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Answer 1

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Answer 2

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Given cos alpha = 8/17, alpha in quadrant IV, and sin beta = -24/25, beta in quadrant III, find sin(alpha-beta)

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Given $\cos\alpha=(8)/(17)$ , $\alpha$ is in Quadrant IV, $\sin\beta=-(24)/(25)$ , and $\beta$ is in Quadrant III, find $\sin(\alpha-\beta)$

We can use the angle subtraction formula of sine to answer this question.

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

We already know that $\cos\alpha=(8)/(17)$ .

We can use the Pythagorean identity $\sin^2\theta+\cos^2\theta=1$ to find $\sin\alpha$ .

$\sin^2\alpha+((8)/(17))^2=1 \n \sin^2\alpha+(64)/(289)=1 \n \sin^2\alpha=(225)/(289) \n \n\sin\alpha=\pm(15)/(17)$

Since $\alpha$ is in Quadrant IV, and sine is represented as y value on the unit circle, we must assume the negative value $\sin\alpha=-(15)/(17)$ .

As similar process is then done with $\sin\beta=-(24)/(25)$ .

$(-(24)/(25))^2+\cos^2\beta=1 \n (576)/(625)+\cos^2\beta=1 \n \cos^2\beta=(49)/(625) \n \n\cos\beta=\pm(7)/(25)$

And since $\beta$ is in Quadrant III, and cosine in represented as x value on the unit cercle, we must assume the negative value $\cos\beta=-(7)/(25)$ .

Now we can fill in our angle subtraction formula!

$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta \n\n \sin(\alpha-\beta)=(-(15)/(17)*-(7)/(25))-((8)/(17)*-(24)/(25)) \n\n\sin(\alpha-\beta)=(105)/(425)-(-(192)/(425)) \n\n \boxed{\sin(\alpha-\beta)=(297)/(425)}$

What s the equation of a line that passes through points (-1,3) and (0,1) what is the equation of the line that passes through the points (-1,3) and (o,1)
what is the equation of the line that passes through the points (-1,3) and (0,1)?

Answers

the equation of the line is : y +2x = 1

Answer:

y = -2x + 1

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

using (-1,3) and (0,1)

m = (1 - 3)/(0 - -1)

m = (-2)/(1) = -2

Slope-intercept: y = mx + b

using (-1,3)

then 3 = -2(-1) + b

3 = 2 + b

b = 1

y = -2x + 1

The profit a company earns every month depends of the amount of product sold, p, for $855 each and the amount spent in rent, utilities and other expenses, which always totals to $6,780. The CEO of the company earns 1 this profit. How much the CEO eam if the company sells 250 products in a given month?

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so the ceo gains 855 for every product sold but losses 6780. you can make it into an equation

profit = 855p - 6780

just sub the number of products sold in p

It takes 8 cups of chicken broth to make a chicken soup recipe. How much is this in quarts?

Answers

There are 4 cups per 1 quart...

4/1 × 2/2 = 8/2

There are 8 cups in 2 quarts.

A sailboat’s sail has three sides that are all the same length. Each side measures x−10 units. The sail’s perimeter is 63 units.What is the value of x?

Answers

63/3=21
1 sail =21
21+10=31
x=31

Your new job guarantees you an eight percent raise for each year with the company. If your initial salary is $42,200, write an equation to model your salary after t years