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3 years ago

Martha purchased a car for $17,500. The value of a car decreases by 7% each year.

Mathematics

1 answer:

marishachu [46]3 years ago

6 0

Answer:

9 years = .000000706$

Step-by-step explanation:

convert 7% to decimal 0 .07

17,500 x .07 = 1,225

1 year 1,225

2 year 85.75

3 year 6.0

4 year .42

5 year .029

6 year .002

7 year .000144

8 year .000010088

9 years = .000000706$

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By Linear Algebra, we can calculate the angle by definition of dot product:

$\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}$ (1)

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$\theta$ - Angle between vectors, in sexagesimal degrees.

$\|\vec a\|, \|\vec b \|$ - Norms of vectors $\vec {a}$ and $\vec{b}$

If $\theta$ is acute, then the cosine function is bounded between 0 a 1 and if we know that $\vec {a} = (p, 3, -7)$ and $\vec {b} = (p, -p, 4)$ , then the possible values for $p$ are:

Minimum ( $\cos \theta = 0$ )

$\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0$

Maximum ( $\cos \theta = 1$ )

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With the help of a graphing tool we get the family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

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