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anonymous
 5 years ago
Find the point(s) where the line through the origin with slope 7 intersects the unit circle.
anonymous
 5 years ago
Find the point(s) where the line through the origin with slope 7 intersects the unit circle.

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asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1a unit circle has the equation:\[x^2+y^2=1\]a line through the origin with slope 7 would have the equation:\[y=7x\]

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1substitute one into the other and solve for x.

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1do you need more help or can you solve this from here?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm still a little confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i understand what to do, but why do y=7x?

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1ok, we know the equation of the straight line is \(y=7x\). so we can substitute this value of y into the first equation to get:\[x^2+(7x)^2=1\]\[x^2+49x^2=1\]\[50x^2=1\]\[x^2=\frac{1}{50}\]\[x=\pm\frac{1}{\sqrt{50}}\]

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1y=7x is the equation of a straight line through the origin with slope 7.

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1so now you have two values for x, substitute each one into the equation \(y=7x\) to get the corresponding value for y and you have then solved this question.

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1the general equation of a straight line is given by:\[y=mx+c\]where 'm' is the slope and 'c' is the yintercept. In your case, you are told that the slope is 7 (so m=7) and it passes through the origin (so yintercept is zero, therefore c=0).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so it would be 7*1/\[\sqrt{50}\] and then 7*1/\[\sqrt{50}\]

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1correct, so the two values of y will be:\[y=\pm\frac{7}{\sqrt{50}}\]

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1\[x=\pm\frac{1}{\sqrt{50}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh right okay. this is starting to make sense

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1so the two points where the line intersects the circle are:\[(\frac{1}{\sqrt{50}}, \frac{7}{\sqrt{50}})\quad\text{and}\quad(\frac{1}{\sqrt{50}}, \frac{7}{\sqrt{50}})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so so much! you are a saint

asnaseer
 5 years ago
Best ResponseYou've already chosen the best response.1you are very welcome  I'm glad I was able to help :)
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