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hram777 [196]
3 years ago
7

Help me on this question? log x-log 9=1

Physics
2 answers:
DanielleElmas [232]3 years ago
6 0
\log { x } -\log { 9 } =1\\ \\ \log { \left( \frac { x }{ 9 }  \right)  } =1\\ \\ \log _{ 10 }{ \left( \frac { x }{ 9 }  \right)  } =1\\ \\ { 10 }^{ 1 }=\frac { x }{ 9 } \\ \\ 9\cdot 10=x\\ \\ x=90

This is because:

\log _{ a }{ \left( \frac { x }{ p }  \right)  } \\ \\ =\log _{ a }{ \left( \frac { { a }^{ m } }{ { a }^{ n } }  \right)  } \\ \\ =\log _{ a }{ \left( { a }^{ \left( m-n \right)  } \right)  } \\ \\ =\left( m-n \right) \cdot \log _{ a }{ a } \\ \\ =m-n\\ \\ =\log _{ a }{ x } -\log _{ a }{ p } \\
Alika [10]3 years ago
4 0

   log(x) - log(9) = 1

Subtracting the logs of numbers gives you the log of
the quotient of the numbers.

     Log(x) - log(9)  is the log of  (x/9).

So the equation says:    log (x/9) = 1

Raise 10 to the power of each side:  10^(log of x/9) = 10^1

But  10^(log of x/9) is x/9, and 10^1 is 10.

So        x/9 = 10

             x  =  90

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According to Newton’s law of universal gravitation, which statements are true?
andreyandreev [35.5K]

Before we solve this, we should know this fact:

According to Newton's Law of Gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the centres of the two objects. It can be shown by this:

F ∝ \frac{Mm}{ {d}^{2} }

Now, let us check all the options.

A. As we move to higher altitudes, the force of gravity on us decreases.

<em>This </em><em>statement </em><em>is </em><em>true.</em>

The force of gravity is inversely proportional to the square of distance from the centre of the earth. If, we go up the surface of the earth, the distance from the centre of the earth increases and hence the value of force of gravity decrease. So, force of gravity decreases with altitude.

B. As we move to higher altitudes, the force of gravity on us increases.

<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>

We have already got the result in option A. that the force of gravity decreases with altitude. It never increases with altitude.

C. As we gain mass, the force of gravity on us decreases.

<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>

The force of gravity is directly proportional to the product of the masses. So, if increase our mass, then the force of gravity will also increase and if we decrease our mass, then the force of gravity decreases.

D. As we gain mass, the force of gravity on us increases.

<em>This </em><em>statement</em><em> is</em><em> </em><em>true.</em>

As mentioned earlier in option C., the force of gravity is directly proportional to the product of the masses of the earth and another object. So, as we gain mass, the force of gravity on us increases.

E. As we move faster, the force of gravity on us increases.

<em>This </em><em>statement</em><em> is</em><em> </em><em>true</em><em>.</em>

Here, we have to consider a different formula. According to Newton's Second Law,

F = ma, where F is the force, m is the mass and a is the acceleration.

In other words,

F ∝ a, i.e., force is directly proportional to acceleration.

We know, acceleration is the rate of change of velocity of an body within a time period.

So, if speed is increased, then acceleration will also be greater, which results in the increase of force. So, as we move faster, the force of gravity on us increases.

<u>Answers:</u>

A: As we move to higher altitudes, the force of gravity on us decreases.

D: As we gain mass, the force of gravity on us increases.

E: As we move faster, the force of gravity on us increases.

Hope you could understand.

If you have any query, feel free to ask.

7 0
2 years ago
How can a soccer ball and a small tennis ball bouncing relates to newtons first law interita?
Anna35 [415]

Answer:

I think it has something to do with both inertia and gravity?

7 0
3 years ago
Technician A says that the freezing point of a substance is the temperature at which the substance changes state from a solid to
pashok25 [27]

Answer:

Technician B is correct

Explanation:

Freezing is a method of conversion of substance in its liquid state to solid state. It is the process by which a liquid substance changes to a solid at a particular temperature.

Increasing the pressure and decreasing the temperature of a liquid increases its freezing point. For example, in other to freeze water i.e to change water to ice, it has to be kept in a fridge at a temperature lower than the temperature of the water. The essence of covering the fridge after placing the water in the fridge is to increase the pressure of the liquid hence increasing its freezing rate.

Based on the above explanation, it can be concluded that technician B is correct.

5 0
3 years ago
In the bohr model, what is the ratio of its kinetic energy to its potential energy?
stich3 [128]

The centrifugal force C = mv^2/r = kq^2/r^2 = P centripetal force. m is the electron mass, q are the proton and electron charges (opposites), and r is the Bohr radius.

Thus 1/2 mv^2/r = 1/2 kq^2/r^2 and KE = 1/2 mv^2 = 1/2 kq^2/r = 1/2 PE

Therefore KE/PE = 1/2, no matter what state the electron is in.

8 0
3 years ago
The objects listed are placed at the top of a ramp and roll down to the bottom without slipping. Assuming that there is no air r
Thepotemich [5.8K]

Explanation:

For each object, the initial potential energy is converted to rotational energy and translational energy:

PE = RE + KE

mgh = ½ Iω² + ½ mv²

For the marble (a solid sphere), I = ⅖ mr².

For the basketball (a hollow sphere), I = ⅔ mr².

For the manhole cover (a solid cylinder), I = ½ mr².

For the wedding ring (a hollow cylinder), I = mr².

If we say k is the coefficient in each case:

mgh = ½ (kmr²) ω² + ½ mv²

For rolling without slipping, ωr = v:

mgh = ½ kmv² + ½ mv²

gh = ½ kv² + ½ v²

2gh = (k + 1) v²

v² = 2gh / (k + 1)

The smaller the value of k, the higher the velocity.  Therefore:

marble > manhole cover > basketball > wedding ring

7 0
3 years ago
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