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3 years ago

How can i find the angle between two vectors, given in the format '' i+j ''

Mathematics

1 answer:

vivado [14]3 years ago

5 0

You use the formula below...,

Angle theta = cos^-1 [scalar product of the two vectors ÷ multiplication of their moduli]

For example...the angle between

(2i + 3j) and (4i + 5j)

Angle theta = cos^-1 [( 2(4) + 3(5))÷((square root of (2^2 + 3^2))×(square root of (4^2 + 5^2))

Angle theta = cos^-1 [ 23 ÷ ((square root of(13)) × (square root of (41)]

Angle theta = 5°

You might be interested in

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

Alekssandra [29.7K]

Using the z-distribution and the formula for the margin of error, it is found that:

a) A sample size of 54 is needed.

b) A sample size of 752 is needed.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

90% confidence level, hence $\alpha = 0.9$ , z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$ , so $z = 1.645$ .

Item a:

The estimate is $\pi = 0.213 - 0.195 = 0.018$ .

The sample size is n for which M = 0.03, hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}$

$\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2$

$n = 53.1$

Rounding up, a sample size of 54 is needed.

Item b:

No prior estimate, hence $\pi = 0.05$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2$

$n = 751.7$

Rounding up, a sample of 752 should be taken.

A similar problem is given at brainly.com/question/25694087

5 0

2 years ago

Which of the following measures cannot be determined from a box plot?

ad-work [718]

<h3>3 Answers:</h3>

B) Mean
C) Mean absolute deviation
E) Mode

==========================================================

Explanation:

The box plot, aka "box-and-whisker plot", visually represents five things. These things are:

Minimum
Q1 = first quartile
Median (sometimes referred to as Q2 or second quartile)
Q3 = third quartile
Maximum

This list of five items is known as the five number summary.

The min is the tip of the left most whisker, assuming there aren't any small outliers. The max is the opposite side, being the tip of the right most whisker (assuming no large outliers). If there are any outliers, then they'll be shown as "island" dots on their own separated from the main box plot. The left and right edges of the box are Q1 and Q3 respectively. The median is the vertical line inside the box. The vertical line does not have to be at the midpoint of the left and right edges of the box. It simply needs to be somewhere in the box.

--------

Since the box plot lets us know the min and max, we can compute the range because

range = max - min

and we can also calculate the interquartile range (IQR) because

IQR = Q3 - Q1

--------

So to summarize so far, the five number summary is visually represented as the box plot. The range and IQR can be computed using items from the five number summary.

We cannot compute the mean because we would need the actual data set of values, rather than the summary data. The same goes for the mean absolute deviation (MAD) and the mode. Since your teacher is looking for things that cannot be determined from a box plot, we'll go for answers B, C and E.

In other words, we rule out choices A, D, and F because we can compute or determine those values from a box plot.

7 0

2 years ago

Given the system of inequalities:

Margaret [11]

Answer:
First inequality: y > $\frac{4}{5} x - \frac{1}{5}$
Second inequality: y < 3 + x

Explanation:
The inequality in slope-intercept form has the following general formula:
y < mx + c or y > mx + c (according to the given sign)
where m is the slope and c is the y-intercept

This means that to get any inequality in slope-intercept form, we will have to isolate the y on one side of the inequality.

First given inequality:
4x - 5y < 1
4x - 5y + 5y < 1 + 5y
1 + 5y > 4x
1 + 5y - 1 > 4x - 1
5y > 4x - 1
y > $\frac{4}{5} x - \frac{1}{5}$
comparing this to the general form, we would find that:
slope (m) = 4/5
y-intercept (c) = 1/5

Second given inequality:
y - x < 3
y - x + x < 3 + x
y < 3 + x
comparing this to the general form, we would find that:
slope (m) = 1
y-intercept (c) = 3

Hope this helps :)

8 0

3 years ago

Read 2 more answers

PLEASE HELP (unknown answers will be deleted)

Shtirlitz [24]

Answer:

where's the assignment

8 0

3 years ago

HELP PLZ!!! LOTS OF POINTS

Darya [45]

I'm going to assume that the ' 7.51 ' is the angle expressed in radians.
So this is just like any other unit conversion exercise.

You know that 180 degrees = pi radians.

Divide each side by pi radians, and you have

180 degrees / pi radians = 1 .

Great ! Now take the angle you have ... 7.51 radians ...
and multiply it by ' 1 '.

(7.51 radians) x (180 degrees / pi radians) =

  (7.51 x 180 / pi) degrees = 430.29 degrees

As you ( I ) worked through this problem, a very useful number
fell out . . . It's 180/pi = 57.296 , or just 57.3 is close enough.

Here's how you can use that number:

-- 1 radian = 57.3 degrees

-- 1 degree = 1/57.3 of a radian

-- Got some radians ? Multiply by 57.3 to get degrees.

-- Got some degrees ? Divide by 57.3 to get radians.

7 0

3 years ago