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il63 [147K]
3 years ago
11

How are mathematics and science related?

Physics
1 answer:
____ [38]3 years ago
6 0
The relationship between math and science is very complicated, yet at the same time very simple. In fact all scientific equations are expressed into some form of mathematical equations. Science is a body of knowledge about the Universe. Mathematics is a language that can describe relationships and change in relationships in a rational way. Science generally uses mathematics as a tool to describe science and vice versa.
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A mechanic needs to replace the motor for a merry-go-round. The merry-go-round should accelerate from rest to 1.5 rad/s in 7.0 s
marta [7]

Answer

given,

initial speed of merry-go-round = 0 rad/s

final speed of merry-go-round = 1.5 rad/s

time = 7 s

Radius of the disk = 6 m

Mass of the merry-go-round = 25000 Kg

Moment of inertia of the disk

I = \dfrac{1}{2}MR^2

I = \dfrac{1}{2}\times 25000\times 6^2

   I = 450000 kg.m²

angular acceleration

\alpha = \dfrac{\omega_f-\omega_0}{t}

\alpha = \dfrac{1.5-0}{7}

\alpha =0.214\ rad/s^2

we know,

\tau= I \alpha

\tau= 450000\times 0.214

\tau=96300\ N.m

8 0
3 years ago
The Cartesian coordinate of a point in the xy plane are (x,y)=(-3.50,-2.50)m. Find the poler coordinate of this point
Masja [62]

Answer:

The polar coordinate of P(x,y) = (-3.50\,m,-2.50\,m) is P (r,\theta) = (4.301\,m, 215.538^{\circ}).

Explanation:

Given a point in rectangular form, that is P(x,y) = (x,y), its polar form is defined by:

P(x,y) = (r,\theta) (1)

Where:

r - Norm, measured in meters.

\theta - Direction, measured in sexagesimal degrees.

The norm of the point is determined by Pythagorean Theorem:

r = \sqrt{x^{2}+y^{2}} (2)

And direction is calculated by following trigonometric relation:

\theta = \tan^{-1} \frac{y}{x} (3)

If we know that x = -3.50\,m and y = -2.50\,m, then the components of coordinates in polar form is:

r = \sqrt{(-3.50\,m)^{2}+(-2.50\,m)^{2}}

r \approx 4.301\,m

Since x < 0\,m and y < 0\,m, direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula:

\theta = 180^{\circ}+\tan^{-1} \left(\frac{-2.50\,m}{-3.50\,m} \right)

\theta \approx 215.538^{\circ}

The polar coordinate of P(x,y) = (-3.50\,m,-2.50\,m) is P (r,\theta) = (4.301\,m, 215.538^{\circ}).

5 0
2 years ago
Please help 40 points!!!!
Nutka1998 [239]

The answers to all the research related questions are written below.

<h3>What is atom?</h3>

Atom is the smallest unit of the element. Different elements have different size atoms and same element have same size atoms.

James Chadwick tracked down the neutron in 1932 and was conceded the Nobel Prize for science in 1935  held in a German prison camp for all of World War 1, he driven the British gathering inside the Manhattan Extend, in which the UK and Canada maintained the USA's World War 2 effort to build the world with nuclear bomb.

Chadwick and Rutherford were the first scientists who measured the nucleus radius using the alpha particles. He did Gold foil experiment to find the size of nucleus.

The contributions are present in the modern atomic model. They are: All matter consists of atoms. Atoms of the same element are the same in size and atoms of different elements are different. Atoms combine in whole-number ratios to form compounds.

Learn more about atoms.

brainly.com/question/1566330

#SPJ1

8 0
2 years ago
____ are solid while lines stretching across one or more lanes in the same direction, indicating the proper place to come to a s
Natalka [10]
Stop lines are solid white lines painted across the traffic lanes at intersections and pedestrian crosswalks, indicating the exact place to stop.
8 0
3 years ago
Are any rocks that form from another rock as a result of change in blank or blank
charle [14.2K]
The correct answer is rock cycle
3 0
3 years ago
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