I need help with these problems! will give thanks!

Mathematics

1 answer:

Gnoma [55]3 years ago

4 0

For questions 5 and 6 the angle of the arc will always be half of the total angle of the outer edge of a circle. So for 5 you divide 194 by 2 which gives you 97.
For 6 is the same so divide 144 by 2 which is 72
7 and 8 are different questions from 5 and 6 and use their own method for a solution.
7 requires understanding that opposite angles when lines are crossed equal each other. For 7 the two angles will be 85 and opposite it is 85 so add them together and subtract from 360 which is the total angle of a circle. Which is 190 and divide that by 2 which is 95. So angle D for 7 is 95 degrees. 8 is just an opposite angle so it’s 120 degrees

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Elden [556K]

Answer:

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Step-by-step explanation:

$x^2+\dfrac{1}{x^2} =18\\\\(x-\dfrac{1}{x} )^2=x^2+\dfrac{1}{x^2} -2=18-2=16\\\\x-\dfrac{1}{x}=4\ or\ x-\dfrac{1}{x}-4\\\\(x-\dfrac{1}{x} )^3=x^3-\dfrac{1}{x^3} -3x^2*\dfrac{1}{x}+3x*\dfrac{1}{x^2}\\\\=x^3-\dfrac{1}{x^3}-3(x-\dfrac{1}{x})\\\\x^3-\dfrac{1}{x^3}=(x-\dfrac{1}{x} )^3+3(x-\dfrac{1}{x})\\\\if\ x-\dfrac{1}{x}=4\ then \ x^3-\dfrac{1}{x^3}=4^3+3*4=64-12=76\\\\if\ x-\dfrac{1}{x}=-4\ then \ x^3-\dfrac{1}{x^3}=(-4)^3+3*(-4)=-64-12=-76\\\\$