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Fed [463]
3 years ago
14

For what values of θ, −π ≤ θ ≤ π, is y = tan θ undefined?

Mathematics
1 answer:
pogonyaev3 years ago
3 0

Answer:

The answer is II and IV ⇒ the 3rd answer

Step-by-step explanation:

* lets check the domain of angle Ф

∵ -π ≤ Ф ≤ π

∵ y = tanФ

∵ tanФ = sinФ/cosФ

* The effective term which makes tanФ undefined is cosФ

- If cosФ = 0, than tanФ will be undefined

* Lets check the angles that have cosФ = 0

∵ The unit circle intersect x-axis at point (1 , 0) and (-1 , 0)

∵ The unit circle intersect y-axis at point (0 , 1) and (0 , -1)

∵ cosФ = x-coordinates of the points

∵ The points of intersection with the y-axis have x- coordinates = 0

∴ The angles on the y-axis have cosФ = 0

* The angles on the +ve part of y-axis are π/2 and -3π/2

 The angles on the -ve part of y-axis are -π/2 and 3π/2

∴ The tan of π/2 , 3π/2 , -π/2 , -3π/2 undefined

* In the problem

I. -π ⇒ defined ⇒ on the -ve part of x-axis

II. -π/2 ⇒undefined

III. 0 ⇒ defined ⇒ on the +ve part of the x-axis

IV. π/2 ⇒ undefined

V. π ⇒ defined ⇒ on the -ve part of x-axis

∴ The answer is II and IV ⇒ the 3rd answer

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The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b
masha68 [24]

Answer:

The fraction is \frac{4}{6}

Option (B) is correct.

3n-2d=0  and 4n+8=3d+6

Step-by-step explanation:

Let n denotes numerator and d denotes denominator of the fraction.

Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.

That is \frac{n}{d}=\frac{2}{3}

Cross multiply , we get,

3n=2d

Or, 3n-2d=0   ........(1)

Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4

That is \frac{n+2}{d+2}=\frac{3}{4}

Cross multiply , We get,

4{n+2}={3}{d+2}

4n+8=3d+6  .........(2)

3d-4n=2  .......(3)

Thus, from (1) and (2) , option (B) follows.

Solving equation (1) and (3) to get the original fraction using elimination method,

3n - 2d = 0    ............(1)

and 3d - 4n = 2       .........(3)

Multiply equation (1) by 3 , we get ,

9n - 6d = 0  ..........(4)

Multiply equation (3) by 2 , we get ,

-8n + 6d = 4 ..........(5)

Adding (4) and  (5) , we get,

9n - 6d -8n + 6d = 4 + 0

⇒ n = 4

Put n = 4 in (1), we get

3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0  ⇒  12 = 2d ⇒ d = 6

so, the numerator is 4 and  the denominator is 6.

Thus, the fraction is \frac{4}{6}


6 0
3 years ago
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.2 years, with a standard devia
elena-14-01-66 [18.8K]

Answer:

a. z-score = -1.2

b. The age 23 years old is -1.2 standard deviations below the mean

c. The age is not unusual

Step-by-step explanation:

a. Transformation to z-score

Mathematically;

z-score = (x - μ)/σ

where σ and μ are the standard deviation and the mean respectively.

From the question, x = 23, μ = 27.2 and σ = 3.5

Let’s put these into the equation;

z-score = (23-27.2)/3.5 = -1.2

b. Interpretation of result

The interpretation is that 23 years old is -1.2 standard deviations below the mean

c. Determination

The age is not unusual. This is because any z-value below -2 or above 2 is considered unusual

-1.2 is above -2 and thus it is not unusual

7 0
2 years ago
How do I solve #7? do i add all the angles together like a normal triangle and make it equal to 180?
kobusy [5.1K]

Answer:

126 degrees

Step-by-step explanation:

Triangle: y = 180 - (5x + 4x)

Straight angle: y = 180 - (4x + 30)

180 - (5x + 4x) = 180 - (4x + 30)

5x + 4x = 4x + 30

5x = 30

x = 6

Angle:

y = 180 - (5x + 4x)

y = 180 - 9x

y = 180 - 9(6)

y =  126

7 0
2 years ago
8 identical pens cost £12 work out the cost of 10 of these pens
katen-ka-za [31]

Ok. So, if 8 pens cost £12. Then we would divide £12 by 8. Each pen costs £1.5.

So now we are going to multiply £1.5 and 10. £1.5*10=15.

The total of 10 pens is £15.

I hope this helps, if you need any additional help, just ask. I am here to help you as needed.

3 0
3 years ago
What is the equation of this line in standard form?
bazaltina [42]

Answer:

Step-by-step explanation: 11x-6y=13

7 0
2 years ago
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