All Answers 358108 Answers

I answered this one before.   What happened to MY answer.  It must have been the Gremlims!

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{15}}}{{\mathtt{9}}}}\right)} = {\mathtt{59.036\: \!243\: \!467\: \!926^{\circ}}}$$

Okay - I made a really stupid mistake on one - I will fix that now - and the rest of mine are okay.

Thank you Alan.

9% as a fraction is 0.09, so you multiply $1000 by 0.09 to get $90.

If x = 64^2/3 then x³ = 64² so x is a number which, when cubed is the same as 64 squared.  That is, 64^2/3 is a number which when cubed is the same as 64².

$${{\mathtt{16}}}^{{\mathtt{3}}} = {\mathtt{4\,096}}$$

$${{\mathtt{64}}}^{{\mathtt{2}}} = {\mathtt{4\,096}}$$

So 16 is 64^2/3 because 16³ is the same as 64².

Here are my solutions:

I heard it's OK to talk to yourself, but you are crazy if you answer.

What do you think?

I think it's OK

Yeah, me too.

Nah, you are both nuts!

I'm not crazy! You are!

ME?! I just asked, you were the one that answered.

Ahh! you are driving me crazy!

Yes, there has to be a third component; but it is zero!

So p = −2i − 3j + 0k and q =4i +7j + 0k.  It measn p and q are both in the i,j plane; and their cross-product will be in the k direction. 

ur welcome !

i too would like to know more about this! i didnt even know that those problems were real ! a new thing discovered by me ! btw thanks for it ND ! 

 $$LOL !$$

ur right Strider , i feel that too !sometimes !

welcome Strider to the world of learning maths ! lol !  i hope u enjoy here as well as learn as we all do ! welcome to the forum!and when everyone is giving points why should i step back so welcome points for u or should i say thumbs up !

Hi Jedithious,

It is always great to see you in the forum!  

1) The ratio of the surface areas of two cubes is 64:81. What is the ratio of the edges of the cubes?

the answer will just be sqrt(64):sqrt(81) = 8:9

Now I will show you why

$$\dfrac{6l_1^2}{6l_2^2}=\frac{64}{81}\qquad so \qquad \dfrac{l_1^2}{l_2^2}=\frac{64}{81}\qquad so \qquad \dfrac{l_1}{l_2}=\frac{8}{9}$$

2) If the ratio of the volumes of two similar cylinders is 125:27, what is the ratio of their surface areas?

volume is U3,  Surface area is U2

so ratio of surface areas will be  125^(2/3):27^(2/3) = 25:9

3) A model of a rocket was built to a scale of 1:40. 

a) The length of the model was 75 cm. What was the length of the actual rocket, in metres?

75*40=3000cm=30m

b) The area of metal used to cover the curved surfaces of the model was 2750 cm². What area of metal covered the curved suraces of the actual rocket, in square metres?

1:1600 = 2750:2750*1600=4,400,000cm²=440m²     (Little edit here)

c) The nose cone of the rocket had a volume of 96 m³. What was the volume of the nose cone of the model, in cubic centimetres?

1:40³ = x:96  

$$\frac{1}{64000}=\frac{x}{96}\\\\
96\times \frac{1}{64000}=x\\\\
x=1.5\times 10^{-3}\quad m^3$$

100cm in a metre

100³cm³ in a m³

$$x=1.5\times 10^{-3}\times 10^6 = 1.5\times 10^{3} = 1500cm^3$$

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NOW I have taken shourt cuts (maybe I am not allowed to) and my answers are different from CPhill if I get time I will check the long way but I think one of the other mathematicians will validate one of our answers before then. 

"One or more nights' is the same thing as saying "at least" one night.

And the probability of freezing at least one night is the same probability as 1 minus the probability that it doesn't freeze ANY of those nights. And the probability that it doesn't freeze on any particular night is 45% or just .45

So we have .....

1 - (.45)¹⁴ = 0.9999860371139801  .......(In effect, it's almost guaranteed to freeze on at least one night!!)

64^2/3 = (64^1/3)², or (³√64)²

So..what times itself 3 times equals 64?

4*4*4 = 64.

(³√64)²

(4)²

16 is our answer.

Does this make sence?

1000*9%=90/12=7.5

It means that we are raising 64 to the 2/3rds power (exponent).

By a property of exponents, we can write this as (64^1/3)².   And 64^1/3 means the same thing as ³√64 which is the "cube root" of 64 which = 4.

So, we have  (4)²  = 16

And there's your answer  !!!

Sunday 15/6/14

I put both these posts up to promote discussion.

That is really nice of you Strider.  You certainly did not need to appologise for this post.

Welcome to the forum.  I know you have been here for awhile but now it is official!

I hope that you continue to learn lots and to have a good time here!

Here is some more starter points.

Melody.

$${\frac{{\mathtt{1}}}{{\mathtt{5}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{20}}$$

I use this method all  the time!  It is the BEST way to do it!

Factoring trinomials using the grouping method.  

This is a really good clip. 

do you actually mean

f(x)=x+(1/x)-2  

which is what you have written

OR

do you mean

f(x)=(x+1)(x-2)

Really Ninja?  I'd like to hear more.

I love trains!