anonymous
  • anonymous
Can you please help me with this? This is part of an assignment that is due tonight.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
genson0 If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are related by the lens equation \[\frac{ 1 }{ F }=\frac{ 1 }{ x }+\frac{ 1 }{ y }\] Suppose that a lens has a focal length of 4.2 cm, and that the image of an object is 8 cm closer to the lens than the object itself. How far from the lens is the object?
anonymous
  • anonymous
Could you explain please? Sorry.
anonymous
  • anonymous
6.1cm doesn't seem to be write according to webassign.

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anonymous
  • anonymous
the question is, what is "x" ? the information given is F= 4.2 and " image of an object is 8 cm closer to the lens than the object itself" which can be expressed as the equation y= x-8
anonymous
  • anonymous
substituting the given information into the given equation \[\frac{1}{4.2}= \frac{1}{x} + \frac{1}{x-8}\] from here, you just need to solve for x
anonymous
  • anonymous
Yes I got to this point, I am lost at this point. Please help.
anonymous
  • anonymous
combine the right side
anonymous
  • anonymous
what is the common denominator?
anonymous
  • anonymous
I am at this point \[\frac{ d(d-8) }{ 4.2d(d-8) }=\frac{ 4.2d -33.6 +4.2d }{ 4.2d(d-8 }\]
anonymous
  • anonymous
right, now get rid of the denominators
anonymous
  • anonymous
you if multiplied 4.2 d ( d- 8) to both sides, then the denominators would cancel out
anonymous
  • anonymous
then move everything to one side, at this point, you will have a 2nd degree polynomial equal to zero solve either by factoring or by using the quadratic equation
anonymous
  • anonymous
\[d^2-16.4d+33.6=0\] Alright this is where I dont know, I dont know any factor of 16.4 and 33.6
anonymous
  • anonymous
Are these the right numbers?
anonymous
  • anonymous
i have no idea, i dont have a piece of paper in front of me
anonymous
  • anonymous
assuming you didnt make a mistake earlier, the numbers seem fine
anonymous
  • anonymous
I'm lost at this point :/ I don't know what numbers to instert
anonymous
  • anonymous
quadratic equation for \[ax^2+bx+c = 0\] \[x= \frac{-b\pm \sqrt{b^2 - 4ac}}{2a}\]
anonymous
  • anonymous
OH how could i not think of that.
anonymous
  • anonymous
I got d=14, and d=2.4 So how do I get the answer? it asks for only one
anonymous
  • anonymous
They both work also into the equation.
anonymous
  • anonymous
y= x-8 which answer makes sense now?

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