1. ## units Maths

hey guys

more questions

1) convert 7428 kNm into kNmm and express in scientific notation.

2) the heel of a shoe has an area of 100mm^2 and a force of 650 kg m/s^2 is exerted on this heel due to persons weight. what pressure in N/cm^2 is exerted on the Heel?

3) find the area of the triangle which have sides at these lengths

2.87m, 3.69m, 4.58m and show working

also how do you work out a parallelogram, it says AB = 24m BC = 13m and the distance between AB and CD is 5m i need to find area and length of the shorter diagonal.

thats it for now but i need some answers on algebra on simplifing a question like 2p x 6q does that simplify to 12pq.

thanks guys

dan

1) convert 7428 kNm into kNmm and express in scientific notation.
I typically have my students use the "factor-label" method. It's longer to write out but is the easiest way (in my opinion) to check your work.

We want to express kNm in terms of kNmm. We know that 1 m = 1000 mm. So:
$\displaystyle 7248~kNm = \frac{7248~kNm}{1} \cdot \frac{1000~mm}{1~m} = \frac{7248 \cdot 1000}{1} \cdot \frac{kN \not{m} \cdot mm}{\not{m}}$$\displaystyle = 7248000~kNmm = 7.248 \times 10^6~kNmm$

2) the heel of a shoe has an area of 100mm^2 and a force of 650 kg m/s^2 is exerted on this heel due to persons weight. what pressure in N/cm^2 is exerted on the Heel?
$\displaystyle P = \frac{F}{A} = \frac{650~N}{100~mm^2} = 6.5~N/mm^2$

Again use factor-label. We know that $\displaystyle 1 N = 1 kgm/s^2$ so there is no real conversion there. We also know that 10 mm = 1 cm. We have two of these, though, so the factor needs to be squared.

So
$\displaystyle 6.5~N/mm^2 = \frac{6.5~N}{1~mm^2} \cdot \left ( \frac{10~mm}{1~cm} \right ) ^2$ $\displaystyle = \frac{6.5~Nmm^2}{100~mm^2cm^2} = 6.5 \times 10^{-2}~N/cm^2$

-Dan

3) find the area of the triangle which have sides at these lengths

2.87m, 3.69m, 4.58m and show working
Heron's formula.

thats it for now but i need some answers on algebra on simplifing a question like 2p x 6q does that simplify to 12pq.
$\displaystyle 2p \cdot 6q = (2 \cdot 6)(p \cdot q) = 12pq$

Yup, you're right!

-Dan

also how do you work out a parallelogram, it says AB = 24m BC = 13m and the distance between AB and CD is 5m i need to find area and length of the shorter diagonal.
Sketching your parallelogram I see that your question has at least one typo in it.

Being literal about this you have just given me two different lengths for the distance BC, the first being 13 m and the second being 5 m.

Are you trying to say that the distance between A and C is 5 m? This can't be because such a distance would have to represent the short diagonal, not the long one.

Finally, what are you trying to find the area of? The whole parallelogram?

-Dan

5. thanks heaps

and for the last question i found that same problem too. it didnt make sence to what they where asking i also put it into my maths helper program and it errored. will have to leave that one blank and tell them.

once again thanks for the help and i will post more in another post or email you as you sound very helpful and i need some help.

dan