Tutor MathsGuru: Ask me for your burning Maths questions!

[MathIzzzFun]

Essential:

Hi, Need help on this question.

1) A rectangular cardboard measures 33 cm by 24 cm. What is the maximum number of rectangular pieces that can be cut from the cardboard if each piece of rectangle measures t6 cm by 4cm? Please help me confirm the answer is 28 , 32 , 30 or 34
Thanks.

Hi

34 is out because 33 x 24 / (6x4) = 33

The max number possible is 32- first cut out 24cm by 24cm --> 24/6 x 24/4 = 24 pieces

The remaining piece is of dimension 9 cm x 24 cm --> cut out 8 cm x 24cm --> 8/4 x 24/6 = 8 pieces

Total 32 pieces, leaving a strip of 1cm x 24cm

cheers.

[MathIzzzFun]

kwcllf:

Hi please help with the following question.


Roy, Sam and Ted had a sum of money. Roy had 4/5 of Sam's money. Sam had 60% of Ted's. After Roy gave $12 to Sam, he had 5/7 of what Sam had. How much more money did Ted have than Sam in the end?

Thanks:-)

Hi

initially
roy : sam = 4 : 5

in the end,
roy: sam = 5 : 7

total amount that roy and sam had remained the same so make the total the same
initially, roy : sam = 4:5 = 16u : 20u
in the end, roy: sam = 5:7 = 15u: 21u
so, 1u = $12
Sam, at first = 20u = $ 240, Ted = 5/3 x $240 = $400
Sam, in the end = 21u = $252
... I think you can complete the rest..

cheers.

[kwcllf]

Hi MathIzzzFun,


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

[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?