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

Answers

Answer 1

Answer: 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!

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

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Answers

lateral area=(pi)(r)(slantheight)
totalarea=(pi)(r)(slantheight)+(pir^2)

slantheight=24
r=11
lateralarea=pi*11*24=264pi aprox=829.4 ft^2

total area=pi*11^2+264pi=121pi+264pi=385pi=aprox 1209.5 ft^2

pick first option

Consider the graphs of f(x) and g(x). If g(x) = f(x)+k, find the value of k.

edit: added image

Answers

Answer:

The value of k is -7

Step-by-step explanation:

We are given the graph of f(x) and g(x). If g(x)=f(x)+k

If we shift f(x) k unit vertical get g(x).

If k>0 then shift up

If k<0 then shift down.

f(x) and g(x) are both parabola curve.

First we find the vertex of f(x) and g(x)

Vertex of f(x) = (3,1)

Vertex of g(x) = (3,-6)

We can see change in y co-ordinate only.

f(x) shift 7 unit down to get g(x)

g(x)=f(x)-7

Therefore, The value of k is -7

movement up k units means add k to whole function
moved from 1 to -6
movement up -7 units

k=-7

-3 (-4) ×
1 = –16
The answer babesss!!!!!

Answers

Answer:

x = -(4/3)

Step-by-step explanation:

$-3 (-4) *1 = -16\n\n\mathrm{Divide\:both\:sides\:by\:}-3\left(-4\right)*\:1\n\n(-3\left(-4\right)x*\:1)/(-3\left(-4\right)*\:1)=(-16)/(-3\left(-4\right)*\:1)\n\nSimplify\n\nx=-(4)/(3)$

the world's narrowest electric vehicle is about 35 inches wide .how wide is the vehicle to the nearest foot

Answers

Well the conversion factor between inches and feet is that

12 inches = 1 foot
35 inches = ? Feet

? Feet = 35 X 1 / 12
? Feet = 35/12
? Feet = 2.91666 feet about.

The vehicle is about 3 feet in terms of width.

What is the value of X?

SOMEONE PLEASE HELP!!

Answers

Remember, one whole circle is 360 degrees. This means that the side that looks to be the same as 43 degrees is 43 degrees. The side that looks the same as (6x+5) should be (6x+5).

Now just set up your equation like this and solve:

43+43+6x+5+6x+5=360

Hope I could be of help! :)

How to reduce fractions

Answers

To reduce fractions, simply divide both the numerator and the denominator by the GCD of the numerator and the denominator.

For example, to reduce 18/42, you divide the numerator and denominator by 6, since 6 is the GCD of 18 and 42, to get 3/7. However, a fraction such as 7/17 is already reduced entirely, because the GCD of 7 and 17 is 1.

Hope I helped! Feel free to respond to my answer if anything is unclear.

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