Advanced Placement (AP), 29.04.2021 23:00 Kemby12

Ribbon windows at the Villa Savoye have a precedent in the Five Points of Frank Lloyd Wright
artistic use of glass in Falling Water
innovative use of glass in the Crystal Palace
International Style of House in New Castle

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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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attend a weekly support group and hang out with people who live a clean lifestyle : )

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then, government officials implement the solution

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Black minnaloushe’ was maud’s cat (or iseult gonne’s cat…or lady gregory’s cat…depending on which source you credit); nevertheless the cat in this poem can be seen to represent yeats. it is made obvious in other of yeats’ poems from the time that he is unhappy with the fact that he never took enough action (political? pursuing his love for maud? ) and therefore believed himself somewhat predictable and sedentary
‘the moon’ represents maud; in literature the moon is a traditional symbol/metaphor for women – the waxing and waning of the moon having long been associated with the menstrual cycle. other reasons that yeats may have chosen the moon to act as a metaphor for maud is that she was a traveller and a revolutionary – constancy was not her forte! moonlight can also be seen from everywhere and therefore you cannot get away from it. yeats almost feels tormented by maud, not being able to get her off his mind. yet she facilitates his own importance because her moonlight lights the cat – the implication here is that despite his frustrations with her, maud is behind yeats’ greatness. she is the muse which drives his art – without her, neither he nor his poetry, can exist.

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