An object 4 cm high is placed at a distance of 10cm from a convex lens of focal length20cm . Find the position, nature and size of the image
Answers
Explanation:
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20thanks = 2inbox
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
(32t2 - 64t) - 64 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 9t2-64t-64
The first term is, 9t2 its coefficient is 9 .
The middle term is, -64t its coefficient is -64 .
The last term, "the constant", is -64
Step-1 : Multiply the coefficient of the first term by the constant 9 • -64 = -576
Step-2 : Find two factors of -576 whose sum equals the coefficient of the middle term, which is -64 .
-576 + 1 = -575
-288 + 2 = -286
-192 + 3 = -189
-144 + 4 = -140
-96 + 6 = -90
-72 + 8 = -64 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -72 and 8
9t2 - 72t + 8t - 64
Step-4 : Add up the first 2 terms, pulling out like factors :
9t • (t-8)
Add up the last 2 terms, pulling out common factors :
8 • (t-8)
Step-5 : Add up the four terms of step 4 :
(9t+8) • (t-8)
Which is the desired factorization
Equation at the end of step
2
:
(t - 8) • (9t + 8) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.