Expand & simplify 5 ( p + 5 ) + 6 ( p + 6 )

Mathematics

2 answers:

Elis [28]2 years ago

8 0

$5(p+5)+6(p+6)\\\\=5p+25+6p+36\\\\=11p+61$

Aloiza [94]2 years ago

4 0

5(p+5) + 6(p+6)

First step: Distribute (PEMDAS --> Parenthesis)

5p + 25 + 6p + 36 Now, combine like terms

11p + 61

Thus, the answer is 11p + 61

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Step-by-step explanation:

Given that "The force F between two charges $Q_1$ and $Q_2$ in a vacuum is proportional to the product of the charges and is inversely proportional to the square of the distance between two charges"

<h3>The given statement is a Coulomb's law.</h3>

Coulomb's law states that the magnitude of the electrostatic force F of attraction or repulsion between the two point charges $Q_1$ and $Q_2$ is directly proportional to the product of the magnitudes of charges $Q_1$ and $Q_2$ and it is inversely proportional to the square of the distance between the two charges.

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Step-by-step explanation

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Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)