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4 years ago

How do I prove that 2 cot 2x = cot x-tan x?

1 answer:

7 0

We will start off working on the right hand side.
cot x - tan x 
= [cos x / sin x] - [sin x / cos x] 
= [(cos x)^ 2 - (sin x)^2] / [sin x cos x] 

This is where it gets a bit tougher if you do not have your formula list with you. 
(cos x)^ 2 - (sin x)^2 = cos(2x) 
sin 2x = 2 sin x cos x 

Note that by arranging the second formula, we will have sin x cos x = (1/2) sin 2x 

Hence, we will get: 
[(cos x)^ 2 - (sin x)^2] / [sin x cos x] 
= [cos 2x] / (1/2)[sin 2x] 
= 2[cos 2x] / [sin 2x] 
= 2cot 2x

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Which characteristic of a data set makes a linear regression model unreasonable?

LiRa [457]

Which characteristic of a data set makes a linear regression model unreasonable?

Answer: A correlation coefficient close to zero makes a linear regression model unreasonable.

If the correlation between the two variable is close to zero, we can not expect one variable explaining the variation in other variable. For a linear regression model to be reasonable, the most important check is to see whether the two variables are correlated. If there is correlation between the two variable, we can think of regression analysis and if there is no correlation between the two variable, it does not make sense to apply regression analysis.

Therefore, if the correlation coefficient is close to zero, the linear regression model would be unreasonable.

6 0

4 years ago

Read 2 more answers

1. Divide 6x^4 + 2x^3 – 6x^2 – 14x – 1 by 3x + 1 by using synthetic division or long division. Show all

iris [78.8K]

      2x^3 - 2x - 4

3x + 1 6x^4 + 2x^3 - 6x^2 - 14x - 1
      6x^4 + 2x^3

       -6x^2 - 14x - 1
   -6x^2 - 2x

   -12x - 1
   -12x - 4

   3

3x + 1 is not a factor of the dividend because, dividing the dividend with 3x + 1 gives a remainder.

5 0

4 years ago

Consider the probability that greater than 77 out of 131 computers will crash in a day. Assume the probability that a given comp

sweet-ann [11.9K]

Answer:

A Normal approximation to binomial cannot be applied to approximate the distribution of X, the number of computer crashes in a day.

Step-by-step explanation:

Let X = number of computers that will crash in a day.

The probability of a computer crashing in a day is, p = 0.99.

A random sample of n = 131 is selected.

A random computer crashing in a day is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 131 and p = 0.99.

But the sample size is quite large, i.e. n > 30.

So the distribution of X can be approximated by the normal distribution if the following conditions are fulfilled:

np ≥ 10
n(1 - p) ≥ 10

Check whether the conditions satisfy or not:

$np=131\times 0.99=129.69>10\\n(1-p)=131\times (1-0.99)=1.31$

The second condition is not fulfilled.

A Normal approximation to binomial cannot be applied to approximate the distribution of X, the number of computer crashes in a day.

6 0

3 years ago

Substitute (2, 1) into x + 3y = 5 to get ✔ 2 + 3(1) = 5 . Simplify the equation to get . Substitute (2, 1) into y = –x + 3 to ge

nikdorinn [45]

Answer:

See explanation

Step-by-step explanation:

x + 3y = 5

(x, y) = (2,1)

x + 3y = 5

2 + 3(1) = 5

2 + 3 = 5

5 = 5

The equation is true

y = –x + 3

(x, y) = (2, 1)

y = –x + 3

1 = -2 + 3

1 = 1

The equation is true

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3 years ago

Write an expression for the sequence of operations described below.

pickupchik [31]

Answer:

Step-by-step explanation:

Its 7+8+5

5 0

3 years ago