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Sloan [31]
3 years ago
10

Which of the following are vertical asymptotes of the function y = 2cot(3x) + 4? Check all that apply. A.x = pi/3 B.x = +/- pi/2

C.x = 2pi D.x = 0
Mathematics
2 answers:
Kisachek [45]3 years ago
6 0
Vertical asymptotes occur when the denominator of a rational is 0, whilst not zeroing out the numerator, making the rational, undefined, in this case

\bf y=2cot(3x)+4\implies y=2\cdot \cfrac{cos(3x)}{sin(3x)}+4\impliedby \textit{if \underline{sin(3x)} turns to 0}\\\\
-------------------------------\\\\
\textit{let's check}
\\\\\\
A)\qquad \cfrac{cos(3x)}{sin\left( 3\frac{\pi }{3} \right)}\implies \cfrac{cos(3x)}{sin\left( \pi \right)}\implies \cfrac{cos(3x)}{0}\impliedby unde f ined

\bf B)\qquad \cfrac{cos(3x)}{sin\left( 3\frac{\pm\pi }{2} \right)}\implies\cfrac{cos(3x)}{sin\left( \frac{\pm3\pi }{2} \right)}\implies \cfrac{cos(3x)}{\pm 1}\implies \pm cos(3x)
\\\\\\
C)\qquad \cfrac{cos(3x)}{sin\left( 3(2\pi )\right)}\implies \cfrac{cos(3x)}{sin(6\pi )}\implies \cfrac{cos(3x)}{0}\impliedby unde f ined
\\\\\\
D)\qquad \cfrac{cos(3x)}{sin(3(0))}\implies \cfrac{cos(3x)}{sin(0)}\implies \cfrac{cos(3x)}{0}\impliedby unde f ined
jenyasd209 [6]3 years ago
3 0
Yeah it’s A C D for apex
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University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some studen
ira [324]

Answer:

A. 0.1

B. 0.8

C. 0.5

Step-by-step explanation:

Given:

P(Science) = 0.3

P(Arts) = 0.6

P(none) = 0.2

From the above, it is understood that the events are independently events; meaning that the probability that a students gets a Bachelor of Science degree does not affect the probability of the same student getting a Bachelor of Arts degree.

A. The probability that a student gets a Bachelor of Science and Bachelor of Arts degree

Let P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degree

For independent events,

P(A) + P(B) - P(A and B) + P(none)= 1

If we translate the above formula to suit our needs, we have something like this

P(Science) + P(Arts) - P(Arts and Science) + P(none) = 1

Or

P(Arts) + P(Science) - P(Arts and Science) + P(none) = 1

From this, we have

0.3 + 0.6 - P(Arts and Science) + 0.2 = 1

1.1 - P(Arts and Science) = 1

-P(Arts and Science) = 1 - 1.1

-P(Arts and Science) = -0.1

P(Arts and Science) = 0.1

B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degree

For independent events

P(A or B) = P(A) + P(B) - P(A and B)

So, P(Arts or Science) = P(Arts) + P(Science) - P(Arts and Science)

P(Arts or Science) = 0.3 + 0.6 - 0.1

P(Arts or Science) = 0.8

C. The probability that a student gets only Bachelor of Arts

P(A only) = P(A) - P(A and B)

P(Arts) = P(Arts) - P(Arts and Science)

P(Arts) = 0.6 - 0.1

P(Arts) = 0.5

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