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Gelneren [198K]
3 years ago
15

A walkway forms one diagonal of a square playground. The walkway is 14 m long. How long is a side of the playground?

Mathematics
1 answer:
Vilka [71]3 years ago
5 0

Answer: The side of the playground is around 10 meters long

Step-by-step explanation:

use the diagonal as the hypotenuse of a right triangle, where the sides of the square form the legs of said triangle.

Usually

a^{2} +b^{2} =c^{2}

since we know a and b are the same length (sides of a square are congruent) we would have

a^{2} +a^{2} =c^{2} \\2a^{2} =c^{2}

We know that c is 14 so

2a^{2} =14^{2} \\2a^{2} =196\\a^{2} =98\\a=\sqrt{98} \\a= 9.999

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Express the complex number in trigonometric form.<br><br> -6 + 6\sqrt(3) i
horrorfan [7]

Answer:

<h2>12(cos120°+isin120°)</h2>

Step-by-step explanation:

The rectangular form of a complex number is expressed as z = x+iy

where the modulus |r| = \sqrt{x^{2}+y^{2} and the argument \theta = tan^{-1}\frac{y}{x}

In polar form, x = rcos\theta \ and\ y = rsin\theta

z = rcos\theta+i(rsin\theta)\\z = r(cos\theta+isin\theta)

Given the complex number, z = -6+6\sqrt{3} i. To express in trigonometric form, we need to get the modulus and argument of the complex number.

r = \sqrt{(-6)^{2}+(6\sqrt{3} )^{2}}\\r = \sqrt{36+(36*3)} \\r = \sqrt{144}\\ r = 12

For the argument;

\theta = tan^{-1} \frac{6\sqrt{3} }{-6} \\\theta = tan^{-1}-\sqrt{3}  \\\theta = -60^{0}

Since tan is negative in the 2nd and 4th quadrant, in the 2nd quadrant,

\theta =180-60\\\theta = 120^{0}

z = 12(cos120°+isin120°)

This gives the required expression.

4 0
4 years ago
Please explain step by step! 100 points!!
Mademuasel [1]

Answer:

First you want to multiply 13.25 by 40 meters. Your answer will be 530. Once you get your answer you will have to label it. 13 x 40 = 520 x 0.25 530 Hope this helps

8 0
3 years ago
Please help :'(<br> dhjehdkhkduiu
mariarad [96]

Answer:

lol good luck with that but you add them

Step-by-step explanation:

7 0
4 years ago
Help me please I don’t understand
Mamont248 [21]
For question between 13 -> 17 replace n with the number.

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13.) n = 2;  2+(-1) = 1
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3 years ago
What's is a supplementary angle
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Either of two Angles whose sum is 180 degrees
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