A student pushes a 51.5 kilogram bookshelf across a smooth floor with a net force of 67 N.

Mathematics

1 answer:

iren [92.7K]3 years ago

7 0

The acceleration of the bookshelf is equal to 1.30 $m/s^2$

<u>Given the following data:</u>

Mass of bookshelf = 51.5 kilogram

Net force = 67 Newton

To determine the acceleration of the bookshelf, we would apply Newton's Second Law of Motion:

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object while being inversely proportional to its mass.

Mathematically, Newton's Second Law of Motion is given by this formula;

$Acceleration = \frac{Net\;force}{Mass}$

Substituting the given parameters into the formula, we have;

$Acceleration = \frac{67}{51.5}$

Acceleration = 1.30 $m/s^2$

Read more on net force here: brainly.com/question/1121817

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What is the value of AAA when we rewrite 2^{x-6}+2^{x}2 x−6 +2 x 2, start superscript, x, minus, 6, end superscript, plus, 2, st

Nuetrik [128]

Answer:

$A=\frac{65}{64}\ or\ A=1.015625$

Step-by-step explanation:

Given:

The expression is given as:

$2^{x-6}+2^{x}$

The equivalent expression to the above expression is given as:

$A\cdot 2^{x}$

Now, simplifying the original expression using the law of indices:

$a^{m-n}=\frac{a^m}{a^n}$

So, $2^{x-6}=\frac{2^x}{2^6}$ . The expression becomes:

$=\frac{2^x}{2^6}+2^x$

Now, $2^x$ is a common factor to both the terms, so we factor it out. This gives,

$=2^x(\dfrac{1}{2^6}+1)\\\\=2^x(\frac{1}{64}+1)\\\\=2^x(\frac{1}{64}+\frac{64}{64})\\\\=2^x(\frac{1+64}{64})\\\\=2^x(\frac{65}{64})\\\\=(\frac{65}{64})\cdot 2^x$