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sierraurb
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0@dangerousjesse any luck?

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

phi
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0Simplify \[\sqrt{\left( 1\sin \Theta \right)\left( 1+\sin \Theta \right)}\]

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

phi
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0For some reason i divided 16 in 2 idk why haha thank you!!

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

sierraurb
 8 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
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0yeah when i foil i get sqrt(1sin O)

sierraurb
 8 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
 8 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
 8 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
 8 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
 8 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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