1)
x^2 - 49 = 0
factor
(x+7)(x-7) = 0
x+7 = 0; x = -7
x -7 = 0; x = 7
2)x^2 - 18x + 81 = 0
factor
(x- 9)(x - 9) = 0
x - 9=0; x = 9
3)
x^2 + 3x = 40
x^2+3x - 40 = 0
factor
(x + 8)(x - 5) = 0
x+8 = 0; x = -8
x -5 = 0; x = 5
4)
3x^2 - 75 = 0
3(x^2 - 25) = 0
3(x+5)(x-5) = 0
x + 5 = 0; x = -5
x - 5 = 0; x = 5
5)
2x^2 - 15 = 7x
2x^2 - 7x - 15 = 0
(2x + 3)(x - 5) = 0
2x+3 = 0; x = -3/2
x - 5= 0; x = 5
6)
4x^2 + 16x - 48 = 0
4(x^2 + 4x - 12) = 0
4(x + 6)(x - 2) = 0
x + 6 = 0; x = -6
x - 2 = 0 ; x = 2
Let n represent the number.
<span>.. (3/5)n - 1 = 23 ... three-fifths of a number decreased by one is twenty-three. </span>
<span>Please note that the same English description might be interpreted as </span>
<span>.. (3/5)(n-1) = 23. </span>
<span>We'll use the first interpretation, as it results in the number being an integer. </span>
<span>.. (3/5)n = 24 ... add 1 </span>
<span>.. n = (5/3)*24 ... multiply by 5/3 </span>
<span>.. n = 40 ... carry out the multiplication </span>
<span>The number is 40.</span>
To solve for y, all you have to do is just separate r from all of the others and make it equal to the rest of the equation. So first it was, a=pi*r squared.
Divide by pi on each side,
a/pi=r^2
Take the square root of each side;
square root of (a/pi) =r
and that's all
Hope this helps.
If there is some scalar function such that as given, then this satisfies the following partial differential equations:
Integrate the first PDE with respect to :
Differentiate with respect to :
Differentiate with respect to :
So is indeed conservative.