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Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

It's 15.70796. Won't go in-depth since time seems to be of the essence

Step-by-step explanation:

Won't go in-depth since time seems to be of the essence

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The petronas towers in Kuala Lumpur, Malaysia, are 452 meters tall. A woman who is 1.75 meters tall stands 120 meters from the b

bazaltina [42]

Answer:

$75.1^{\circ}$

Step-by-step explanation:

In this problem, we have:

H = 452 m is the height of the Petronas tower

h = 1.75 m is the height of the woman

d = 120 m is the distance between the woman and the base of the tower

First of all, we notice that we want to find the angle of elevation between the woman's hat the top of the tower; this means that we have consider the difference between the height of the tower and the height of the woman, so

$H' = H-h = 452-1.75=450.25 m$

Now we notice that $d$ and $H'$ are the two sides of a right triangle, in which the angle of elevation is $\theta$ . Therefore, we can write the following relationship:

$tan \theta = \frac{H'}{d}$

since

H' represents the side of the triangle opposite to $\theta$

d represents the side of the triangle adjacent to $\theta$

Solving the equation for $\theta$ , we find the angle of elevation:

$\theta = tan^{-1}(\frac{H'}{d})=tan^{-1}(\frac{450.25}{120})=75.1^{\circ}$

3 0

3 years ago

Graph y = 3(x + 2)3 - 3 and describe the end behavior.

-BARSIC- [3]

1) The function is 3(x + 2)³ - 3

2) The end behaviour is the limits when x approaches +/- infinity.

3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.

4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).

5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).

6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.

7) x-intercepts ⇒ y = 0

⇒ 3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0


⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒ x = - 1


8) y-intercepts ⇒ x = 0

y = 3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21


9) Critical points ⇒ first derivative = 0


i) dy / dx = 9(x + 2)² = 0


⇒ x + 2 = 0 ⇒ x = - 2


ii) second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.


y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.


Then the function does not have local minimum nor maximum, but an inflection point at x = -2.


Using all that information you can graph the function, and I attache the figure with the graph.