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3 years ago

Given f(x) =x^2 -10x+22 what is the domain of f

Mathematics

1 answer:

fomenos3 years ago

7 0

Answer:

$f(x) = x^2 -10x +22$

And we want to find the domain. And that represent the possible values for x. Since we have a quadratic function we have that the domain would be all the reals, and we can write:

$D= [x \in R]$

Where D represent the domain and R the set of the real numbers.

Step-by-step explanation:

For this case we have the following function:

$f(x) = x^2 -10x +22$

And we want to find the domain. And that represent the possible values for x. Since we have a quadratic function we have that the domain would be all the reals, and we can write:

$D= [x \in R]$

Where D represent the domain and R the set of the real numbers.

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Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle

Sindrei [870]

The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

<h3>How can the distance between Vic and Dan be calculated?</h3>

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

$tan( \theta) = \frac{opposite}{adjacent}$

$tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower}$

$distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7$

Vic's distance from the tower ≈ 306.7 m

Similarly, we have;

$Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8$

Dan's distance from the tower ≈ 179.8 m

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan <em>d </em>is found as follows;