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Arlecino [84]
3 years ago
10

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x minus 24?

Mathematics
2 answers:
ANEK [815]3 years ago
4 0
Dividing x^2 - 16 by 4x - 24  gives the quotient (1/4)x + 3/2

y = (1/4)x + 3/2  would be an asymptote  ( discontinuity)

Another would be a vertical discontinuity  when x =  6  (this would make the denominator 4x-24  = 0.
Ilya [14]3 years ago
3 0

Answer:

x=6 is only the point of discontinuity for the function f(x).      

Step-by-step explanation:

Given a function f(x)=\frac{x^2-16}{4x-24}.

We have to find the discontinuities of the function.

Point of discontinuities are the points at which the function is not defined.

To find the point of discontinuities we have to put the denominator 0 to find the value of x or to find the point of discontinuity.

∴ 4x-24=0

⇒ 4x=24 ⇒ x=6

Ar x=6 the denominator becomes 0 and the function f(x) is not defined.

Hence, x=6 is only the point of discontinuity for the function f(x).

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Answer:

S = 15π = 47.12

length of arc S = 15π

Attached is the image of the arc.

Step-by-step explanation:

Given;

Radius arc r = 10

Angle at the center of arc ⍉ = 3π/2

The length of the arc S can be derived using the formula;

S = r × ⍉

Substituting the values;

S = 10 × 3π/2

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length of arc S = 15π

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