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anonymous
 one year ago
A windmill has its center at (0, 0). Its blades make a complete rotation every 40 seconds. If the tip of one blade is positioned at (5, 6), after 30 seconds where is the tip of the blade located?
anonymous
 one year ago
A windmill has its center at (0, 0). Its blades make a complete rotation every 40 seconds. If the tip of one blade is positioned at (5, 6), after 30 seconds where is the tip of the blade located?

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DanJS
 one year ago
Best ResponseYou've already chosen the best response.3do you know how to determine the equation of a circle given the center point and a point on the circle?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3the general form for a circle is (xh)^2 + (yk)^2 = r^2 (h,k) is the center point, and r is the radius

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3centered at the origin , and the radius is the distance from (0,0) to (5,6) right?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3actually, here is a simple way to see the solution ....

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3since the angle of rotation is a nice one, it makes it pretty simple

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3you understand the picture?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would the answer be( 6,5)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3almost, since it travels 30/40 of the way around, or 270 degrees, you end here...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3sorry, you start moving at angle A, not at angle zero, let me redo that

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3the overall angle after moving is 270 plus the initial angle A

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3the whole circle totals 360, so you can show that the remaining distance to the + x axis is 90  A

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So would it be (56)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry this is still confusing for me _.

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3the tangent of an angle in a right triangle is the side opposite divided by the adjacent side...remember that?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3tangent of angle A is 5/6

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3you can see the tan(angle) = y/x from that draw a vertical line from the point to the x axis, forms a right triangle

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3th eside lengths of the triangle are the components of the coordinate (5,6)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Basically you have two unknown values you need to find, the x and the y of that point. To do that you need to equations that relate x and y. This tangent is one way then i will use the circle equation

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3again, the tan(angle) = opposite /adjacent = y / x Angle A tan(A) = 6/5, so A = tan^(1)(6/5) = 50.2 so (90  A) = 39.8

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3now the triangle ending on the point (x,y) Tan(90A) = Tan(39.8056) = 0.833333333... = y/x that is the first relationship for x and y, since that is a rational decimal we can actually just finish it with this one equation... 0.8333333333.. = y/x any rational number can be converted to a ratio a/b or in this case x / y

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Convert 0.83333.... to a fraction. let  s = 0.83333... so, 10s = 8.3333.... and 100s = 83.3333...  100s  10s = 83.3333...  8.3333... 90s = 83  8 90s = 75 s = 75/90 or 5/6 0.833333333 = 5/6 = y/x y = 5 and x = 6 the point is (x , y) = (6 , 5)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3keep in mind that those are the lengths of the side of the triangle, the x value is still +6, but the y value is negative there, y=5 point with respect to xyaxis (x,y) = (6 , 5)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3if you had to, you could use a second equation with x and y unknown, the circle centered at origin, and radius is distance from origin to the given point \[r = \sqrt{5^2+6^2} = \sqrt{61}\] x^2 + y^2 = r^2 (circle centered at the origin) \[x^2 + y^2 = [\sqrt{61}]^2 = 61\] Two equations and two unknown values x and y, you can solve it x^2 + y^2 = r^2 and tan(Angle) = y/x solvable for x and y with a known Angle
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