Alan

You can fit an order 8 polynomial to these numbers.  The coefficients look awful but the next term given by the polynomial is 96439.

If we have

\((x+3)^2=0\)

then the only value for x is -3

Now \((x+3)^2\rightarrow x^2+6x+9\)

so m is 6 (and n is 9)

.

Like so:

\(\frac{(4x^2y)(-2xy^3)}{(-2xy)^4}\rightarrow \frac{-8x^3y^4}{16x^4y^4}\rightarrow-\frac{1}{2x}\)

First look at the following diagram:

From this we see that        \(\sin{30°}=\frac{1}{2}\\\\ \cos{30°}=\frac{\sqrt{3}}{2}\)

Can you take it from here?

Bee sting molecules

Here is WolframAlpha's answer:

Or:

\(5^\frac{9}{2}\rightarrow\sqrt{5^8\times5}\rightarrow5^4\sqrt{5}\rightarrow 625\sqrt{5}\)

You don't say in respect to which direction the angle is measured!!

If we assume it is 61° to the horizontal then the component of force in the vertical direction is 182*sin(61°) N

If it is 61° to the vertical then the compponent of force in the vertical direction is 182*cos(61°) N

You could use the graphing calculator at: https://www.desmos.com/calculator 

Or, you could choose a number of values of x, then calcvulate the corresponding values of f(x) and plot one against the other by hand or in a piece of graphing software.

You should get something that looks like:

Expand the bracketed terms on the left hand side to get 

7x^2 + (7a+b)x + ab

For this to equal the right hand side we must have. 

ab = 6   And  7a+b = c

As a and b are positive integers we have the following possibilities:

a = 1.  b = 6

a = 6.  b = 1

a = 2.  b = 3

a = 3.  b = 2

Choose one of these combinations to work out one possible value for c using c = 7a+b