Alan

I'm going to assume you mean sin(a) = √3/2 and sin(b) = 1/2.  If so then these refer to a right angled triangle with sides 1, √3 and 2.  Angle a is 60° and b is 30° so a+b = 90°. 

sin(90°) = 1 and cos(90°) = 0

I did it using Mathcad.  However, in WolframAlpha you can enter the following: int cos(x)/(1+x^2), x=-inf, x=inf to get the same thing.  I'm still thinking about how to do it by hand!

$${\frac{{\mathtt{\pi}}}{{\mathtt{e}}}}$$

Rewrite this as x = (11 -2y)/3

Now 2y is an even number, so 11 - 2y must be an odd number.  So we just look at odd numbers below 11 that are exactly divisible by 3.  We quickly see that there are only two, namely 3 and 9.

When 11 - 2y = 3 we must have x = 1, so y = 4

When 11 - 2y = 9 we must have x = 3, so y = 1

Volume scales as length cubed, surface area scales as length squared, so the length scaling here is the cube root of (125/27), which is 5/3 (as (5/3)³ = 125/27). so area scales as (5/3)² = 25/9.  Therefore the surface area of the larger solid is 36*25/9 = 100cm²

Replace y in the second equation by x - 3 (because the first equation says this is what y is equal to):

x +2(x-3) = 6

Multiply through the bracketed term by 2:

x + 2x - 6 = 6

Collect the x terms

3x - 6 = 6

Add 6 to both sides

3x = 12

Divide both sides by 3

x = 4

Put this back in the first equation

y = 4 - 3

y = 1

You have to move the decimal point 4 places to the right in 7.0 to get 70000, so n is 4.  That is 70000 can be written as 7.0x10⁴

The slope is the difference between the y values divided by the difference between the x values.

slope = (-4 - 1)/(4 - -6) = -5/10 = -1/2

x⁴ + 3x² +2 = (x² + 1)(x² + 2)

It isn't! It's a short approximation to pi, which has an infinite decimal expansion.  Here are a few more decimals:

$${\mathtt{\pi}} = {\mathtt{3.141\: \!592\: \!653\: \!589\: \!793\: \!2}}$$