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Firstly, we differentiate y = x²+7x+3 . This gives dy/dx = 2x+7.The minimum value occurs when dy/dx = 0. So find x and y when dy/dx=0. 2x+7=0 implies x= -3.5, which from the first equation mean...

First we must multiply the coefficient of x2 by the value with no x associated with it3x3 = 9Now we must find two numbers that add to make 6 and multiply to make 9+6x9 3 and 3Now we need to split the coef...

Rewrite the equation for L2 to find an equation for y4y=12x-16; y = 3x - 4 2. The x-coefficient gives the gradient (or slope) of the line, so since the gradient of L1 is 3, and as we have just shown, the ...

3x+3y=5      6x+5y=9Multiply the first equation by 2 to get a workable x coefficient:6x+6y=10Write the equations above each other and subtract them:6x+6y=10                                                ...

By inspection we can tell that the line and the plane are not parallel. Since the dot product between the direction vector of the line with the perpendicular vector of the plane was not equal to 0 (i.e. b...