The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?

1 answer:

4 0

We may answer the question above by dividing the expression y² - 10x + 24 with the given factor, y - 4. The division would give an answer of y - 6. Thus,

<span>y² - 10x + 24 = (y - 4)(y - 6)

The answer is the fourth choice, y - 6.</span>

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A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

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$h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16$

So, in the path that the hiker chose:

$\frac{\partial{h}}{\partial{t}}=0$

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We start differentiating h(x,y) using chain rule as follows:

$\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}$

Now, it´s easy to find all these derivatives:

$\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)$