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3 years ago

Find the magnitude of vector A = i - 2j + 3k O V14 10 O4

Physics

1 answer:

Angelina_Jolie [31]3 years ago

6 0

Answer:

$|A|=\sqrt{1^2+(-2)^2+(3)^2}=3.74$

Explanation:

Given that,

Vector $A=i-2j+3k$ ............(1)

We need to find the magnitude of vector A. Let us suppose vector in the form of, R = xi + yj + zk. Its magnitude is given by :

$|R|=\sqrt{x^2+y^2+z^2}$

In equation (1),

x = 1

y = -2

z = 3

So, the magnitude of vector A is given by :

$|A|=\sqrt{1^2+(-2)^2+(3)^2}$

|A| = 3.74

So, the magnitude of given vector is 3.74. Hence, this is the required solution.

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Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sampl

ollegr [7]

<h2>Answer:</h2>

(a) standard deviation = σ = 4.9996

(b) variance = σ² = 24.996

<h2>Explanation:</h2><h2 />

<em>Given frequency table (find attached as Table 1);</em>

<u></u>

(a) To find the sample standard deviation and sample variance, follow these steps;

<em>i. Calculate the mid-point c for each group by using the mid-point formula;</em>

c = (lower bound + upper bound) / 2

=> c = (6.51 + 8.50) / 2 = 7.505

=> c = (8.51 + 10.50) / 2 = 9.505

=> c = (10.51 + 12.50) / 2 = 11.505

=> c = (12.51 + 14.50) / 2 = 13.505

=> c = (14.51 + 16.50) / 2 = 15.505

<em>So the new table becomes (find attached as Table 2);</em>

<em>ii. Calculate the total number of samples (n) which is the sum of all the frequencies.</em>

n = 50+18+42+20+46

n = 176

<em>iii. Calculate the mean (M)</em>

This is done by first multiplying the midpoints by the corresponding frequencies and then dividing the result by the total number of samples (n).

M = [(7.505 x 50) + (9.505 x 18) + (11.505 x 42) + (13.505 x 20) + (15.505 x 46)] / 176

M = [375.25 + 171.09 + 483.21 + 270.1 + 713.23] / 176

M = [2012.88] / 176

M = 11.44

<em>iv. Find the variance (σ²);</em>

The variance is calculated using the following formula

σ² = [Σ(f x c²) - (n x M²)] / (n - 1) ------------(i)

Where;

f = frequency of each boundary data point

<em>=> Let's first calculate </em>Σ(f x c²).

This is done by finding the sum of the product of the frequency (f) of each boundary point and the square of their corresponding mid-points(c)

Σ(f x c²) = [(50 x 7.505²) + (18 x 9.505²) + (42 x 11.505²) + (20 x 13.505²) + (46 x 15.505²)]

Σ(f x c²) = [(2816.25125) + (1626.21045) + (5559.33105) + (3647.7005) + (11058.63115)]

Σ(f x c²) = 24708.1244

<em>=> Now calculate (n x M²)</em>

n x M² = 176 x 11.44²

n x M² = 23033.7536

<em>=> Now substitute these values into equation (i) to calculate the variance</em>

σ² = [Σ(f x c²) - (n x M²)] / (n - 1)

σ² = [24708.1244 - 23033.7536] / (176 - 1)

σ² = [4374.3708] / (175)

σ² = 24.996

Therefore, the variance is 24.996

<em>v. Find the standard deviation (σ)</em>

The standard deviation is the square root of the variance. i.e

σ = √σ²

σ = √24.996

σ = 4.9996

Therefore, the standard deviation is 4.9996

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3 years ago

Identify the law, write the equation and calculate the answer to the problem below.

lyudmila [28]

Find refractive index first

$\\ \rm\Rrightarrow \mu=\dfrac{c}{v}$

$\\ \rm\Rrightarrow \mu=\dfrac{1.0003}{1.33}$

$\\ \rm\Rrightarrow \mu =0.75$

Now

$\\ \rm\Rrightarrow \dfrac{sini}{sinr}=\mu$

$\\ \rm\Rrightarrow \dfrac{sin45}{sinr}=0.75$

$\\ \rm\Rrightarrow \dfrac{sin45}{0.75}=sinr$

$\\ \rm\Rrightarrow sinr=0.94$

$\\ \rm\Rrightarrow r=sin^{-1}(0.94)$

$\\ \rm\Rrightarrow r=70^{\circ}$

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2 years ago

How are vibration waves and energy related to sounds

Lesechka [4]

In electromagnetic waves, energy is transferred through vibrations of electric and magnetic fields. ... In sound waves, energy is transferred through vibration of air particles or particles of a solid through which the sound travels.

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3 years ago

Read 2 more answers

An automobile with a standard differential turns sharply to the left. The left driving wheel turns on a 20-m radius. Distance be

Inessa05 [86]

Explanation:

The given data is as follows.

Inner wheel Radius = 20 m,

Distance between left and right wheel = 1.5m,

Let us assume speed of drive shaft is N rpm.

Formula to calculate angular velocity is as follows.

Angular velocity of automobile = w = $\frac{V}{R}$

where, V = linear velocity of automobile m/min,

R = turning radius from automobile center in meter

In the given case, angular velocity remains same for inner and outer wheel but there is change in linear velocity of inner wheel and outer wheel.

Now, we assume that

u = linear velocity of inner wheel

and, u' = linear velocity of outer wheel.

Formula for angular velocity of inner wheel w = ,

Formula for angular velocity of outer wheel w =

Now, for inner wheels

w =

= $\frac{u}{(R - d)}$

u = $V \times \frac{(R - d)}{R}$

= $V \times (1 - \frac{d}{R})$

If radius of wheel is r it will cover distance in one min.

Since, velocity of wheel is u it will cover distance u in unit time(min)

Thus, u = $2\pi rn$ = $V \times (1 - \frac{d}{R})$

Now, rotation per minute of inner wheel is calculated as follows.

n = $\frac{V}{2 \pi r \times (1 - \frac{d}{R})}$

= $\frac{V}{2 \pi r \times (1 - \frac{0.75}{20})}$ (since 2d = 1.5m given, d = 0.75m),

= $\frac{V}{r} \times 0.1532$

So, rotation per minute of outer wheel; n' =

= $\frac{V}{2 \pi r \times (1 + \frac{0.75}{20})}$

= $\frac{V}{r} \times 0.1651$

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4 years ago

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Ganezh [65]

Answer:

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