The EVENT space is a subset of the SAMPLE space. In our case:
EVENT SPACE =[(1+5), (2+3), (3+3), (4+2), (5+1)]. In short all favorable outcomes. (against all POSSIBLE outcomes in the SAMPLE space)
Hey
8x^2-4x
4x is the greatest common factor.
B answer
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The critical points of <em>h(x,y)</em> occur wherever its partial derivatives and vanish simultaneously. We have
Substitute <em>y</em> in the second equation and solve for <em>x</em>, then for <em>y</em> :
This is to say there are two critical points,
To classify these critical points, we carry out the second partial derivative test. <em>h(x,y)</em> has Hessian
whose determinant is . Now,
• if the Hessian determinant is negative at a given critical point, then you have a saddle point
• if both the determinant and are positive at the point, then it's a local minimum
• if the determinant is positive and is negative, then it's a local maximum
• otherwise the test fails
We have
while
So, we end up with
I'm not sure if you're already given the length of the rectangle, but the width is either (x + 3) or (x + 15).
We can find this by factoring x² + 18x + 45, as the area of a rectangle is found by multiplying the length and width together, so if we factor this expression we can find what was multiplied together.
Factoring x² + 18x + 45, we get (x + 3)(x + 15), which then tells us the two sides of the rectangle. Again, I'm not sure if you were already told the length, but if you were then the width is the other side. For example, if you were told the length was (x + 3), then the width would be (x + 15).
I hope this helps!