Advanced Placement (AP), 20.09.2020 03:01 robert7248

Match the overall groupings of North American tribes with their most fitting description. Pueblo

Hopewell

Eastern Woodland

Southeast

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Answer from: Quest

Like many students at university, you may be unhappy about the results you attain in exams. you may feel that even with all you are doing there must be something more -- or different-- you could be doing to get better grades. we have all at some time or other heard of that student who only studies a couple of hours for final exams and scores a's every time. we stand in awe of those who seem to breeze through without undue effort and seem to need very little in the way of studying to nail an exam. the reasons for success, in what i think are the vast majority of cases, are less esoteric than many students think: successful students consistently apply a series of productive strategies with view to attaining clearly identified learning and grade goals throughout the academic term.

Answer from: Quest

like many students at university, you may be unhappy about the results you attain in exams. you may feel that even with all you are doing there must be something more -- or different-- you could be doing to get better grades. we have all at some time or other heard of that student who only studies a couple of hours for final exams and scores a's every time. we stand in awe of those who seem to breeze through without undue effort and seem to need very little in the way of studying to nail an exam. the reasons for success, in what i think are the vast majority of cases, are less esoteric than many students think: successful students consistently apply a series of productive strategies with view to attaining clearly identified learning and grade goals throughout the academic term.

Answer from: Quest

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.

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Match the overall groupings of North American tribes with their most fitting description. Pueblo