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Like all equations, you're going to start off by getting all the x's on the same side of the = side and all the rest on the other side. So we start off with 7x-14=4x+7. Moving the x's to one side means that we have to subtract 4x from both sides, which means we end up with 7x-4x-14=4x-4x+7 which is 3x-14=7. Then we move all the rest to the right hand side which means adding 14 to both sides, ending up with 3x=21. The last step is to divide by 3 to get the 3x to change into x (which is 1x). This means we end up with x=7.

cos(x+a)=cosxcosa-sinxsina
so cosa=5
sina=3 which means tana=3/5
a=0.54 RADIANS
R=sqrt(5^{2}+3^{2}). =sqrt(34)
so sqrt(34)cos(x+0.54)

The easiest way to solve a simultaneous equation is by the method of substitution.
First of all, we take the first equation, and rearrange it so that it is in terms of y. Or, in other words, rearrange it so that it becomes y=something, as shown below.
3x+2y=36
Subtracting 3x from both sides and then dividing both sides by 2 gives us:
y=18-1.5x
We then substitute this into the second equation, in place of y. Giving us:
5x+4(18-1.5x)=64
Multiplying out of the brackets gives us.
5x-6x+72=64
Which, with simplification, and 72 subtracted from both sides, gives us:
-x=-8 which is the same as x=8.
Then, all we need to do in put this value of x into either of the original equations, giving us y=6.

cos(x+a)=cosxcosa - sinxsina
therefore: cos(a)=5 and sin(a)=3
so tan(a)=3/5
into calcultor: a=0.54
to find R=square root(5^{2}+3^{2})
=root(34)
so 5cosx - 3sinx = root(34)cos(x+0.54)

The probability of picking a ball from a bag is the number of balls of that colour divided by the total number of balls.
Therefore in the first instance, the probability of a red ball is 3/9 or 1/3rd.
If that ball is now removed the probability of picking a 2nd is 2/8 or 1/4.
Therefore the probability that both these happen is 1/4 * 1/3 which is 1/12.

d/dx (xy) = x dy/dx + y
d/dx (y^2) = 2y dy/dx [This is from the chain rule]
So, d/dx (2x^2 + xy + y^2 = 14)
=> 4x + x dy/dx + y + 2y dy/dx = 0
set dy/dx = 0 as stationary point has gradient 0
Obtains 4x+y=0
y=-4x
Sub this back into our original equation
14x^2 = 14
x^2 = 1
This is only satisfied by +1 and -1
When x=1 y=-4, when x=-1 y=4
So stationary points are (1,-4) and (-1,4)

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Version: | 3.58.1 |

Build: | f7bd28992702-RR |

Time: | 2018-02-20T13:06:53Z |

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