Question

Can you please help me with this? This is part of an assignment that is due tonight.

Answer 1

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?

Answer 2

Could you explain please? Sorry.

Answer 3

6.1cm doesn't seem to be write according to webassign.

Answer 4

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

Answer 5

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

Answer 6

Yes I got to this point, I am lost at this point. Please help.

Answer 7

combine the right side

Answer 8

what is the common denominator?

Answer 9

I am at this point
\[\frac{ d(d-8) }{ 4.2d(d-8) }=\frac{ 4.2d -33.6 +4.2d }{ 4.2d(d-8 }\]

Answer 10

right, now get rid of the denominators

Answer 11

you if multiplied 4.2 d ( d- 8) to both sides,
then the denominators would cancel out

Answer 12

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

Answer 13

\[d^2-16.4d+33.6=0\]
Alright this is where I dont know, I dont know any factor of 16.4 and 33.6

Answer 14

Are these the right numbers?

Answer 15

i have no idea,
i dont have a piece of paper in front of me

Answer 16

assuming you didnt make a mistake earlier, the numbers seem fine

Answer 17

I'm lost at this point :/ I don't know what numbers to instert

Answer 18

quadratic equation

for
\[ax^2+bx+c = 0\]

\[x= \frac{-b\pm \sqrt{b^2 - 4ac}}{2a}\]

Answer 19

OH how could i not think of that.

Answer 20

I got d=14, and d=2.4
So how do I get the answer? it asks for only one

Answer 21

They both work also into the equation.

Answer 22

y= x-8

which answer makes sense now?