Question

please answer this quick
it is urgent ​

Answer 1

Question (a)

Solve (a) by using the sine-cosine identity.

$\sf{sin^2\theta+cos^2\theta=1}$

⇒ $\sf{sin^2\theta+\dfrac{4mn}{(m+n)^2} =1}$

⇒ $\sf{sin^2\theta=\dfrac{(m+n)^2-4mn}{(m+n)^2} }$

⇒ $\sf{sin^2\theta=\dfrac{(m-n)^2}{(m+n)^2} }$

As m-n>0 here, the positive sine value is

⇒ $\sf{sin\theta=\dfrac{m-n}{m+n} }$

Question (b)

Solve (b) by finding the sum of all numbers.

Since the mean of 5 numbers is 20, so the sum of 5 numbers is 100.

The mean of 4 numbers is 23, so the sum is 92.

The excluded number is 8.

Question (c)

Solve (c) with the surface area.

Let the surface area of one square be S.

If they are placed adjacently:

The surface area is $\sf{6S+6S+6S-2S=16S}$

If they are placed differently:

The surface area is $\sf{6S+6S+6S=18S}$

So, the ratio obtained is $\sf{8:9}$.