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3 years ago

Solve 5 - 2x < 7. A.) x<-1 B.) x>-1 C.) x<-12 D.) x>-12

Mathematics

1 answer:

Serggg [28]3 years ago

4 0

Answer:

Step-by-step explanation:

-2x<7-5

-2x<2 multiplied by -1 gives 2x>-2 and devided by 2 you have x>-1

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3 years ago

Solve the equation for exact solutions over the interval [0, 2π).

quester [9]

Answer:

$\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}$

Step-by-step explanation:

We want to solve the equation:

$-2\cos^2(x)=-\cos(x)-1$

Over the interval [0, 2π).

First, notice that this is in quadratic form. So, to make things simpler, we can let <em>u</em> = cos(x). Substitute:

$-2u^2=-u-1$

Rearrange:

$2u^2-u-1=0$

Factor:

$(2u+1)(u-1)=0$

Zero Product Property:

$2u+1=0\text{ or } u-1=0$

Solve for each case:

$\displaystyle u=-\frac{1}{2}\text{ or } u=1$

Back-substitute:

$\displaystyle \cos(x)=-\frac{1}{2}\text{ or } \cos(x)=1$

Using the unit circle:

$\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}$

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3 years ago