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andrew11 [14]
3 years ago
15

Write a list of steps that are needed to find the measure of angle B if angle A is 72 and angle C is 113 ( the figure is a trian

gle :D ).... please help
Mathematics
1 answer:
Nuetrik [128]3 years ago
5 0
Triangle has 3 angles, A, B, C. The total interior angle of a triangle is 180. 
180 = A + B + C
180 = 72 + B + 113
180 = B + 185
B = 180 - 185
B = -5

This only proves that the figure is not a triangle because angle B is negative.
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3.
area=legngth tiimes width
legnth is 10 more than 2 times width
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area=3600
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so divide by 2
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subtract 1800 from both sides
(note they used x instead of w)
0=w^2+5w-1800
then the facotred form is (w-40)(w+45)=0

0 product property measn if you have xy, then x and or y =0

therefor
w-40=0 and w+45=0
w=40 or -45
discard negative because negative legnth is not possible


explian how solution relates to situation
it is math so it is correct because we represented it corrrectly


the other solution is because of math and eliminate negative legnth becasue tha tis not possible
basically because we represented it correctly
not a very clear quetion to answer

basically 'because it represents the solution so we solved it and it is correct'


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Answer:

\boxed{\boxed{x=\dfrac{\pi}{3}\ \vee\ x=\pi\ \vee\ x=\dfrac{5\pi}{3}}}

Step-by-step explanation:

\cos(3x)=-1\iff3x=\pi+2k\pi\qquad k\in\mathbb{Z}\\\\\text{divide both sides by 3}\\\\x=\dfrac{\pi}{3}+\dfrac{2k\pi}{3}\\\\x\in[0,\ 2\pi)

\text{for}\ k=0\to x=\dfrac{\pi}{3}+\dfrac{2(0)\pi}{3}=\dfrac{\pi}{3}+0=\boxed{\dfrac{\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=1\to x=\dfrac{\pi}{3}+\dfrac{2(1)\pi}{3}=\dfrac{\pi}{3}+\dfrac{2\pi}{3}=\dfrac{3\pi}{3}=\boxed{\pi}\in[0,\ 2\pi)\\\\\text{for}\ k=2\to x=\dfrac{\pi}{3}+\dfrac{2(2)\pi}{3}=\dfrac{\pi}{3}+\dfrac{4\pi}{3}=\boxed{\dfrac{5\pi}{3}}\in[0,\ 2\pi)\\\\\text{for}\ k=3\to x=\dfrac{\pi}{3}+\dfrac{2(3)\pi}{3}=\dfrac{\pi}{3}+\dfrac{6\pi}{3}=\dfrac{7\pi}{3}\notin[0,\ 2\po)

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I hope this helps you



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