Alan

Draw the graph near the minimum (maximum) of the curve.  If there are no real solutions the curve will be completely above (below) the x-axis.

The area of any triangle is given by half base times height.

6²² mod 53 = The answer to life, the universe and everything!

Use the calculator on this site to evaluate this (use the 2nd key to show the mod key).

Expanding the bracketed terms we have 

2x - 3x -1 = 4x - 2

or -x -1 = 4x - 2

add x to both sides

-1 = 5x - 2

add 2 to both sides 

1 = 5x

divide both sides by 5

x = 1/5  

(or x = 0.2)

If you mean how to convert °F to °C then the relationship is:  °C = (°F - 32)*5/9

3x+5y = 9      ...(1)

3x - y  = -7     ...(2)

Subtract (2) from (1) term by term:

3x-3x + 5y-(-y) = 9 - (-7)

6y = 16

y = 16/6 = 8/3

Rearrange (2) to get x = (y-7)/3 or x = (8/3-7)/3 or x = -13/9

There are an infinite number of possibilities!  However, perhaps the simplest is to assume f(x,y) takes the form a*x+b*y+c, where a, b and c are constants. f_x (the partial derivative of f with respect to x) is a, so a = 2; f_y is b, so b = 3, f(-9,9) is -4 so:

2*(-9)+3*(9)+c=-4  so c = -13.

Therefore f(-9,10) = 2*(-9)+3*(10)-13 = -1

and f(-8,9) = 2*(-8)+3*(9)-13 = -2

The only way I've found to do this at present is to clear your browsing history (including images and files) from your browser.

As written, this 2nd order differential equation is highly non-linear and almost certainly has no analytical solution.  If you meant to put t² on the right-hand side instead of x², and if cos(a) is also a constant, then there is an analytical solution.

A combination is the arrangement of a number of objects from a group such that the order of the arrangement doesn't matter.