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2 years ago

6

PLS HELP DO ALL PROBLEMS 100 PTS

1 answer:

padilas [110]2 years ago

3 0

Answer

4. - x ^ 2 + 13x - 42 <= 0524211r

5. x ^ 2 - 11x - 42 < 0

16 - x ^ 2 + 9x - 8 <= 0

17. x^ 2 -11x+80<0

18. - x ^ 2 + 3x + 4 <= 0

19. x ^ 2 - 12x + 36 <= 0

20. 2x ^ 2 - 32x + 56 < 0

21. x ^ 2 - 10x - 96 < 0

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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

If the range of the coordinate transformation f(x,y) = (x – 5, y – 3) is (-6,-6) and (2,-3).

lina2011 [118]

Answer:

(-2,1),(-1,2),(-3,5/3)

Step-by-step explanation:

6 0

2 years ago

Twenty-one people brought a chocolate cake to a community potluck dinner each cake was split into 8 slices how many slices of ch

dexar [7]

Answer:

168

Step-by-step explanation:

Multiply 21 by 8 so

21 × 8 = 168

6 0

3 years ago

How do you write 0.334 in expanded form?

NikAS [45]

0.300+0.030+0.004 hope this helps

4 0

3 years ago

The residence of a city voted on whether to raise property taxes the ratio of yes to no votes was 2 to 3 is there were 4795 tota

Vinvika [58]

Answer: The number of yes votes = 1918.

Step-by-step explanation:

Given : The ratio of yes to no votes = 2:3

Then the ratio of yes to total votes = $\dfrac{2}{2+3}=\dfrac25$

Total votes = 4795

Number of yes votes = (ratio of yes to total votes) x (Total votes )

= $\dfrac{2}{5}\times4795=1918$

Hence, the number of yes votes = 1918.

4 0

3 years ago