. John spent $100, buying 100 pens in total. How many roller ball pen did he buy?

[paperaeroplanes]

[quote]can someone help with this question

John went to a stationery shop to buy some pens. A fountain pen cost $6, a roller ball pen cost $3 while a ballpoint pen costs $0.10. John spent $100, buying 100 pens in total. How many roller ball pen did he buy?[/quote]let the number of fountain pen be a, roller ball pen be b and ballpoint pen be c.

a+b+c = 100. 6a+3b+0.1c = 100
3b + 5.9c = 500
possible values of b = 147, 88, 29
a = 1, b = 29, c = 70
[quote]1. Express the equation 100^x-10^(x+1)=11 as a quadratic equation in 10^x. Hence, find the value of x,correct to 2 decimal places.

2. (lgx)^2-lgx=0

3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0[/quote]1. 100^x-10^(x+1)=11
(10^x)^2 - 10(10^x) = 11
(10^x - 11)(10^x+1) = 0
10^x = 11 or 10^x = -1

2. (lgx)^2-lgx=0
(lgx)(lgx-1) = 0
lgx = 0 or lgx = 1

[pinkapple]

LOL123:

3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0

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[lost boy]

Solve xy= -5

3x-2y= -11

Thanks

[jieheng]

lost boy:

Solve xy= -5

3x-2y= -11

Thanks

3x - 2y = -11
=> y = (3x + 11) / 2

xy = -5
x [ (3x + 11) / 2 ] = -5
3x^2 + 11x + 10 = 0
(3x+5)(x+2) = 0
(3x+5) = 0 or (x+2) = 0
=> x = - 5/3 or x = -2

when x = - 5/3 , y = 3

when x = -2 , y = 5/2

[lost boy]

Thanks jieheng

[pinkapple]

lost boy:

Solve xy= -5

3x-2y= -11

Thanks

i feel it's easier to sub (1) into (2) instead.

From (1), x = -5/y

Subst x = -5/y into (2):
3 (-5/y) -2y= -11

Multiply throughout by y (to get rid of fractions):
-15 - 2y^2 = -11y

Make one side zero:
0 = 2y^2 - 11y + 15
(2y -5)(y - 3) = 0
y =3 or 5/2

[KiausuLormee]

Can someone help in this questions:

1. Calculate the number of sides of a regular polygon if each interior angle is 170 degree.Proof 2 of the methods
2. Calculate the number of sides of a regular polygon if each exterior angle is 36 degree.

[kelvinsoh]

KiausuLormee:

Can someone help in this questions:

1. Calculate the number of sides of a regular polygon if each interior angle is 170 degree.Proof 2 of the methods
2. Calculate the number of sides of a regular polygon if each exterior angle is 36 degree.

The two relevant formulae for this question are:

Angle sum of n-sided polygon = (n-2)*180 degrees
Sum of exterior angles of any polygon = 360 degrees

(Note: as important as knowing the formulae is knowing a bit about their significance and why they exist. For example, we can think of random triangles, squares or quadrilaterals and see how the formulae work for any shape we can draw.)

Moreover, a regular polygon is one where every side is the same length. Consequently, every angle is the same.

See if these hints help (it's good to try questions after some hints and see if we can progress further with them). The answers \"hidden\" below.

Answer 1 (Highlight to reveal):

Let the number of sides of the polygon be n. There are n interior angles.
Since each interior angle is 170 degrees, the angle sum is 170n.
Applying formula 1,
180(n-2) = 170n
10n = 360
n = 36
Hence there are 36 sides
** The second method is to consider the exterior angles and use equation 2. I've leave this for practice. Do feel free to ask again if you're not sure how to get it.

Answer 2 (Highlight to reveal):

Let the number of sides of the polygon be n. There are n exterior angles.
Since each exterior angle is 36 degrees,
36n = 360 (using formula 2)
n = 10
Hence there are 10 sides