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2 years ago

Visualise the representation of 5.37(Bar over 7). Using number line.

Mathematics

1 answer:

lana66690 [7]2 years ago

5 0

$\: \: \:$

$\pink{ 5.37}$

To visualize 5.37 more accurately, divide line segment between 5.37 and 5.38 in ten equal parts. 5.37 lies between 5.377 and 5.378.

Again use divide above portion between 5.377 and 5.378 into 10 equal parts, which shows 5.37 is located closer to 5.3778 than to 5.3777 so we can get the answer

<h2>hope it helps</h2>

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8-5x =2x + 20 Simplify I’ll give brainliest

kobusy [5.1K]

Answer:

X= - 12/7 i hope it is helpful have a nice day if you want steps i will show you

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3 years ago

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The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an a

satela [25.4K]

Answer:

7 feet is the length of the blade of the windmill.

Step-by-step explanation:

We have the equation

h = 7 sin(pi/21t) + 28 ------ eq1

At time 't' = 0, the end of the blade is pointing to the right parallel to the ground meaning it is at the same height as the other end. (Ф = 0°)

So, by calculating the maximum height of this end at Ф = 90°. we can calculate the length of the blade.

Now, we know that a general model equation of a circular simple harmonic motion is represented as : y = A sinωt + k ----- eq2

Where A is the amplitude that is, maximum displacement from mean to maximum position.

ω is the angular frequency.

Comparing eq1 and eq2:

A = 7

so the difference in blades end height at Ф = 0° and Ф = 90° is 7 feet.

Hence, the length of the blade is 7 feet.

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3 years ago

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Ans: 720cm

UkoKoshka [18]

Answer:

663

Step-by-step explanation:

the total number of students can be determined using this equation :

(total ratio of Chinese and Indian students / total ratio of students) x n = 468

total ratio of Chinese and Indian students = 4 + 8 = 12

total ratio of students 4 + 8 + 5 = 17

N = TOTAL NUMBER OF STUDENTS

12/17) x n = 468

multiply both sides of the equation by 17/12

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3 years ago

Particle P moves along the y-axis so that its position at time t is given by y(t)=4t−23 for all times t. A second particle, part

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a) The limit of the position of particle $Q$ when time approaches 2 is $-\pi$ .

b) The velocity of particle $Q$ is $v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}$ for all $t \ne 2$ .

c) The rate of change of the distance between particle $P$ and particle $Q$ at time $t = \frac{1}{2}$ is $\frac{4\sqrt{82}}{9}$ .

<h3>How to apply limits and derivatives to the study of particle motion</h3>

a) To determine the limit for $t = 2$ , we need to apply the following two algebraic substitutions:

$u = \pi t$ (1)

$k = 2\pi - u$ (2)

Then, the limit is written as follows:

$x(t) = \lim_{t \to 2} \frac{\sin \pi t}{2-t}$

$x(t) = \lim_{t \to 2} \frac{\pi\cdot \sin \pi t}{2\pi - \pi t}$

$x(u) = \lim_{u \to 2\pi} \frac{\pi\cdot \sin u}{2\pi - u}$

$x(k) = \lim_{k \to 0} \frac{\pi\cdot \sin (2\pi-k)}{k}$

$x(k) = -\pi\cdot \lim_{k \to 0} \frac{\sin k}{k}$

$x(k) = -\pi$

The limit of the position of particle $Q$ when time approaches 2 is $-\pi$ . $\blacksquare$

b) The function velocity of particle $Q$ is determined by the derivative formula for the division between two functions, that is:

$v_{Q}(t) = \frac{f'(t)\cdot g(t)-f(t)\cdot g'(t)}{g(t)^{2}}$ (3)

Where:

$f(t)$ - Function numerator.
$g(t)$ - Function denominator.
$f'(t)$ - First derivative of the function numerator.
$g'(x)$ - First derivative of the function denominator.

If we know that $f(t) = \sin \pi t$ , $g(t) = 2 - t$ , $f'(t) = \pi \cdot \cos \pi t$ and $g'(x) = -1$ , then the function velocity of the particle is:

$v_{Q}(t) = \frac{\pi \cdot \cos \pi t \cdot (2-t)-\sin \pi t}{(2-t)^{2}}$

$v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}$

The velocity of particle $Q$ is $v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t -\sin \pi t}{(2-t)^{2}}$ for all $t \ne 2$ . $\blacksquare$

c) The vector rate of change of the distance between particle P and particle Q ( $\dot r_{Q/P} (t)$ ) is equal to the vectorial difference between respective vectors velocity:

$\dot r_{Q/P}(t) = \vec v_{Q}(t) - \vec v_{P}(t)$ (4)

Where $\vec v_{P}(t)$ is the vector velocity of particle P.

If we know that $\vec v_{P}(t) = (0, 4)$ , $\vec v_{Q}(t) = \left(\frac{2\pi\cdot \cos \pi t - \pi\cdot t \cdot \cos \pi t + \sin \pi t}{(2-t)^{2}}, 0 \right)$ and $t = \frac{1}{2}$ , then the vector rate of change of the distance between the two particles:

$\dot r_{P/Q}(t) = \left(\frac{2\pi \cdot \cos \pi t - \pi\cdot t \cdot \cos \pi t + \sin \pi t}{(2-t)^{2}}, -4 \right)$

$\dot r_{Q/P}\left(\frac{1}{2} \right) = \left(\frac{2\pi\cdot \cos \frac{\pi}{2}-\frac{\pi}{2}\cdot \cos \frac{\pi}{2} +\sin \frac{\pi}{2}}{\frac{3}{2} ^{2}}, -4 \right)$

$\dot r_{Q/P} \left(\frac{1}{2} \right) = \left(\frac{4}{9}, -4 \right)$

The magnitude of the vector rate of change is determined by Pythagorean theorem:

$|\dot r_{Q/P}| = \sqrt{\left(\frac{4}{9} \right)^{2}+(-4)^{2}}$

$|\dot r_{Q/P}| = \frac{4\sqrt{82}}{9}$

The rate of change of the distance between particle $P$ and particle $Q$ at time $t = \frac{1}{2}$ is $\frac{4\sqrt{82}}{9}$ . $\blacksquare$

<h3>Remark</h3>

The statement is incomplete and poorly formatted. Correct form is shown below:

Particle $P$ moves along the y-axis so that its position at time $t$ is given by $y(t) = 4\cdot t - 23$ for all times $t$ . A second particle, $Q$ , moves along the x-axis so that its position at time $t$ is given by $x(t) = \frac{\sin \pi t}{2-t}$ for all times $t \ne 2$ .

a) As times approaches 2, what is the limit of the position of particle $Q?$ Show the work that leads to your answer.

b) Show that the velocity of particle $Q$ is given by $v_{Q}(t) = \frac{2\pi\cdot \cos \pi t-\pi\cdot t \cdot \cos \pi t +\sin \pi t}{(2-t)^{2}}$ .

c) Find the rate of change of the distance between particle $P$ and particle $Q$ at time $t = \frac{1}{2}$ . Show the work that leads to your answer.

To learn more on derivatives, we kindly invite to check this verified question: brainly.com/question/2788760

3 0

2 years ago

Mr. Bennett owns 4 restaurants. The mean number of tables is 30. Which number line shows what could happen to the mean if he buy

expeople1 [14]

Number of tables al four restaurants have;
= 4 * 30
=120 tables
Two new restaurants + 4
=6 restaurants
(120+15+9)= 144 tables
Mean = total # of tables/ total # of restaurants;
144/6
=24
This is the mean so it decreases. I hope this helps even though you didn’t actually post the number line

7 0

4 years ago

Read 2 more answers

Visualise the representation of 5.37(Bar over 7). Using number line.​

Visualise the representation of 5.37(Bar over 7). Using number line.