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2 years ago

13

Which sequences are arithmetic? Check all that apply.

1 answer:

abruzzese [7]2 years ago

5 0

The arithmetic sequences are 3rd one, and 5th one as they are increasing or decreasing by a constant rate of change

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Find the surface area of the prism.

Maurinko [17]

Answer:

326m²

Step-by-step explanation:

Find the area of each side and find the total sum from each individual area:

2(15*4)+2(7*4)+2(7*15)=2(60)+2(28)+2(105)=2(163)=326

So the surface area of the prism is 326m²

5 0

2 years ago

Please help me for the love of God if i fail I have to repeat the class

Elena-2011 [213]

$\theta$ is in quadrant I, so $\cos\theta>0$ .

$x$ is in quadrant II, so $\sin x>0$ .

Recall that for any angle $\alpha$ ,

$\sin^2\alpha+\cos^2\alpha=1$

Then with the conditions determined above, we get

$\cos\theta=\sqrt{1-\left(\dfrac45\right)^2}=\dfrac35$

and

$\sin x=\sqrt{1-\left(-\dfrac5{13}\right)^2}=\dfrac{12}{13}$

Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

$\sin2\alpha=2\sin\alpha\cos\alpha$

$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

6. $\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=-\dfrac{24}7$

7. A bit more work required here. Recall the half-angle identities:

$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

$\sin^2\dfrac\alpha2=\dfrac{1-\cos\alpha}2$

$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

$\tan\dfrac x2=\sqrt{\dfrac{1-\cos x}{1+\cos x}}=\dfrac32$

8. $\sin3\theta=\sin(\theta+2\theta)=\dfrac{44}{125}$

6 0

3 years ago

How long are mid term goals?

Irina-Kira [14]

Answer:

three months-three years

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

What are the input and output value for determining the sine of 60?

inna [77]

<h2>Explanation:</h2><h2 />

The input of a function is also called the domain and are those x-values for which the function is defined.

The output of a function is also called the range and are those y-values for which the function is defined.

Here we have the following function:

$y=f(x)=sin(x)$

And we know that:

Input:

$\boxed{x=60^{\circ}}$

Output:

$y=sin(60^{\circ}) \\ \\ \therefore \boxed{y=\frac{\sqrt{3}}{{2}}}$

7 0

3 years ago

Read 2 more answers

A person is given one push on a tire swing and then allowed to swing freely. On the first swing the person travels a distance of

Colt1911 [192]

How many times were they swung? 0.0 .....
if swung twice.. I think the answer would be 27.16

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6 0

3 years ago