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Sunny_sXe [5.5K]
4 years ago
10

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Mathematics
1 answer:
sergejj [24]4 years ago
7 0

Answer:

Step-by-step explanation:

Given is a function

f(x) = x^2 + 5x + 6

Since leading term is positive,

the parabola is open up.

Let us write this in vertex form after completing the square

f(x) = x^2 +2(\frac{5}{2})x+\frac{25}{4}  -\frac{25}{4}+6\\=(x+(\frac{5}{2})^2-\frac{1}{4}

Hence we get vertex= (-5/2,-1/4)

Since this is a parabola open up we have the minimum point is only one at x=-5/2

So we have the function decreasing for x<-2.5 and increasing for x>-2.5

Decreases in (-\infty, -2.5)

Increases in (-2.5,\infty)

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The angle of depression is 29.0521°. So it is a safe landing.

Step-by-step explanation:

Step 1:

The plane is flying at a height of 25,000 feet and 45,000 feet away from the landing strip. Assume it lands with an angle of depression of x°.

So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 25,000 feet while the adjacent side measures 45,000 feet. The angle of the triangle is x°.

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Step 2:

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tan x = \frac{25,000}{45,000} = 0.5555.

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4 years ago
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Choosing a color, number, or restaurant
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If point C is not located between points A and B then AC+CB__ AB
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\neq

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