# Answer Checks!!

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• Feb 12th 2008, 08:39 AM
mathlete
Answer Checks!!
ok so i did these problems and i would like someone to check my answers and telll me how i did...thanks alot

find an exact solution for each problem.

4x+19=e^(2ln(x))

so i rearanged this equation to

x^2-4x-19=0

then from there i used the quadratic eq. and came up with

x= 2+sqrt(23) and x=2-sqrt(23)

next one

1-2sin(t)/ln(t)=0

rearranged this to get

1-2sin(t)=0

then

sin(t)=1/2

i did inverse sin of 1/2 and came up with pi/6
the problem wanted the exact solution for

2pi<t<5pi/2

and with that i came up with 13pi/6

and for the last one

f(x)=4^x, and the slope of the tangent line of f(x) at x=0 is
f`(x)=ln4. use the tangent line to estimate f(0.11) and f(0.2)

i used ln4 for m is the equation

y=mx+b

then plugged one of the given points in 4^x to get a y value, then used the x and y to find b in the tangent line equation, once i found b i plugged in the given values to find y

i came up with

f(0.11) = 1.14

f(0.2) = 1.28

if someone could check my answers and let me know how i did that would be great thanks alot

mathlete
• Feb 12th 2008, 08:59 AM
TKHunny
mathlete, mathlete, mathlete... I expect more from you.

Rule #1 -- It's not an equation if you don't see one of these "=".

Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

After requiring x > 0, how do you feel about your answers?
• Feb 12th 2008, 09:14 AM
mathlete
yes i know its not an equation without an = sign...

i meant to put

x^2-4x-19=0

sorry

Quote:

Originally Posted by TKHunny
mathlete, mathlete, mathlete... I expect more from you.

Rule #1 -- It's not an equation if you don't see one of these "=".

Rule #2 -- NEVER mess with an equation without thinking about Domain Issues.

The very first thing I thought, when reading your first problem, was x > 0. After that, I wouldn't DARE suggest an answer that was zero or negative.

My second thought, was that 4x+19 > 0. Why? This turns our to be less restricitve that x > 0, so it is of no consequence.

After requiring x > 0, how do you feel about your answers?

• Feb 12th 2008, 10:29 AM
TKHunny
You didn't address the Domain Issues.
• Feb 12th 2008, 11:31 AM
mathlete
Ok, well tell me what was wrong with the equation that i rearranged

Quote:

Originally Posted by TKHunny
You didn't address the Domain Issues.

• Feb 13th 2008, 05:59 AM
TKHunny
Already did. See Rule #2, Above.

$e^{2ln(x)}$ is not quite $x^{2}$. What's the difference?

Note: If we allow x to be complex, and the logarithm to provide complex values, then maybe they are EXACTLY the same. I still don't like it, but I guess I can deal with my emotional issues. :-)