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3 years ago

11

What is the distance between point G(−4, 1) and point H(−12, 1) ? would be (8)

1 answer:

Greeley [361]3 years ago

3 0

Answer:

Yes, the distance between the points would be 8

Step-by-step explanation:

Since the y is the same, you can just find the distance between 12 and 4

12-4=8

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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

4 years ago

9(4b-1)=2(b+3) Slove for b plz answer as quick as u can please

Jobisdone [24]

$36b - 9 = 2b + 6 \\ 34b = 15 \\ b = \frac{15}{34}$

3 0

3 years ago

If it takes Charlie 45 minutes walking at 2.5 km/hr to get to the chocolate factory and it takes Willy Wonka 15 minutes walking

Mrac [35]

Answer:

Willy Wonka

Step-by-step explanation:

Given data

it takes Charlie 45 minutes walking at 2.5 km/hr

speed = distance /time

distance= speed*time

distance= 2.5*45

distance= 112.5 km

it takes Willy Wonka 15 minutes walking at 3.5 km/hr

distance= speed*time

distance= 3.5*15

distance= 52.5 km

Hence Willy Wonka stays closer

7 0

3 years ago

Each side of a professional baseball base must measure 15inches what is the base side length in feet

Lyrx [107]

1-1/4 feet is the base side length.

6 0

3 years ago

Plz help will mark brainless if right answer ;)

Pavel [41]

Answer:

A

Step-by-step explanation:

Since each triangle is an equilateral triangle all side are the same length. Thus, one side is 15/3=5 inches. The perimeter of the entire figure would then be 3x6=18 since there are 6 sides.

7 0

3 years ago

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