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3 years ago

this is geometry i need help so please help. i know the answer is 72 3/8 degrees i just need help solving it

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

now, keeping in mind that 1 degree has 60 minutes, and that 1 minute has 60 seconds and therefore there are 60*60 seconds in 1 degree, or 3600 seconds.

72°22'30", has 72 degrees, plus 22 minutes and 30 seconds.

or 72 degrees plus 22/60 degrees plus 30/3600 degrees.

$\bf 72+\boxed{\cfrac{22}{60}+\cfrac{30}{3600}}\implies \cfrac{11}{30}+\cfrac{1}{120}\implies \stackrel{\textit{LCD of 120}}{\cfrac{44+1}{120}}\implies \cfrac{45}{120}\implies \cfrac{3}{8}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 72+\cfrac{3}{8}\implies 72\frac{3}{8}^o$

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The equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

<h3>Equation of a circle</h3>

The standard equation of a circle is expressed as:

$(x-a)^2+(y-b)^2=r^2$

Given the equation $x^2 + y^2 + 20x + 12y + 111 =0$

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Complete the squares to have:

$(x^2 +20x)+(y^2+ 12y) + 111 =0\\(x^2+20x+10^2-10^2)+(y^2+12y+6^2-6^2)+111=0\\(x+10)^2+(y+6)^2 -100-36+111=0\\(x+10)^2+(y+6)^2-25=0\\(x+10)^2+(y+6)^2=25\\(x+10)^2+(y+6)^2=5^2$

Hence the equation in the given standard form is $(x+10)^2+(y+6)^2=5^2$

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