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2 years ago

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Short-term financial goals include saving for _ A.spending in the near future

1 answer:

docker41 [41]2 years ago

6 0

The answer to this is C.

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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

Someone help please

ratelena [41]

Answer:

77

Step-by-step explanation:

HAV A GREAT DAY hope this helps

4 0

3 years ago

Write 16.76 correct to the nearest whole number

emmasim [6.3K]

16.76 rounds off to 17
After the dot if it’s 1-4 then they it would’ve been 15
5-9 is 17

4 0

3 years ago

Read 2 more answers

Math help!! This is really difficult

Reptile [31]

Answer:

y = -3/2 x +13

Step-by-step explanation:

We want our line to be perpendicular to

y = 2/3 x -1

The slope of this line is 2/3 (since it is written in the form y = mx+b and m is the slope)

Perpendicular lines have negative reciprocal slopes

m = -(3/2)

The slope of our new line is -3/2

We can use point slope form of the equation

y-y1 - m (x-x1)

y - 7 = -3/2 (x-4)

Distribute

y-7 = -3/2x +6

Add 7 to each side

y-7+7 = -3/2 x +6+7

y = -3/2 x +13

4 0

3 years ago

What is the probability of randomly selecting a day of the week and not getting Monday?

mrs_skeptik [129]

Days in a week n(S)=7

DAYS to not getting monday n(M)=6

probability P(M)=n(M)/n(S)

=6/7(ans)

6 0

2 years ago