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3 years ago

13

On reading at An artic research station showed that the temperature was -35 C. What is this temperature in degrees Fahrenheit?

1 answer:

Travka [436]3 years ago

5 0

the answer is -22 F

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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

I need to know the answer to 1,847,304,738 divided by 3

schepotkina [342]

Answer:

615,768,246

Step-by-step explanation:

If u divide 1847304738÷3 you get that.

3 0

3 years ago

Ms. Snyder is giving a 28-question test that is made up of multiple choice questions worth 2 points each and open response quest

zlopas [31]

Answer:

x *2 + (28-x)*4 = 100

Step-by-step explanation:

Given

Total number of questions in the paper = 28

Out of these 28 questions let us say that x number of questions are of 2 points and 28-x questions are of 4 points.

Also, the complete test is of 100 marks

Thus, the linear equation representing the

x *2 + (28-x)*4 = 100

8 0

2 years ago

3. 0.7kg : 800g<br> I’m pretty bad with ratios lol

julsineya [31]

Answer:

7:8

Step-by-step explanation:

Convert o.7 Kg to Gram

It will be 700 grams

Divide it by 800

<u>700</u>

800

= <u>7</u>

8

7 0

3 years ago

Read 2 more answers

Autumn drives 825 miles to Florida. The trip takes her 17 hours. She uses 38 gallons of gas on the trip, which cost her $125. Fi

Dmitry [639]

$speed \: equals \: distance \div time$
speed equals 825 divided by 17
speed equals to 48.5miles per hour

gas mileage equals to 825/38
gas mileage equals to 21.7

125/38 equals to 3.3 unit price

8 0

3 years ago