3 years ago

What is the best approximation of a 15% tip on a $38 car wash?

Mathematics

2 answers:

Anni [7]3 years ago

7 0

Should be B) 6 dollars. The answer is 5.7 then you round to 6.

dusya [7]3 years ago

7 0

15% of 38= 5.7
Round up to 6
Answer: b) $6

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A child builds two wooden train sets. The path of one of the trains can be represented by the function y = 2cos2x, where y repre

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Using a trigonometric equation, it is found that it will take 2.28 minutes until the two trains are first equidistant from the child.

<h3>What is the distance of each train to the child?</h3>

The distance of the first train is:

$y_1 = 2\cos^{2}x$

The distance of the second train is:

$y_2 = 3 + \cos{x}$

<h3>When are the trains equidistant to the child?</h3>

When $y_1 = y_2$ , hence:

$2\cos^{2}x = 3 + \cos{x}$

The following substitution is made:

$z = \cos{x}$

Hence:

$2z^2 = 3 + z$

$2z^2 - z - 3 = 0$

Which is a quadratic equation with coefficients $a = 2, b = -1, c = -3$ , hence:

$\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-3) = 13$

$z_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{13}}{4} = 1.5$

$z_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{13}}{4} = -0.65$

Then, applying the trigonometric equation, considering that $-1 \leq z \leq 1$ due to the range of the cosine function:

$z_2 = \cos{x_2}$

$x_2 = \arccos{z_2} = \arccos{-0.65} = 2.28$

It will take 2.28 minutes until the two trains are first equidistant from the child.

You can learn more about trigonometric equations at brainly.com/question/2088730

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