Tutor MathsGuru: Ask me for your burning Maths questions!

[MathIzzzFun]

kwcllf:

Hi MathIzzzFun,


Thanks again. Missed your expertise. Hope you had a great trip!

u r welcome

cheers.

[archie2]

Hi there

pls help with this question
Express 12 cos x - 5 sin x in the form R cos(x+a) where R is positive constant and a is an acute angle. Hence find the maximum and minimum values of the following and also the values of x between 0 deg and 360 deg at which they occur.
a) (12 cos x - 5 sin x )^2
b) (12 cos x - 5 sin x )^3
thank you

[MathIzzzFun]

archie2:

Hi there

pls help with this question
Express 12 cos x - 5 sin x in the form R cos(x+a) where R is positive constant and a is an acute angle. Hence find the maximum and minimum values of the following and also the values of x between 0 deg and 360 deg at which they occur.
a) (12 cos x - 5 sin x )^2
b) (12 cos x - 5 sin x )^3
thank you

Hi

expand Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a) = 12cos(x) - 5 sin (x)
so, Rcos(a) = 12, Rsin(a) = 5
Dividing, tan(a) =5/12, sin(a) = 5/13, cos(a) = 12/13, R= 13... you can then find value of a

a) (12 cos x - 5 sin x )^2 = (13cos(x+a))^2 --> min value at cos(x+a)=0 ie when x+a = 90. max value at cos (x+a) =1 or -1 ie x+a = 0 or x+a=180

b) min value when cos(x+a) = -1, max value when cos (x+a)=1... you should be able to work out the values.

cheers.

[babydragon]

pls help me with this problem

Q>> Using the identities cos (2x) = 2 cos^2 (x) - 1 and a cos (x) + b sin (x) = (a^2 + b^2)^0.5 cos ( x - y ), where (y) is a constant, or otherwise, find the maximum and mimimum values of
11 cos^2 (x) + 3 sin^2 (x) + 6 sin(x)cos(x) + 5

Hence or otherwise solve the equation
11 cos^2 (x) + 3 sin^2 (x) + 6 sin(x)cos(x) + 5 = 15 for 0 deg <= (x) >= 360 deg

thank you
Cheers

[KSP]

i thought thread this is a Pri level maths??

[babydragon]

Hi

I have a physics question which i do not understand. If you know, please help.
three conducting balls, X, Y and Z are suspended vertically, side by side, without touching each other, by light insulating threads. X is charged positively. Y is negatively charged. Z is positively charged.
The following procedures are carried out:
1> Z is earthed and the earthing connection is then removed.
2> Y&Z are brought into contact and then separated
3> X&Y are brought into contact and then separated.
What is the resulting charges on Y & Z?

[kwcllf]

Hi,


Please help with the following question. Thanks!

9 oranges cost $11.00.
James bought a total of 1000 apples and oranges for $999.00.
How many apples and how many oranges did he buy?

[archie2]

babydragon:

Hi

I have a physics question which i do not understand. If you know, please help.
three conducting balls, X, Y and Z are suspended vertically, side by side, without touching each other, by light insulating threads. X is charged positively. Y is negatively charged. Z is positively charged.
The following procedures are carried out:
1> Z is earthed and the earthing connection is then removed.
2> Y&Z are brought into contact and then separated
3> X&Y are brought into contact and then separated.
What is the resulting charges on Y & Z?

Hi babydragon
1>>When Z is earthed, free electron will flows from earth to the positively charged balls --> neutralising it.
2>>Next, when Y&Z are in contact, -ve charged from ball Y will flows into ball Z. When separated, both balls Y & Z will be negatively charged.
3>>Then, when balls X&Y are in contact, +ve & -ve will neutralise each other. Assuming all balls have equal number of -ve or +ve charge initially, then ball X will have more +ve charge while ball Y has less negative charge. The +ve charge from ball X will neutralise the -ve charged in ball Y. In the end, there will be more +ve charge balance and both balls will be positively charged.
Therefore the resulting charge in ball Y is +ve and ball Z is -ve.
Hope this help

[MathIzzzFun]

kwcllf:

Hi,


Please help with the following question. Thanks!

9 oranges cost $11.00.
James bought a total of 1000 apples and oranges for $999.00.
How many apples and how many oranges did he buy?

Hi

apples cost ?

cheers.

[kwcllf]

Hi please help with the following question.


Dolly had 80 more stickers than Jenny. Dolly gave 25% of her stickers to Jenny. Jenny in return gave 60% of her stickers to Dolly. In the end, Dolly had 100 stickers more than Jenny. How many stickers did Dolly have at first.

Thanks!