Advanced Placement (AP), 10.12.2021 07:40 jadensababe9151

A teacher has to learn 170 new student names every year and finds it difficult to remember the names of former students. The teacher's memory problem most likely
results from

O retroactive amnesia
Othe misinformation effect
O proactive interference
O retroactive interference
O anterograde amnesia

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Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Answer from: Quest

You should ease the seat belt back slightly and slowly

Answer from: Quest

Answerradius is the lateral bone of the forearm when considering the anatomical position, it is wide at its distal, and narrow at its proximal;

ulna forms the elbow joint with humerus at its proximal end with its olecranon process. the ulna is slightly larger than the radius;

ok i looked up raial, and theres no such bone in the human body /// check the spelling/// both of the above bones are in your lower forearm you'll get it good luck/

Answer from: Quest

answer: following the publication of mysterium and with the blessing of the graz school inspectors, kepler began an ambitious program to extend and elaborate his work. he planned four additional books: one on the stationary aspects of the universe (the sun and the fixed stars); one on the planets and their motions; one on the physical nature of planets and the formation of geographical features (focused especially on earth); and one on the effects of the heavens on the earth, to include atmospheric optics, meteorology, and astrology.[24]

he also sought the opinions of many of the astronomers to whom he had sent mysterium, among them reimarus ursus (nicolaus reimers bär)—the imperial mathematician to rudolph ii and a bitter rival of tycho brahe. ursus did not reply directly, but republished kepler's flattering letter to pursue his priority dispute over (what is now called) the tychonic system with tycho. despite this black mark, tycho also began corresponding with kepler, starting with a harsh but legitimate critique of kepler's system; among a host of objections, tycho took issue with the use of inaccurate numerical data taken from copernicus. through their letters, tycho and kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and copernican theory (particularly its theological viability). but without the significantly more accurate data of tycho's observatory, kepler had no way to address many of these issues.[25]

instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences. by assuming the earth to possess a soul (a property he would later invoke to explain how the sun causes the motion of planets), he established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena. by 1599, however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in graz. in december of that year, tycho invited kepler to visit him in prague; on january 1, 1600 (before he even received the invitation), kepler set off in the hopes that tycho's patronage could solve his philosophical problems as well as his social and financial one

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