Melody

I learned that shortcut of Alan.  Nifty isn't it.    

Thanks Alan   ♬       

$$\begin{array}{rll}
\\\mbox{Lateral area }&=&2\pi rh\\\\
&=& 2\pi \times7\times 45\\\\
&=& 1,979.203372\\\\
&=& 1,979\:\:cm^2 \mbox{ to the nearest square metre}
\end{array}$$

Ninja, you gave a great explanation as always but you forgot your units (2) and you were out by just a little because you did not use enough decimal places for pi.

Rounding errors always get compounded so you have to be careful not to round more than necessary until the very end.  

I think if a length dimension is 2*original then the volume is 2cubed=8 times original.

$$71*8=568cm^3$$

I'm another mathematician will look at my answer.

Sounds right to me!

  -1/5y-1/2=-3/7  

The lowest common denominator is 70 so mult everything by 70

$$\begin{array}{rll}
\\70\left(\frac{-1y}{5}-\frac{1}{2}\right)&=&70\times \frac{-3}{7}\\\\
-14y-35&=&-30\\\\
-14y&=&5\\\\
y&=&\frac{-5}{14}
\end{array}$$

[(27)^(2/3)*250/(50*5)+290-14.5*20]*(63/(3^2*-7))

hi again Natasza,

You would have been better to put these questions in different threads.

Anyway, the second one isjust a very simple trig question.

tan(6degrees)=x/5   solve to 2 decimal places.     ♬

Thou are the one who said "offences against royalty are unpardonable", are thou not? So why doth thou add the word "apparently".  I thought thee were a Queens Councillor since thee quotes the laws of the Medes and Persians. Am I but mistaken? Are thee an imposter? 

hi Natasha,

The sides are 10,15 and 7

The largest angle is opposite the longest side.  You can use cosine rule to work this out.

You don't need to go all the way.  If cos(angle) is positive then it is an acute angle and if neg then it is an obtuse angle.

Either way, the other 2 have to be acute angles.

You can finish it can't you Natasza?

Post again if you have problems.

Natasza, do you mean that the arch is a half the area between 2 concentric cicles where the difference in the 2 radii is 1.25m?  the question is quite confusing.  What has the 11 sebments got to do with anything?

Like this ?