Which of the following are vertical asymptotes of the function y = 3cot(1/2x) - 4?

Answers

Answer 1

Answer: A vertical asymptote is a line that the graph of the function does not cross.
If: $\lim_(x \to a) 3 cot (1/2 x)-4 =$ +/- ∞
then the line x = a is a vertical asymptote.
For x = 0:
f ( 0 ) = 3 * cot 0 - 4 = ∞
For x = +/- 2 π :
f ( 2 π ) = 3 * cot π - 4 = - ∞
Answer:
A ) x = 0 and C ) x = +/- 2π

Answer 2

Answer:

Answer:

x=0 or ±2 nπ where n belongs to natural numbers.

Step-by-step explanation:

The " vertical asymptote " is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptotes of a rational function we set denominator=0.

We are given function y=3 cot((1/2)x)-4

which could also be written as $y=3*(cos((1/2)x))/(sin((1/2)x)) -4\n\ny=(3 cos((1/2)x)-4 sin((1/2)x))/(sin((1/2)x))$

for denominator to be equal to 0 we must have sin((1/2)x)=0

⇒ (1/2)x=0

⇒ x=0 or ±2 nπ where n belongs to natural numbers.

Hence, the vertical asymptotes of the given function is x=0 or ±2 nπ where n belongs to natural numbers.

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The graph below shows the solution to which system of inequalities

Solve for a. You must write your answer in fully simplified form
-14 = 4a

Answers

Answer:

a = -3 1/2

Step-by-step explanation:

To solve the equation for a, divide each side by 4.

-14 = 4a

-14/4 = 4a/4

-14/4 = a

Simplify the fraction by dividing the top and bottom by 2.

-7/2 =a

This is an improper fraction, so change to a mixed number.

2 goes into 7 3 times with 1 left over.

-7/2 = -3 1/2

a = -3 1/2

-14=4a

$(-14)/(4)$ = $(4a)/(4)$

a= $(-7)/(2)$

What is the equation in point-slope form of the line passing through (−2, 0) and (2, 8)?

Answers

To express the equation in a point-slope form, obtain first the slope of the line between the points. The slope, m, of this line is,

(y2 - y1)/(x2 - x1) = (8 - 0)/(2--2) = 2

The point-slope form of the line is generally expressed as

y - y2 = m (x - x2)

Thus, in this given the point-slope form is,

y - 8 = 2 (x - 2)

What is 7d+12-4d-3=? and how do i figure it out ive been stuck for 4 hours on it help?

Answers

We must simplify the expression. Simplify the like terms. 7d-4d=3d and 12-3=9. Put them together. Our answer is 3d+9.

Simplify them like terms 7d-4d=3d and 12-3=9 put them together then the answer is 3d+9

72/100 in simplest form

Answers

the answer is 31/50 (just half both sides)

In fractional simplest form we would begin by dividing both by 2 (always start this way, it's easier).

72/2 = 36
100/2 = 50

Now, we have 36/50 which could also be divided by 2.

36/2 = 18
50/2 = 25

Now, we have 18/25. From here, you would look to see if either number can be simplified using a common factor. With these numbers, nothing could be further simplified, so it would stay this way. :)

Given the function f(x) = x2 and k = –3, which of the following represents a vertical shift? A. f(x) + kB. kf(x)
C. f(x + k)
D. f(kx)