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sierraurb
 10 months ago
PLEASE HELP!!
A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle Θ. The area A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 90°, what is the area of the opening?
When i plug 90 in i keep getting 15, but my choices are:
21.8 in2
16.0 in2
7.9 in2
1.0 in2
sierraurb
 10 months ago
PLEASE HELP!! A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle Θ. The area A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 90°, what is the area of the opening? When i plug 90 in i keep getting 15, but my choices are: 21.8 in2 16.0 in2 7.9 in2 1.0 in2

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sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0@dangerousjesse any luck?

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @MATHMALE

phi
 10 months ago
Best ResponseYou've already chosen the best response.1first, you can do this without a calculator. But if you do use a calculator, be sure it is in degree mode. you should(!) know sin(90º)= 1 and cos(90º)= 0

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0@phi i just figured it out actually!! C right? and could you please help me with one more!! im stuck on it :/

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0Simplify \[\sqrt{\left( 1\sin \Theta \right)\left( 1+\sin \Theta \right)}\]

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0@phi i have no idea what to do

phi
 10 months ago
Best ResponseYou've already chosen the best response.1First, How did you get C 7.9? It seems if sin(90) is 1 and cos(90) is 0 you would do 16 sin Θ • (cos Θ + 1) 16 • 1 •(0+1) and now we add 0+1 (not *too* hard) and multiply that by 16*1 you don't get 7.9

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0For some reason i divided 16 in 2 idk why haha thank you!!

phi
 10 months ago
Best ResponseYou've already chosen the best response.1any idea what the answer is for your first question?

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0any idea on how to solve the second one? i really have no idea what to do @phi

phi
 10 months ago
Best ResponseYou've already chosen the best response.1do you know how to multiply the two binomials inside the square root (some people use FOIL)

phi
 10 months ago
Best ResponseYou've already chosen the best response.1if you don't see http://www.khanacademy.org/math/algebra/multiplyingfactoringexpression/multiplyingbinomials/v/multiplyingbinomials

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0yeah when i foil i get sqrt(1sin O)

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0is that right? @phi

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0F: 1*1=1 O: 1*sinO=sinO I: sinO*1=sinO L: sinO*sinO=sin2 so its sqrt(1sin^2) oops!

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0these are my options btw @phi ±sin Θ cos Θ ±tan Θ square root sine theta

phi
 10 months ago
Best ResponseYou've already chosen the best response.1ok looks better there is a *very useful* identity you should remember for trig problems \[ \sin^2 x + \cos^2 x = 1 \] which you can rewrite as \[ \sin^2 x = 1  \cos^2 x \] or \[ \cos^2 x= 1  \sin^2 x \]

phi
 10 months ago
Best ResponseYou've already chosen the best response.1yes. replace 1 sin^2 with cos^2 inside the square root sqrt(cos^2) = cos is the only choice that looks close (they must only want the positive root)  cos Θ 

sierraurb
 10 months ago
Best ResponseYou've already chosen the best response.0@phi thank you so so much!! i really truly appreciate it :)
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