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3 years ago

11

Joe and Antonio need to read a book for their English class. Joe is 5/8 of the way through the book, and Antonio has read 7/12 o

f the book. Who has read more?

2 answers:

frosja888 [35]3 years ago

8 0

Answer:

joe

Step-by-step explanation:

mr_godi [17]3 years ago

7 0

Answer:

the answer is antonio

Step-by-step explanation:

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Which equation is the inverse of y = 2x^2 - 8?

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Step-by-step explanation:

$y=2x^2-8$

1. Swap x and y.

$x=2y^2-8$

2. Solve for the new y.

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3 years ago

Solve sin x - (3sin x-1) = 0

soldi70 [24.7K]

Answer:

$\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}$

Step-by-step explanation:

$\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}$

$\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.$

$\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}$

$\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi$

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3 years ago