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vodka [1.7K]
2 years ago
7

Explain why x=-8 is not part of the domain of the function y=log2(x)

Mathematics
1 answer:
Masteriza [31]2 years ago
3 0

Answer:

See Below.

Step-by-step explanation:

By the definition of the logarithm, if we have:

y=\log_{2}x

This means that we have some value <em>y</em> such that:

\displaystyle 2^y=x

If <em>x</em> is -8, then:

2^y=-8

As you can see,<em> </em>there is no real value* that can make the result negative. No matter what the value of <em>y</em> is, we will simply get another positive value.

So, -8 or any other negative value or zero is not included in our domain. 0 is not included because, likewise, we can’t raise 2 to a power and get 0 as a result.

*There is no <em>real</em> value for which 2 raised to <em>y</em> is -8. However, as you will learn much much later, there are in fact <em>infinitely</em> many <em>complex </em>(imaginary) solutions such that 2 raised to <em>y </em>is indeed -8.

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A large rock (mass = 4.0 kg) moving at a velocity of 2.0 m/s has a momentum of _______ kg*m/s
Elodia [21]

Step-by-step explanation:

❁ \underline{ \underline{ \text{Given} }}:

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  • Velocity ( v ) = 2.0 m/s

❁ \underline{ \underline{ \text{ \: To \: find}}}:

  • Momentum ( p )

✑ \underline{ \underline{ \text{Solution}}} :

\boxed{ \underline{ \sf{Momentum \:  =  \: mass \:  \times  \: velocity}}}

plug the known values :

⟹ \sf{Momentum = 4.0 \: kg \:  \times  \: 2.0 \:m/s }

⟹ \sf{Momentum = 8 \: kg \: m/s}

\red{ \boxed{ \boxed{ \tt{⟿ \: Our \: final \: answer :   \bold{ \underline{8} }\: kg*m/s}}}}

⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆

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Imagine that a car and a truck both have the same speed on the road. Which one can stop easily ? Of course , it is hard to stop the truck relative to the car. The reason is that the car and the truck have the same speed bit different masses. Thus , we can say that to stop a heavier body is harder than to stop a lighter one even both of them have the same speed.

If two tennis balls are hit towards you in different velocities , it is not equally easier to stop them. The ball in more velocity is difficult to stop relatively. Thus , we can say that to stop a body in more velocity is harder than to stop a body with less velocity , eventhough they have the same speed.

The physical quantity that describes the quantity of motion of a body is called momentum. The momentum of a moving body or linear momentum is defined as the product of mass & velocity of a moving body.

Mathematically ,

Momentum = mass × velocity

i.e p = m × v

The SI unit of momentum is kg • m/s. Since velocity is a vector quantity and multiplied with mass ( scalar quantity) , momentum becomes a vector quantity. Direction of momentum is the same as velocity.

Hope I helped ! ♡

Have a wonderful day / night ツ

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7 0
2 years ago
( 1 0 3) + (4 1 7) The first entry of the resulting matrix is:
Mamont248 [21]
Hello!

When adding matrices you add the numbers that are in the same position

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7 0
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Answer:

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Step-by-step explanation:

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4

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Answer:

Step-by-step explanation:

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