A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be
2 answers:
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Use the law of cosines:
We have:
substitute:
To graph it, just graph 
and 
and see where they intersect
I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it
hmm
multiply both sides by -1
multiply both sides by
minus 1 from both sides and minus 6(3^x) from both sides
use u subsitution
we can rewrite it as
now factor
I mean use quadratic formula
for
so for 0=u^2-16u-1, a=1, b=-16, c=-1
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
if you take the log base 3 of both sides you get
if you use ln then
then
I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it
hmm
multiply both sides by -1
multiply both sides by
minus 1 from both sides and minus 6(3^x) from both sides
use u subsitution
we can rewrite it as
now factor
I mean use quadratic formula
for
so for 0=u^2-16u-1, a=1, b=-16, c=-1
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
if you take the log base 3 of both sides you get
if you use ln then
then