Advanced Placement (AP), 27.08.2021 19:50, oscargonzalez1991

9x - 10 less than x - 10 less than 9x + 6

-compound inequalities

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answered: Guest

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule. $\begin{aligned} f(x) & = (0.5)^{2x} \\ f'(x) & = 0.5^{2x} \cdot \ln(0.5) \cdot (2x)' \\ f'(x) & = 0.5^{2x} \cdot \ln(0.5) \cdot 2 \\ f'(x) & = 2\ln(0.5) \cdot 0.5^{2x} \end{aligned}$ set the derivative to equal -1 and solve for x. $\begin{aligned} -1 & = 2\ln(0.5) \cdot 0.5^{2x} \\ -\frac{1}{2} & = \ln(0.5) \cdot 0.5^{2x} \\ -\frac{1}{2\ln(0.5)} & = 0.5^{2x} \end{aligned}$ take log base 10 of both sides. also recall that $\log_c(m^n) = n \log_c m$ . $\begin{aligned} \log\left[ -\frac{1}{2\ln(0.5)}\right] & = \log\left[0.5^{2x}\right] \\ \log\left[ -\frac{1}{2\ln(0.5)}\right] & = 2x \log(0.5) \\ \dfrac{\log\left[ -\frac{1}{2\ln(0.5)}\right]}{2\log(0.5)} & = x \\ x & \approx 0.2356 \end{aligned}$ so the x-coord of the point of tangency is $x \approx 0.2356$ .the y-coordinate of this point of tangency can be calculated using the original function: $\begin{aligned} f(x) & = (0.5)^{2x} \\ f(0.2356) & = (0.5)^{2 \cdot 0.2356} \\ & \approx 0.7213 \end{aligned}$ using point-slope form, the equation of the tangent line is $y - 0.7213 = -1(x-0.2356)$ the x-intercept of this tangent line is when the graph is at y=0. $\begin{aligned} 0 - 0.7213 & = -1(x-0.2356)\\ - 0.7213 & = -(x-0.2356) \\ 0.7213 & = x-0.2356\\ x & = 0.9569 \end{aligned}$ this rounds off to $x & = 0.957$ .choice c.

answered: Guest

There really doesn't seem to be anything remotely advanced about this question, especially for high school.that being said, the actual correct answer may depend on the lesson you received.but i'll use common knowledge to you out here. an atlas is a map, a flat map which depicts the world, all the continents and large bodies of water and etc. an almanac is basically a yearly calendar. this depicts all the stuff that happened during the year it was released after, such as important events, sporting stuff, astronomical data, etc. it really depends on what type of almanac you go for.encyclopedias contain vast knowledge about just about everything important around the globe. each encyclopedia is generally focused on a topic and it's relating topics, ordered by each book alphabetically. information resource can be anything. internet, newspaper, talking dog of pure wisdom (joking), the bible (or the religious book for whatever religion is in question), etc. all of these are considered information resources, as they all provide information on their respective topics (the internet is pretty much all topics)now, once again, your true answer will be based on whatever it is you learned, which i would not know. my answer will simply be using common knowledge.but your answers that line up with weather, sports, and business would be an almanac, information resources, and encyclopedia. unfortunately, in today's world, they have books for everything. they have almanacs for weather, sports, and business, and they also have encyclopedia's for those as well. and of course, you can find all of that using information resources as well. the only truly incorrect answer here is atlases. ~hope this !

answered: Guest

After spending all that time on the research then by all means modify the hypothesis or aim by reporting such. for example the findings did not bring forth what was expected but brought about different yet interesting findings worth exploring so the hypothesis is changed to reflect this new findings.

i may be way off but.

answered: Guest

answer:

the answer a,b,d slime : ) fmoi

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9x - 10 less than x - 10 less than 9x + 6

-compound inequalities...