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3 years ago

How can I simplify these?

Mathematics

1 answer:

Schach [20]3 years ago

5 0

Well the square root of 72 is 8.485 and the square root of 45 is 6.708. hope this helps :)

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Every student in your history

kvv77 [185]

It would be a 1 in 4 chance

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3 years ago

Please Help! will give brainlest!

zzz [600]

Answer:

$\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}$

Step-by-step explanation:

we want to solve the following trigonometric equation:

$\displaystyle - 2 { \sin}^{2} (\theta )+ \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)$

The first step of solving trigonometric equation is to rewrite the equation in terms of one trigonometric function . With Pythagorean theorem, we know that sin²x=1-cos²x . It will be helpful to rewrite the equation in terms of one trig functions. Therefore, substitute 1-cos² $\theta$ in the place of sin² $\theta$ :

$\displaystyle - 2 (1 - \cos ^{2} ) + \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)$

simplify:

$\displaystyle\implies - 2 (1 - \cos ^{2} (\theta) + \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)\\\implies- 2 + \cos ^{2} (\theta)+ \cos( \theta) + 1 = 0, \: \theta \in [0,2\pi)\\\implies\cos ^{2} (\theta)+ \cos( \theta) -1 = 0$

Consider cos² $\theta\implies$ x. Thus,

$2 {x}^{2} + x - 1 = 0$

solving the quadratic equation yields:

${x}^{} = \frac{1}{2} \\ x = - 1$

back-substitute:

$\begin{cases} \cos( \theta) = \dfrac{1}{2} \\ \cos( \theta) = - 1 \end{cases} \theta \in[0,2\pi)$

take inverse trig in both sides

$\implies \begin{cases} \theta = \dfrac{\pi}{3} + 2n\pi\\\theta= \frac{5\pi}{3} + 2n\pi \\ \theta = \pi + 2n\pi\end{cases} \theta \in[0,2\pi) \\\\\implies\theta= \frac{\pi}{3}+\dfrac{2n\pi}{3},\theta\in [0,2\pi)\\\text{when n=0}\\ \implies \theta = \frac{\pi}{3} \\ \text{when n=1}\\ \theta= \pi\\ \text{when n=2}\\\theta=\frac{5\pi}{ 3}$

In conclusion,

$\displaystyle\theta = \frac{\pi}{3} , \pi, \frac{5\pi}{ 3}$

7 0

2 years ago

The sample space, S, of a coin being tossed three times is shown below, where Hand T denote the coin

Vilka [71]

Answer:

x : 1 | 2 | 3. | 4. | 5. | 6. | 7 | 8 |

p(x) : 1 | 2/3 | 2/3 | 1/3 | 2/3 | 1/3 | 1/3 | 0 |

8 0

4 years ago

Answer plz ASAP thx

Lyrx [107]

Answer:

D 540 mm cubed

Step-by-step explanation:

all you have to do is multiply the base area and the height together to get the volume. I can not see from what was given if the base area was divided by two because it is a triangle, if so this would be the anser if you not you want to divide the base area by half and then multiply it by the height to get your answer.

5 0

3 years ago

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PLSSS HELP IMMEDIATELY!!! ILL GIVE BRAINIEST!!! (if u provide a link, i’m not giving u brainiest!)

Tems11 [23]

Answer: B. (2,1)

Step-by-step explanation:

its not c because if you look at R you see that it is going 4,3 not 3,4 because when you doing ratios on a number line it goes x-axis then y-axis next not y-axis then the x-axis.

It's not D because if you look at Q you see that it is going 3,5 not 5,3 because when you doing ratios on a number line it goes x-axis then y-axis next not y-axis then x-axis.

That's the same thing for A so your answer is b.

7 0

3 years ago

Read 2 more answers