Alan

Ok rosala, I'll have a go, though I doubt I will do better than Melody did!

The question is If √(0.09 * 0.9 * x) = 0.9 * 0.09.√y , then find x/y

First let's simplify how it looks by calculating 0.09*0.9

$${\mathtt{0.09}}{\mathtt{\,\times\,}}{\mathtt{0.9}} = {\frac{{\mathtt{81}}}{{\mathtt{1\,000}}}} = {\mathtt{0.081}}$$

Now replace 0.09*0.9 in the original equation wherever it occurs (noting that 0.9*0.09 is the same as 0.09*0.9)

√(0.081*x) = 0.081*√y

Now square both sides of the equation

Left-hand side:  (√(0.081*x))² = 0.081*x                            ...(1)

Right-hand side:  (0.081*√y)² = 0.081²*(√y)² = 0.081²*y   ...(2)

Equate (1) and (2)

0.081*x = 0.081²*y

Divide both sides by 0.081

x = 0.081*y

Divide both sides by y

x/y = 0.081

Is this any clearer?

You are on the right track!

4a + 3b = 22    ...(1)

5a - 4b = 43     ...(2)

Multiply (1) by 4 and (2) by 3 (as you did):

16a + 12b = 88   ...(3)

15a - 12b = 129  ...(4)

Add (3) and (4)

31a = 217          ...(5)

Divide both sides of (5) by 31

a = 7                 ...(6)

Substitute (6) into (1)

4*7 + 3b = 22

Subtract 28  (=4*7) from both sides

3b = -6

Divide both sides by 3

b = -2

You can enter D + M/60 + S/3600 as there are 60 minutes in a degree and 3600 seconds in a degree.  The result will be in degrees.

ln(8 - 4x) - ln(x²) = ln(4)

Using the property of logarithms that ln(a) - ln(b) = ln(a/b) we have

ln((8-4x)/x²) = ln(4)

This means we must have

(8 - 4x)/x² = 4

Multiply both sides by x²

8 - 4x = 4x²

Divide through by 4 and rearrange

x² + x - 2 = 0

This factorizes nicely as

(x - 1)*(x + 2) = 0

So the solutions are x = 1 and x = -2

It doesn't exist.

$$\lim_{x\rightarrow \infty}(e^{-x}+2\cos{3x})=\lim_{x\rightarrow \infty}(e^{-x})+\lim_{x\rightarrow \infty}(2\cos{3x})=0+\lim_{x\rightarrow \infty}(2\cos{3x})$$

The limit of cos(3x) as x goes to infinity is undefined as cos(3x) continues to oscillate between maximum and minimum values of 1 and -1 forever.

0.0625 = 1/16 so:

$$5.0625=5\frac{1}{16}$$

or, as an improper fraction:

$$5.0625=\frac{5*16+1}{16}=\frac{81}{16}$$

It isn't clear what you are asking.  Did you mean to write f(x) = -5x⁵ or something else?

Also, you need to specify what values (or range of values) x takes in the table.

2 - 2*[3 - (4y -1)]

Inner bracket first

2 - 2*[3 - 4y + 1]

Multiply out the remaining bracketed term 

2 - 6 + 8y -2

Collect constant terms

8y - 6

I assume you want this simplified.

$$4\sqrt{y^8x^4}=4y^4x^2$$