Answered: (3, 60°) 1 L (4, 210°)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.CR: Chapter Review

Problem 16E: Find the intensity of light at a depth of 12 meter if I0=14 and k=0.7. Round to two decimals.

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Question

calculate the Y coordinate (to at least 2 significant digits).

Expert Solution

Step 1

Given-

To find- The value of the Y-co-ordinate.

Concept used- As the above co-ordinate in polar co-ordinate , so we have to change in the rectangular co-ordiante which is as follows,

$r = \sqrt{x^{2} + y^{2}} and \tan θ = \frac{y}{x}$

Step 2

Explanation- From the given figure the polar co-ordinates are $(3, 60 °) and (4, 210 °)$ .

Now, taking first polar co-ordinate $(3, 60 °)$ and using the identity as $r = \sqrt{x^{2} + y^{2}} and \tan θ = \frac{y}{x}$ , we get,

$3 = \sqrt{x^{2} + y^{2}} 9 = x^{2} + y^{2} \dots \dots (1)$

And,

$\tan 60 ° = \frac{y}{x} \sqrt{3} = \frac{y}{x} y = x \sqrt{3}$

Substituting the value of y in equation (1), we get,

$x^{2} + {(x \sqrt{3})}^{2} = 9 x^{2} + 3 x^{2} = 9 4 x^{2} = 9 x = \pm \frac{3}{2}$

Now, for the y- coordiante, we can write as,

$y = \pm \frac{3 \sqrt{3}}{2}$

As y-coordinate is postive, so,

$y = \frac{3 \sqrt{3}}{2} = 2.598$

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