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inna [77]
2 years ago
11

When introduced in 1997, a DVD player sold for about $500. Five years later, the average price was $155. Find and interpret the

average rate of change in price per year.
Mathematics
1 answer:
ziro4ka [17]2 years ago
6 0

Answer:

-69

Step-by-step explanation:

Use rise over run (change in y/change in x)

The change in y is -345, since that is how much the price decreased

The change in x is 5 years

-345/5

= -69

So, the average rate of change in price per year is -69

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3 0
2 years ago
Find dy/dx for y= x^3 ln (cot x)
ICE Princess25 [194]
<h3>Answer</h3>

  \dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)

<h3>Explanation</h3>

By the product rule (d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x), we have

  \begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}

By the chain rule:

  \begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}

By the power rule:

  (x^3)' = 3x^2

thus

  \begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}

Nothing to do to simplify any further, other than factoring out x^2.

4 0
3 years ago
Calculators were purchased at $62 per dozen and sold for $38 for three calculators. Find the profit for selling 5 dozen calculat
dedylja [7]
Each calculator sold for $12.67 . So 5 would be $63.35
8 0
2 years ago
Read 2 more answers
2L plus 2L plus 1.5L plus 2.5L=8L just making shore it is right?
julia-pushkina [17]

Answer: yes you are right hope this helped

plz make brainly

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Solve <br> x=1001+75.55x
gregori [183]

x=1001+75.55x

Simplify

x=<span><span>75.55x</span>+1001</span>

Subtract

x−<span>75.55x</span>=<span><span><span>75.55x</span>+1001</span>−<span>75.55x</span></span>

−<span>74.55x</span>=1001

Divide

<span><span>−<span>74.55x/</span></span><span>−74.55 = </span></span>

<span><span><span><span><span>1001/<span>−74.55</span></span><span><span>your answer is:</span></span><span>x=<span>−<span>13.42723</span></span></span></span></span></span></span>


8 0
3 years ago
Read 2 more answers
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