Tutor MathsGuru: Ask me for your burning Maths questions!

[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.

[kwcllf]

Please help with the following question:


Jerry bought four times as many pencils as notebooks and spent a total of $21.60. He spent $2.40 more on notebooks than the pencils. Given that a notebook cost $3.20 more than a pencil, find the cost of a pencil. Thanks!

[MathIzzzFun]

kwcllf:

Please help with the following question:


Jerry bought four times as many pencils as notebooks and spent a total of $21.60. He spent $2.40 more on notebooks than the pencils. Given that a notebook cost $3.20 more than a pencil, find the cost of a pencil. Thanks!

Hi

Just came back from a trip..

First, find how much is spent on Pencils and Notebooks.
Amount spent on Pencils = [C]
Amount spent on Notebooks = [C][$2.40]

So, 2[C] + $2.40 = $21.60, [C]= $9.60
Amount spent on Pencil= $9.60
Amount spent on Notebooks = $9.60+ $2.40= $12.00

Number of pencils bought is 4 times as many as notebook--> ie we have 4 packs of pencils and 1 pack of notebooks and each pack contains same number of pencils/notebooks.

Each pack of pencils cost $9.60 / 4 = $ 2.40
Each pack of notebooks cost $12.00 --> $12.00 - $2.40= $9.60 than each pack of pencils.

Since each notebook cost $3.20 more than a pencil, so number of notebooks/pencils in each pack = $9.60/$3.20 =3

So, cost of each pencil = ocst of each pack of pencils / number of pencils in each pack = $2.40/3 = $0.80

cheers.

[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